The poster session will be on Tuesday afternoon (see schedule). The posters will stay up all week in the Department of Mathematics.
The online poster presentations will take place through dedicated Audio/Video channels on the TQC Discord server. You can present your poster during the poster session or at any other time during the conference; all instructions can be found on the Discord server.
Note that not all accepted posters will be presented at the conference due to author availability constraints. If you cannot present your poster, you don’t need to email us.
61.
Victoria Sánchez Muñoz
CHSH game with 3 players in a triangle with bi-partite and tri-partite entanglement Poster
2023.
@Poster{P5787,
title = {CHSH game with 3 players in a triangle with bi-partite and tri-partite entanglement},
author = {Victoria Sánchez Muñoz},
url = {https://tqc-conference.org/wp-content/uploads/cfdb7_uploads/1687445204-poster-5787.pdf},
year = {2023},
date = {2023-01-01},
keywords = {},
pubstate = {published},
tppubtype = {Poster}
}
62.
Arkin Tikku, Isaac Kim
Circuit depth versus energy in topologically ordered systems Workshop
2023.
Abstract | Links:
@Workshop{T6087,
title = {Circuit depth versus energy in topologically ordered systems},
author = {Arkin Tikku and Isaac Kim},
url = {https://tqc-conference.org/wp-content/uploads/cfdb7_uploads/1688308043-poster-6087.pdf https://tqc-conference.org/wp-content/uploads/cfdb7_uploads/1688308043-video-6087.mp4},
year = {2023},
date = {2023-01-01},
urldate = {2023-01-01},
abstract = {We prove a nontrivial circuit-depth lower bound for preparing a low-energy state of a locally interacting quantum many-body system in two dimensions, assuming the circuit is geometrically local. For preparing any state which has an energy density of at most ε with respect to Kitaev's toric code Hamiltonian on a two dimensional lattice Λ, we prove a lower bound of $Ømegałeft(minłeft(1/epsilon^frac1-alpha2, sqrtabsŁambdaright)right)$ for any $alpha >0$. We discuss two implications. First, our bound implies that the lowest energy density obtainable from a large class of existing variational circuits (e.g., Hamiltonian variational ansatz) cannot, in general, decay exponentially with the circuit depth. Second, if long-range entanglement is present in the ground state, this can lead to a nontrivial circuit-depth lower bound even at nonzero energy density. Unlike previous approaches to prove circuit-depth lower bounds for preparing low energy states, our proof technique does not rely on the ground state to be degenerate.},
howpublished = {Talk},
keywords = {},
pubstate = {published},
tppubtype = {Workshop}
}
We prove a nontrivial circuit-depth lower bound for preparing a low-energy state of a locally interacting quantum many-body system in two dimensions, assuming the circuit is geometrically local. For preparing any state which has an energy density of at most ε with respect to Kitaev's toric code Hamiltonian on a two dimensional lattice Λ, we prove a lower bound of $Ømegałeft(minłeft(1/epsilon^frac1-alpha2, sqrtabsŁambdaright)right)$ for any $alpha >0$. We discuss two implications. First, our bound implies that the lowest energy density obtainable from a large class of existing variational circuits (e.g., Hamiltonian variational ansatz) cannot, in general, decay exponentially with the circuit depth. Second, if long-range entanglement is present in the ground state, this can lead to a nontrivial circuit-depth lower bound even at nonzero energy density. Unlike previous approaches to prove circuit-depth lower bounds for preparing low energy states, our proof technique does not rely on the ground state to be degenerate.
63.
Yuki Shirakawa
Classical complexity assumptions necessary for PRSGs Poster
2023.
@Poster{P1013,
title = {Classical complexity assumptions necessary for PRSGs},
author = {Yuki Shirakawa},
year = {2023},
date = {2023-01-01},
howpublished = {Poster},
keywords = {},
pubstate = {published},
tppubtype = {Poster}
}
64.
Dominik Wild, Alvaro Alhambra
Classical simulation of short-time quantum dynamics Workshop
2023.
Abstract | Links:
@Workshop{T8698,
title = {Classical simulation of short-time quantum dynamics},
author = {Dominik Wild and Alvaro Alhambra},
url = {https://arxiv.org/abs/2210.11490},
year = {2023},
date = {2023-01-01},
abstract = {Recent progress in the development of quantum technologies has enabled the direct investigation of dynamics of increasingly complex quantum many-body systems. This motivates the study of the complexity of classical algorithms for this problem in order to benchmark quantum simulators and to delineate the regime of quantum advantage. Here we present classical algorithms for approximating the dynamics of local observables and nonlocal quantities such as the Loschmidt echo, where the evolution is governed by a local Hamiltonian. For short times, their computational cost scales polynomially with the system size and the inverse of the approximation error. In the case of local observables, the proposed algorithm has a better dependence on the approximation error than algorithms based on the Lieb–Robinson bound. Our results use cluster expansion techniques adapted to the dynamical setting, for which we give a novel proof of their convergence. This has important physical consequences besides our efficient algorithms. In particular, we establish a novel quantum speed limit, a bound on dynamical phase transitions, and a concentration bound for product states evolved for short times.},
howpublished = {Talk},
keywords = {},
pubstate = {published},
tppubtype = {Workshop}
}
Recent progress in the development of quantum technologies has enabled the direct investigation of dynamics of increasingly complex quantum many-body systems. This motivates the study of the complexity of classical algorithms for this problem in order to benchmark quantum simulators and to delineate the regime of quantum advantage. Here we present classical algorithms for approximating the dynamics of local observables and nonlocal quantities such as the Loschmidt echo, where the evolution is governed by a local Hamiltonian. For short times, their computational cost scales polynomially with the system size and the inverse of the approximation error. In the case of local observables, the proposed algorithm has a better dependence on the approximation error than algorithms based on the Lieb–Robinson bound. Our results use cluster expansion techniques adapted to the dynamical setting, for which we give a novel proof of their convergence. This has important physical consequences besides our efficient algorithms. In particular, we establish a novel quantum speed limit, a bound on dynamical phase transitions, and a concentration bound for product states evolved for short times.
65.
Matthias C. Caro, Marcel Hinsche, Marios Ioannou, Alexander Nietner, Ryan Sweke
Classical Verification of Quantum Learning Talk
2024.
@Talk{T24_26,
title = {Classical Verification of Quantum Learning},
author = {Matthias C. Caro and Marcel Hinsche and Marios Ioannou and Alexander Nietner and Ryan Sweke},
year = {2024},
date = {2024-01-01},
abstract = {Quantum data access and quantum processing can make certain classically intractable learning tasks feasible. However, quantum capabilities will only be available to a select few in the near future. Thus, reliable schemes that allow classical clients to delegate learning to untrusted quantum servers are required to facilitate widespread access to quantum learning advantages. Building on a recently introduced framework of interactive proof systems for classical machine learning by Goldwasser et al. (ITCS 2021), we develop a framework for classical verification of quantum learning. We exhibit learning problems that a classical learner cannot efficiently solve on their own, but that they can efficiently and reliably solve when interacting with an untrusted quantum prover. Concretely, we consider the problems of agnostic learning parities and Fourier-sparse functions with respect to distributions with uniform input marginal. We propose a new quantum data access model that we call "mixture-of-superpositions" quantum examples, based on which we give efficient quantum learning algorithms for these tasks. Moreover, we prove that agnostic quantum parity and Fourier-sparse learning can be efficiently verified by a classical verifier with only random example or statistical query access. Finally, we showcase two general scenarios in learning and verification in which quantum mixture-of-superpositions examples do not lead to sample complexity improvements over classical data. Our results demonstrate that the potential power of quantum data for learning tasks, while not unlimited, can be utilized by classical agents through interaction with untrusted quantum entities.},
keywords = {},
pubstate = {published},
tppubtype = {Talk}
}
Quantum data access and quantum processing can make certain classically intractable learning tasks feasible. However, quantum capabilities will only be available to a select few in the near future. Thus, reliable schemes that allow classical clients to delegate learning to untrusted quantum servers are required to facilitate widespread access to quantum learning advantages. Building on a recently introduced framework of interactive proof systems for classical machine learning by Goldwasser et al. (ITCS 2021), we develop a framework for classical verification of quantum learning. We exhibit learning problems that a classical learner cannot efficiently solve on their own, but that they can efficiently and reliably solve when interacting with an untrusted quantum prover. Concretely, we consider the problems of agnostic learning parities and Fourier-sparse functions with respect to distributions with uniform input marginal. We propose a new quantum data access model that we call "mixture-of-superpositions" quantum examples, based on which we give efficient quantum learning algorithms for these tasks. Moreover, we prove that agnostic quantum parity and Fourier-sparse learning can be efficiently verified by a classical verifier with only random example or statistical query access. Finally, we showcase two general scenarios in learning and verification in which quantum mixture-of-superpositions examples do not lead to sample complexity improvements over classical data. Our results demonstrate that the potential power of quantum data for learning tasks, while not unlimited, can be utilized by classical agents through interaction with untrusted quantum entities.
66.
Julien Codsi, John Wetering
Classically Simulating Quantum Supremacy IQP Circuits through a Random Graph Approach Poster
2023.
@Poster{P2402,
title = {Classically Simulating Quantum Supremacy IQP Circuits through a Random Graph Approach},
author = {Julien Codsi and John Wetering},
year = {2023},
date = {2023-01-01},
howpublished = {Poster},
keywords = {},
pubstate = {published},
tppubtype = {Poster}
}
67.
Yijia Xu, Yixu Wang, Victor V. Albert
Clifford operations and homological codes for rotors and oscillators Talk
2024.
@Talk{T24_299,
title = {Clifford operations and homological codes for rotors and oscillators},
author = {Yijia Xu and Yixu Wang and Victor V. Albert},
year = {2024},
date = {2024-01-01},
abstract = {We develop quantum information processing primitives for the planar rotor, the state space of a particle on a circle. By interpreting rotor wavefunctions as periodically identified wavefunctions of a harmonic oscillator, we determine the group of bosonic Gaussian operations inherited by the rotor. This (n)-rotor Clifford group, (textU(1)^n(n+1)/2 rtimes textGL_n(mathbbZ)), is represented by continuous (textU(1)) gates generated by polynomials quadratic in angular momenta, as well as discrete (textGL_n(mathbb Z)) momentum sign-flip and sum gates. We classify homological rotor error-correcting codes arXiv:2303.13723 and various rotor states based on equivalence under Clifford operations. Reversing direction, we map homological rotor codes and rotor Clifford operations back into oscillators by interpreting occupation-number states as rotor states of non-negative angular momentum. This yields new multimode homological bosonic codes protecting against dephasing and changes in occupation number, along with their corresponding encoding and decoding circuits. In particular, we show how to non-destructively measure the oscillator phase using conditional occupation-number addition and post selection. We also outline several rotor and oscillator varieties of the GKP-stabilizer codes arXiv:1903.12615.},
keywords = {},
pubstate = {published},
tppubtype = {Talk}
}
We develop quantum information processing primitives for the planar rotor, the state space of a particle on a circle. By interpreting rotor wavefunctions as periodically identified wavefunctions of a harmonic oscillator, we determine the group of bosonic Gaussian operations inherited by the rotor. This (n)-rotor Clifford group, (textU(1)^n(n+1)/2 rtimes textGL_n(mathbbZ)), is represented by continuous (textU(1)) gates generated by polynomials quadratic in angular momenta, as well as discrete (textGL_n(mathbb Z)) momentum sign-flip and sum gates. We classify homological rotor error-correcting codes arXiv:2303.13723 and various rotor states based on equivalence under Clifford operations. Reversing direction, we map homological rotor codes and rotor Clifford operations back into oscillators by interpreting occupation-number states as rotor states of non-negative angular momentum. This yields new multimode homological bosonic codes protecting against dephasing and changes in occupation number, along with their corresponding encoding and decoding circuits. In particular, we show how to non-destructively measure the oscillator phase using conditional occupation-number addition and post selection. We also outline several rotor and oscillator varieties of the GKP-stabilizer codes arXiv:1903.12615.
68.
Mirko Arienzo, Markus Heinrich, Ingo Roth, Martin Kliesch
Closed-form analytic expressions for shadow estimation with brickwork circuits Workshop
2023.
Abstract | Links:
@Workshop{T7062,
title = {Closed-form analytic expressions for shadow estimation with brickwork circuits},
author = {Mirko Arienzo and Markus Heinrich and Ingo Roth and Martin Kliesch},
url = {https://arxiv.org/abs/2211.09835},
year = {2023},
date = {2023-01-01},
urldate = {2023-01-01},
abstract = {Properties of quantum systems can be estimated using classical shadows, which implement measurements based on random ensembles of unitaries. Originally derived for global Clifford unitaries and products of single-qubit Clifford gates, practical implementations are limited to the latter scheme for moderate numbers of qubits. Beyond local gates, the accurate implementation of very short random circuits with two-local gates is still experimentally feasible and, therefore, interesting for implementing measurements in near-term applications. In this work, we derive closed-form analytical expressions for shadow estimation using brickwork circuits with two layers of parallel two-local Haar-random (or Clifford) unitaries. Besides the construction of the classical shadow, our results give rise to sample-complexity guarantees for estimating Pauli observables. We then compare the performance of shadow estimation with brickwork circuits to the established approach using local Clifford unitaries and find improved sample complexity in the estimation of observables supported on sufficiently many qubits.},
howpublished = {Talk (merged)},
keywords = {},
pubstate = {published},
tppubtype = {Workshop}
}
Properties of quantum systems can be estimated using classical shadows, which implement measurements based on random ensembles of unitaries. Originally derived for global Clifford unitaries and products of single-qubit Clifford gates, practical implementations are limited to the latter scheme for moderate numbers of qubits. Beyond local gates, the accurate implementation of very short random circuits with two-local gates is still experimentally feasible and, therefore, interesting for implementing measurements in near-term applications. In this work, we derive closed-form analytical expressions for shadow estimation using brickwork circuits with two layers of parallel two-local Haar-random (or Clifford) unitaries. Besides the construction of the classical shadow, our results give rise to sample-complexity guarantees for estimating Pauli observables. We then compare the performance of shadow estimation with brickwork circuits to the established approach using local Clifford unitaries and find improved sample complexity in the estimation of observables supported on sufficiently many qubits.
69.
Yujie Zhang, Jiaxuan Zhang, Eric Chitambar
Compatibility Complexity and the Compatibility Radius of Qubit Measurements Poster
2023.
@Poster{P1606,
title = {Compatibility Complexity and the Compatibility Radius of Qubit Measurements},
author = {Yujie Zhang and Jiaxuan Zhang and Eric Chitambar},
year = {2023},
date = {2023-01-01},
howpublished = {Poster},
keywords = {},
pubstate = {published},
tppubtype = {Poster}
}
70.
Maarten Grothus, V. Vilasini
Compatibility of Cyclic Causal Structures with Spacetime in General Theories with Free Interventions Poster
2023.
@Poster{P3117,
title = {Compatibility of Cyclic Causal Structures with Spacetime in General Theories with Free Interventions},
author = {Maarten Grothus and V. Vilasini},
year = {2023},
date = {2023-01-01},
howpublished = {Poster},
keywords = {},
pubstate = {published},
tppubtype = {Poster}
}
71.
Bjarne Bergh, Nilanjana Datta, Robert Salzmann
Composite Classical and Quantum Channel Discrimination Workshop
2023.
@Workshop{T4791,
title = {Composite Classical and Quantum Channel Discrimination},
author = {Bjarne Bergh and Nilanjana Datta and Robert Salzmann},
year = {2023},
date = {2023-01-01},
abstract = {We study the problem of binary composite channel discrimination in the asymmetric setting, where the hypotheses are given by fairly arbitrary sets of channels, and samples do not have to be identically distributed. In the case of quantum channels we prove: (i) a characterization of the Stein's exponent for parallel channel discrimination strategies and (ii) an upper bound on the Stein's exponent for adaptive channel discrimination strategies. We further show that already for classical channels this upper bound can sometimes be achieved and be strictly larger than what is possible with parallel strategies. Hence, there can be an advantage of adaptive channel discrimination strategies with composite hypotheses for classical channels, unlike in the case of simple hypotheses. Moreover, we show that classically this advantage can only exist if the sets of channels corresponding to the hypotheses are non-convex. As a consequence of our more general treatment, which is not limited to the composite i.i.d. setting, we also obtain a generalization of previous composite state discrimination results.},
howpublished = {Talk},
keywords = {},
pubstate = {published},
tppubtype = {Workshop}
}
We study the problem of binary composite channel discrimination in the asymmetric setting, where the hypotheses are given by fairly arbitrary sets of channels, and samples do not have to be identically distributed. In the case of quantum channels we prove: (i) a characterization of the Stein's exponent for parallel channel discrimination strategies and (ii) an upper bound on the Stein's exponent for adaptive channel discrimination strategies. We further show that already for classical channels this upper bound can sometimes be achieved and be strictly larger than what is possible with parallel strategies. Hence, there can be an advantage of adaptive channel discrimination strategies with composite hypotheses for classical channels, unlike in the case of simple hypotheses. Moreover, we show that classically this advantage can only exist if the sets of channels corresponding to the hypotheses are non-convex. As a consequence of our more general treatment, which is not limited to the composite i.i.d. setting, we also obtain a generalization of previous composite state discrimination results.
72.
Alper Cakan, Vipul Goyal, Chen-Da Liu-Zhang, Joao Ribeiro
Computational Quantum Secret Sharing Conference
2023.
Abstract | Links:
@Conference{T3870,
title = {Computational Quantum Secret Sharing},
author = {Alper Cakan and Vipul Goyal and Chen-Da Liu-Zhang and Joao Ribeiro},
url = {https://arxiv.org/abs/2305.00356},
year = {2023},
date = {2023-01-01},
urldate = {2023-01-01},
abstract = {Quantum secret sharing (QSS) allows a dealer to distribute a secret quantum state among a set of parties in such a way that certain authorized subsets can reconstruct the secret, while unauthorized subsets obtain no information about it. Previous works on QSS for general access structures focused solely on the existence of perfectly secure schemes, and the share size of the known schemes is necessarily exponential even in cases where the access structure is computed by polynomial size monotone circuits. This stands in stark contrast to the classical setting, where polynomial-time computationally-secure secret sharing schemes have been long known for all access structures computed by polynomial-size monotone circuits under standard hardness assumptions, and one can even obtain shares which are much shorter than the secret (which is impossible with perfect security).
While QSS was introduced over twenty years ago, previous works only considered information-theoretic privacy. In this work, we initiate the study of computationally-secure QSS and show that computational assumptions help significantly in building QSS schemes, just as in the classical case. We present a simple compiler and use it to obtain a large variety results: We construct polynomial-time computationally-secure QSS schemes under standard hardness assumptions for a rich class of access structures. This includes many access structures for which previous results in QSS necessarily required exponential share size. In fact, we can go even further: We construct QSS schemes for which the size of the quantum shares is significantly smaller than the size of the secret. As in the classical setting, this is impossible with perfect security. We also apply our compiler to obtain results beyond computational QSS. In the information-theoretic setting, we improve the share size of perfect QSS schemes for a large class of $n$-party access structures to $1.5^n+o(n)$, improving upon best known schemes and matching the best known result for general access structures in the classical setting. Finally, among other things, we study the class of access structures which can be efficiently implemented when the quantum secret sharing scheme has access to a given number of copies of the secret, including all such functions in $mathsfP$ and $mathsfNP$.},
howpublished = {Talk and Proceedings},
keywords = {},
pubstate = {published},
tppubtype = {Conference}
}
Quantum secret sharing (QSS) allows a dealer to distribute a secret quantum state among a set of parties in such a way that certain authorized subsets can reconstruct the secret, while unauthorized subsets obtain no information about it. Previous works on QSS for general access structures focused solely on the existence of perfectly secure schemes, and the share size of the known schemes is necessarily exponential even in cases where the access structure is computed by polynomial size monotone circuits. This stands in stark contrast to the classical setting, where polynomial-time computationally-secure secret sharing schemes have been long known for all access structures computed by polynomial-size monotone circuits under standard hardness assumptions, and one can even obtain shares which are much shorter than the secret (which is impossible with perfect security).
While QSS was introduced over twenty years ago, previous works only considered information-theoretic privacy. In this work, we initiate the study of computationally-secure QSS and show that computational assumptions help significantly in building QSS schemes, just as in the classical case. We present a simple compiler and use it to obtain a large variety results: We construct polynomial-time computationally-secure QSS schemes under standard hardness assumptions for a rich class of access structures. This includes many access structures for which previous results in QSS necessarily required exponential share size. In fact, we can go even further: We construct QSS schemes for which the size of the quantum shares is significantly smaller than the size of the secret. As in the classical setting, this is impossible with perfect security. We also apply our compiler to obtain results beyond computational QSS. In the information-theoretic setting, we improve the share size of perfect QSS schemes for a large class of $n$-party access structures to $1.5^n+o(n)$, improving upon best known schemes and matching the best known result for general access structures in the classical setting. Finally, among other things, we study the class of access structures which can be efficiently implemented when the quantum secret sharing scheme has access to a given number of copies of the secret, including all such functions in $mathsfP$ and $mathsfNP$.
While QSS was introduced over twenty years ago, previous works only considered information-theoretic privacy. In this work, we initiate the study of computationally-secure QSS and show that computational assumptions help significantly in building QSS schemes, just as in the classical case. We present a simple compiler and use it to obtain a large variety results: We construct polynomial-time computationally-secure QSS schemes under standard hardness assumptions for a rich class of access structures. This includes many access structures for which previous results in QSS necessarily required exponential share size. In fact, we can go even further: We construct QSS schemes for which the size of the quantum shares is significantly smaller than the size of the secret. As in the classical setting, this is impossible with perfect security. We also apply our compiler to obtain results beyond computational QSS. In the information-theoretic setting, we improve the share size of perfect QSS schemes for a large class of $n$-party access structures to $1.5^n+o(n)$, improving upon best known schemes and matching the best known result for general access structures in the classical setting. Finally, among other things, we study the class of access structures which can be efficiently implemented when the quantum secret sharing scheme has access to a given number of copies of the secret, including all such functions in $mathsfP$ and $mathsfNP$.
73.
Satoshi Yoshida, Shiro Tamiya, Hayata Yamasaki
Concatenate codes, save qubits Talk
2024.
@Talk{T24_120,
title = {Concatenate codes, save qubits},
author = {Satoshi Yoshida and Shiro Tamiya and Hayata Yamasaki},
year = {2024},
date = {2024-01-01},
abstract = {The essential requirement for fault-tolerant quantum computation (FTQC) is the total protocol design to achieve a fair balance of all the critical factors relevant to its practical realization, such as the space overhead, the threshold, and the modularity. A major obstacle in realizing FTQC with conventional protocols, such as those based on the surface code and the concatenated Steane code, has been the space overhead, i.e., the required number of physical qubits per logical qubit. Protocols based on high-rate quantum low-density parity-check (LDPC) codes gather considerable attention as a way to reduce the space overhead, but problematically, the existing fault-tolerant protocols for such quantum LDPC codes sacrifice the other factors. Here we construct a new fault-tolerant protocol to meet these requirements simultaneously based on more recent progress on the techniques for concatenated codes rather than quantum LDPC codes, achieving a constant space overhead, a high threshold, and flexibility in modular architecture designs. In particular, under a physical error rate of 0.1%, our protocol reduces the space overhead to achieve the logical CNOT error rates $10^-10$ and $10^-24$ by more than 90% and 97%, respectively, compared to the protocol for the surface code. Furthermore, our protocol achieves the threshold of 2.4% under a conventional circuit-level error model, substantially outperforming that of the surface code. The use of concatenated codes also naturally introduces abstraction layers essential for the modularity of FTQC architectures. These results indicate that the code-concatenation approach opens a way to significantly save qubits in realizing FTQC while fulfilling the other essential requirements for the practical protocol design.},
keywords = {},
pubstate = {published},
tppubtype = {Talk}
}
The essential requirement for fault-tolerant quantum computation (FTQC) is the total protocol design to achieve a fair balance of all the critical factors relevant to its practical realization, such as the space overhead, the threshold, and the modularity. A major obstacle in realizing FTQC with conventional protocols, such as those based on the surface code and the concatenated Steane code, has been the space overhead, i.e., the required number of physical qubits per logical qubit. Protocols based on high-rate quantum low-density parity-check (LDPC) codes gather considerable attention as a way to reduce the space overhead, but problematically, the existing fault-tolerant protocols for such quantum LDPC codes sacrifice the other factors. Here we construct a new fault-tolerant protocol to meet these requirements simultaneously based on more recent progress on the techniques for concatenated codes rather than quantum LDPC codes, achieving a constant space overhead, a high threshold, and flexibility in modular architecture designs. In particular, under a physical error rate of 0.1%, our protocol reduces the space overhead to achieve the logical CNOT error rates $10^-10$ and $10^-24$ by more than 90% and 97%, respectively, compared to the protocol for the surface code. Furthermore, our protocol achieves the threshold of 2.4% under a conventional circuit-level error model, substantially outperforming that of the surface code. The use of concatenated codes also naturally introduces abstraction layers essential for the modularity of FTQC architectures. These results indicate that the code-concatenation approach opens a way to significantly save qubits in realizing FTQC while fulfilling the other essential requirements for the practical protocol design.
74.
Anurag Anshu, Tony Metger
Concentration bounds for quantum states and limitations on the QAOA from polynomial approximations Workshop
2023.
Abstract | Links:
@Workshop{T4520,
title = {Concentration bounds for quantum states and limitations on the QAOA from polynomial approximations},
author = {Anurag Anshu and Tony Metger},
url = {https://arxiv.org/abs/2209.02715},
year = {2023},
date = {2023-01-01},
abstract = {We prove concentration bounds for the following classes of quantum states:
(i) output states of shallow quantum circuits;
(ii) injective matrix product states;
(iii) output states of dense Hamiltonian evolution, i.e.~states of the form $e^ıota H^(p) cdots e^ıota H^(1) ketpsi_0$ for any $n$-qubit product state $ketpsi_0$, where each $H^(i)$ can be any local commuting Hamiltonian satisfying a norm constraint, including dense Hamiltonians with interactions between any qubits.
Our proofs use polynomial approximations to show that these states are close to local operators. This implies that the distribution of the Hamming weight of a computational basis measurement (and of other related observables) concentrates. An example of (iii) are the states produced by the quantum approximate optimisation algorithm (QAOA). Using our concentration results for these states, we show that for a random spin model, the QAOA can only succeed with negligible probability even at super-constant level $p = o(łog łog n)$, assuming a strengthened version of the so-called overlap gap property. This gives the first limitations on the QAOA on dense instances at super-constant level.},
howpublished = {Talk},
keywords = {},
pubstate = {published},
tppubtype = {Workshop}
}
We prove concentration bounds for the following classes of quantum states:
(i) output states of shallow quantum circuits;
(ii) injective matrix product states;
(iii) output states of dense Hamiltonian evolution, i.e.~states of the form $e^ıota H^(p) cdots e^ıota H^(1) ketpsi_0$ for any $n$-qubit product state $ketpsi_0$, where each $H^(i)$ can be any local commuting Hamiltonian satisfying a norm constraint, including dense Hamiltonians with interactions between any qubits.
Our proofs use polynomial approximations to show that these states are close to local operators. This implies that the distribution of the Hamming weight of a computational basis measurement (and of other related observables) concentrates. An example of (iii) are the states produced by the quantum approximate optimisation algorithm (QAOA). Using our concentration results for these states, we show that for a random spin model, the QAOA can only succeed with negligible probability even at super-constant level $p = o(łog łog n)$, assuming a strengthened version of the so-called overlap gap property. This gives the first limitations on the QAOA on dense instances at super-constant level.
(i) output states of shallow quantum circuits;
(ii) injective matrix product states;
(iii) output states of dense Hamiltonian evolution, i.e.~states of the form $e^ıota H^(p) cdots e^ıota H^(1) ketpsi_0$ for any $n$-qubit product state $ketpsi_0$, where each $H^(i)$ can be any local commuting Hamiltonian satisfying a norm constraint, including dense Hamiltonians with interactions between any qubits.
Our proofs use polynomial approximations to show that these states are close to local operators. This implies that the distribution of the Hamming weight of a computational basis measurement (and of other related observables) concentrates. An example of (iii) are the states produced by the quantum approximate optimisation algorithm (QAOA). Using our concentration results for these states, we show that for a random spin model, the QAOA can only succeed with negligible probability even at super-constant level $p = o(łog łog n)$, assuming a strengthened version of the so-called overlap gap property. This gives the first limitations on the QAOA on dense instances at super-constant level.
75.
Paul Gondolf, Samuel O. Scalet, Alberto Ruiz-de-Alarcón, Álvaro M. Alhambra, Ángela Capel
Conditional independence of 1D Gibbs states with applications to efficient learning Talk
2024.
@Talk{T24_298,
title = {Conditional independence of 1D Gibbs states with applications to efficient learning},
author = {Paul Gondolf and Samuel O. Scalet and Alberto Ruiz-de-Alarcón and Álvaro M. Alhambra and Ángela Capel},
year = {2024},
date = {2024-01-01},
abstract = {We show that spin chains in thermal equilibrium have a correlation structure in which individual regions are strongly correlated at most with their near vicinity. We quantify this with alternative notions of the conditional mutual information defined through the so-called Belavkin-Staszewski relative entropy. Our main result is the superexponential decay of various such measures, under the assumption that the spin chain Hamiltonian is translation-invariant. We use a recovery map associated with these definitions to sequentially construct tensor network approximations in terms of marginals of small (sub-logarithmic) size. This allows for representations of the state that can be learned efficiently from local measurements. We also prove an approximate factorization condition for the purity, from which it follows that the purity of the entire Gibbs state can be efficiently estimated to a small multiplicative error. As a technical step of independent interest, we show an upper bound to the decay of the Belavkin-Staszewski relative entropy upon the application of a conditional expectation.},
keywords = {},
pubstate = {published},
tppubtype = {Talk}
}
We show that spin chains in thermal equilibrium have a correlation structure in which individual regions are strongly correlated at most with their near vicinity. We quantify this with alternative notions of the conditional mutual information defined through the so-called Belavkin-Staszewski relative entropy. Our main result is the superexponential decay of various such measures, under the assumption that the spin chain Hamiltonian is translation-invariant. We use a recovery map associated with these definitions to sequentially construct tensor network approximations in terms of marginals of small (sub-logarithmic) size. This allows for representations of the state that can be learned efficiently from local measurements. We also prove an approximate factorization condition for the purity, from which it follows that the purity of the entire Gibbs state can be efficiently estimated to a small multiplicative error. As a technical step of independent interest, we show an upper bound to the decay of the Belavkin-Staszewski relative entropy upon the application of a conditional expectation.
76.
Matthias Salzger, V. Vilasini
Connecting indefinite causal order processes to composable quantum protocols in a spacetime Workshop
2023.
Abstract | Links:
@Workshop{T5276,
title = {Connecting indefinite causal order processes to composable quantum protocols in a spacetime},
author = {Matthias Salzger and V. Vilasini},
url = {https://arxiv.org/abs/2304.06735 https://tqc-conference.org/wp-content/uploads/cfdb7_uploads/1688052738-video-TQC_talk_summary.mp4},
year = {2023},
date = {2023-01-01},
abstract = {The process matrix framework models quantum protocols without assuming a definite acyclic causal order between the operations of parties in the protocol. This leads to so-called indefinite causal order processes which have been shown to provide advantages for quantum information processing. However, there have been longstanding open questions regarding the subset of practically realisable process matrices, as well as challenges in formulating their composition. We make progress on addressing such questions by connecting an important subset of process matrices, namely quantum circuits with quantum control of causal order (QC-QC) with so-called causal boxes which describe practical quantum information protocols in spacetime. Causal boxes are fully closed under composition and incorporate physical principles such as relativistic causality in spacetime. We first identify a notion of operational equivalence between QC-QCs and causal boxes by connecting state spaces and operations in the two formalisms. We then explicitly construct for each QC-QC an operationally equivalent causal box that satisfies certain special mathematical properties that allows the causal box to be interpreted as a process, this corresponds to a subset of causal boxes previously known as process boxes. This allows us to define composition of QC-QCs in terms of composition of causal boxes which is well-defined. We conjecture with a proof sketch that the spatiotemporal labels involved in their description can be simplified to a certain totally ordered form. Based on this, we establish through a constructive proof that every process box can be mapped to an operationally equivalent QCQC. This indicates that the subset of indefinite causal order processes realisable in a background spacetime correspond to controlled superpositions of acyclic orders, which in particular rules out processes violating so-called causal inequalities. Our results shed light on the practicality and composability questions for indefinite causal structures while introducing new physically-motivated tools for studying their applications for quantum information processing in spacetime.},
howpublished = {Talk},
keywords = {},
pubstate = {published},
tppubtype = {Workshop}
}
The process matrix framework models quantum protocols without assuming a definite acyclic causal order between the operations of parties in the protocol. This leads to so-called indefinite causal order processes which have been shown to provide advantages for quantum information processing. However, there have been longstanding open questions regarding the subset of practically realisable process matrices, as well as challenges in formulating their composition. We make progress on addressing such questions by connecting an important subset of process matrices, namely quantum circuits with quantum control of causal order (QC-QC) with so-called causal boxes which describe practical quantum information protocols in spacetime. Causal boxes are fully closed under composition and incorporate physical principles such as relativistic causality in spacetime. We first identify a notion of operational equivalence between QC-QCs and causal boxes by connecting state spaces and operations in the two formalisms. We then explicitly construct for each QC-QC an operationally equivalent causal box that satisfies certain special mathematical properties that allows the causal box to be interpreted as a process, this corresponds to a subset of causal boxes previously known as process boxes. This allows us to define composition of QC-QCs in terms of composition of causal boxes which is well-defined. We conjecture with a proof sketch that the spatiotemporal labels involved in their description can be simplified to a certain totally ordered form. Based on this, we establish through a constructive proof that every process box can be mapped to an operationally equivalent QCQC. This indicates that the subset of indefinite causal order processes realisable in a background spacetime correspond to controlled superpositions of acyclic orders, which in particular rules out processes violating so-called causal inequalities. Our results shed light on the practicality and composability questions for indefinite causal structures while introducing new physically-motivated tools for studying their applications for quantum information processing in spacetime.
77.
Lorenzo Catani, Ricardo Faleiro, Pierre-Emmanuel Emeriau, Shane Mansfield, Anna Pappa
Connecting XOR and XOR* games Poster
2023.
Abstract | Links:
@Poster{P7280,
title = {Connecting XOR and XOR* games},
author = {Lorenzo Catani and Ricardo Faleiro and Pierre-Emmanuel Emeriau and Shane Mansfield and Anna Pappa},
url = {https://arxiv.org/abs/2210.00397 https://tqc-conference.org/wp-content/uploads/cfdb7_uploads/1688148971-poster-TQC-Poster-46.pdf},
year = {2023},
date = {2023-01-01},
abstract = {In this work we focus on two classes of games: XOR nonlocal games and XOR* sequential games with monopartite resources. XOR games have been widely studied in the literature of nonlocal games, and we introduce XOR* games as their natural counterpart within the class of games where a resource system is subjected to a sequence of controlled operations and a final measurement. Examples of XOR* games are 2→1 quantum random access codes (QRAC) and the CHSH* game introduced by Henaut et al. in [PRA 98,060302(2018)]. We prove, using the diagrammatic language of process theories, that under certain assumptions these two classes of games can be related via an explicit theorem that connects their optimal strategies, and so their classical (Bell) and quantum (Tsirelson) bounds. One main assumption in the theorem is that the sequential transformations in the XOR* games are reversible. However, this does not affect the generality of the theorem in terms of assessing the maximum quantum-over-classical advantage, since we also show that the use of irreversible transformations cannot enhance such advantage. We conclude with several examples of pairs of XOR/XOR* games and by discussing in detail the possible resources that power the quantum computational advantages in XOR* games.},
howpublished = {Poster},
keywords = {},
pubstate = {published},
tppubtype = {Poster}
}
In this work we focus on two classes of games: XOR nonlocal games and XOR* sequential games with monopartite resources. XOR games have been widely studied in the literature of nonlocal games, and we introduce XOR* games as their natural counterpart within the class of games where a resource system is subjected to a sequence of controlled operations and a final measurement. Examples of XOR* games are 2→1 quantum random access codes (QRAC) and the CHSH* game introduced by Henaut et al. in [PRA 98,060302(2018)]. We prove, using the diagrammatic language of process theories, that under certain assumptions these two classes of games can be related via an explicit theorem that connects their optimal strategies, and so their classical (Bell) and quantum (Tsirelson) bounds. One main assumption in the theorem is that the sequential transformations in the XOR* games are reversible. However, this does not affect the generality of the theorem in terms of assessing the maximum quantum-over-classical advantage, since we also show that the use of irreversible transformations cannot enhance such advantage. We conclude with several examples of pairs of XOR/XOR* games and by discussing in detail the possible resources that power the quantum computational advantages in XOR* games.
78.
Jonathan Allcock, Jinge Bao, João F. Doriguello, Alessandro Luongo, Miklos Santha
Constant-depth circuits for Uniformly Controlled Gates and Boolean functions with application to quantum memory circuits Talk
2024.
@Talk{T24_8,
title = {Constant-depth circuits for Uniformly Controlled Gates and Boolean functions with application to quantum memory circuits},
author = {Jonathan Allcock and Jinge Bao and João F. Doriguello and Alessandro Luongo and Miklos Santha},
year = {2024},
date = {2024-01-01},
abstract = {We explore the power of the unbounded Fan-Out gate and the Global Tunable gates generated by Ising-type Hamiltonians in constructing constant-depth quantum circuits, with particular attention to quantum memory devices. We propose two types of constant-depth constructions for implementing Uniformly Controlled Gates. These gates include the Fan-In gates defined by $|xrangle|branglemapsto |xrangle|bøplus f(x)rangle$ for $xın0,1^n$ and $bın0,1$, where $f$ is a Boolean function. The first of our constructions is based on computing the one-hot encoding of the control register $|xrangle$, while the second is based on Boolean analysis and exploits different representations of $f$ such as its Fourier expansion. Via these constructions, we obtain constant-depth circuits for the quantum counterparts of read-only and read-write memory devices — Quantum Random Access Memory ($QRAM$) and Quantum Random Access Gate ($QRAG$) — of memory size $n$. The implementation based on one-hot encoding requires either $O(nłognłogłogn)$ ancillae and $O(nłogn)$ Fan-Out gates or $O(nłogn)$ ancillae and $6$ Global Tunable gates. On the other hand, the implementation based on Boolean analysis requires only $2$ Global Tunable gates at the expense of $O(n^2)$ ancillae.},
keywords = {},
pubstate = {published},
tppubtype = {Talk}
}
We explore the power of the unbounded Fan-Out gate and the Global Tunable gates generated by Ising-type Hamiltonians in constructing constant-depth quantum circuits, with particular attention to quantum memory devices. We propose two types of constant-depth constructions for implementing Uniformly Controlled Gates. These gates include the Fan-In gates defined by $|xrangle|branglemapsto |xrangle|bøplus f(x)rangle$ for $xın0,1^n$ and $bın0,1$, where $f$ is a Boolean function. The first of our constructions is based on computing the one-hot encoding of the control register $|xrangle$, while the second is based on Boolean analysis and exploits different representations of $f$ such as its Fourier expansion. Via these constructions, we obtain constant-depth circuits for the quantum counterparts of read-only and read-write memory devices — Quantum Random Access Memory ($QRAM$) and Quantum Random Access Gate ($QRAG$) — of memory size $n$. The implementation based on one-hot encoding requires either $O(nłognłogłogn)$ ancillae and $O(nłogn)$ Fan-Out gates or $O(nłogn)$ ancillae and $6$ Global Tunable gates. On the other hand, the implementation based on Boolean analysis requires only $2$ Global Tunable gates at the expense of $O(n^2)$ ancillae.
79.
Swayangprabha Shaw, Harsh Gupta, Shahid Mehraj Shah, Ankur Raina
Construction of non-CSS quantum codes using measurements on cluster states Poster
2023.
@Poster{P8098,
title = {Construction of non-CSS quantum codes using measurements on cluster states},
author = {Swayangprabha Shaw and Harsh Gupta and Shahid Mehraj Shah and Ankur Raina},
url = {https://tqc-conference.org/wp-content/uploads/cfdb7_uploads/1688069358-poster-8098.pdf https://tqc-conference.org/wp-content/uploads/cfdb7_uploads/1688069358-video-8098.mp4},
year = {2023},
date = {2023-01-01},
howpublished = {Poster},
keywords = {},
pubstate = {published},
tppubtype = {Poster}
}
80.
Siyuan Niu, Aida Todri-Sanial
Context-dependent Dynamical Decoupling Insertion for Quantum Circuits Poster
2023.
@Poster{P958,
title = {Context-dependent Dynamical Decoupling Insertion for Quantum Circuits},
author = {Siyuan Niu and Aida Todri-Sanial},
year = {2023},
date = {2023-01-01},
howpublished = {Poster},
keywords = {},
pubstate = {published},
tppubtype = {Poster}
}
81.
Martin Plávala, Otfried Guehne
Contextuality as a precondition for entanglement Poster
2023.
@Poster{P6989,
title = {Contextuality as a precondition for entanglement},
author = {Martin Plávala and Otfried Guehne},
year = {2023},
date = {2023-01-01},
howpublished = {Poster},
keywords = {},
pubstate = {published},
tppubtype = {Poster}
}
82.
Ravi Kunjwal, Victoria Wright
Contextuality in composite systems: the role of entanglement in the Kochen-Specker theorem Workshop
2023.
Abstract | Links:
@Workshop{T2989,
title = {Contextuality in composite systems: the role of entanglement in the Kochen-Specker theorem},
author = {Ravi Kunjwal and Victoria Wright},
url = {https://arxiv.org/abs/2109.13594},
year = {2023},
date = {2023-01-01},
abstract = {The fact that quantum theory radically departs from 'classical lines of thought' is a critical driver for its applications in quantum information and computation. A famous example of this radical departure—this nonclassicality—is entanglement. Bell's theorem shows that shared entanglement can be used to generate correlations between non-communicating parties in ways that are impossible to do without communication if one only had access to classical shared randomness. In their very formulation, both entanglement and Bell's theorem are composite notions of nonclassicality, i.e., they require at least two parties to be meaningful. Another key notion of nonclassicality is contextuality that follows from the Kochen-Specker theorem: this notion is applicable to single systems. I will present some recent results on the interplay between contextuality and entanglement in composite systems and their consequences for our understanding of restricted models of multiqubit quantum computation with state injection that have been previously proposed. Based on V.J. Wright and R. Kunjwal, Quantum 7, 900 (2023).},
howpublished = {Talk},
keywords = {},
pubstate = {published},
tppubtype = {Workshop}
}
The fact that quantum theory radically departs from 'classical lines of thought' is a critical driver for its applications in quantum information and computation. A famous example of this radical departure—this nonclassicality—is entanglement. Bell's theorem shows that shared entanglement can be used to generate correlations between non-communicating parties in ways that are impossible to do without communication if one only had access to classical shared randomness. In their very formulation, both entanglement and Bell's theorem are composite notions of nonclassicality, i.e., they require at least two parties to be meaningful. Another key notion of nonclassicality is contextuality that follows from the Kochen-Specker theorem: this notion is applicable to single systems. I will present some recent results on the interplay between contextuality and entanglement in composite systems and their consequences for our understanding of restricted models of multiqubit quantum computation with state injection that have been previously proposed. Based on V.J. Wright and R. Kunjwal, Quantum 7, 900 (2023).
83.
Karol Horodecki, Siddhartha Das, Leonard Sikorski, Mark M. Wilde
Cost of quantum secret key Workshop
2023.
Abstract | Links:
@workshop{T6076,
title = {Cost of quantum secret key},
author = {Karol Horodecki and Siddhartha Das and Leonard Sikorski and Mark M. Wilde},
url = {https://tqc-conference.org/wp-content/uploads/2023/07/key_cost_q_internet_updated.pdf},
year = {2023},
date = {2023-01-01},
urldate = {2023-01-01},
abstract = {In this paper, we develop the resource theory of quantum secret key. Operating under the assumption that entangled states with zero distillable key do not exist, we define the key cost of a quantum state, channel, and device. We study its properties through the lens of a quantity that we call the key of formation. The main result of our paper is that the regularized key of formation equals the key cost of a quantum state. The core protocol underlying this result is privacy dilution, which converts states containing ideal privacy into ones with diluted privacy. Additionally, our main result follows by proving that the key of formation is an entanglement monotone with appealing mathematical properties. We further focus on mixed-state analogues of pure quantum states in the domain of privacy, and we prove that a number of entanglement measures are equal to each other for these states, similar to the case of pure entangled states. The privacy cost in the single-shot regime exhibits a yield-cost relation, and basic results for quantum channels and devices are also provided.},
howpublished = {Talk},
keywords = {},
pubstate = {published},
tppubtype = {workshop}
}
In this paper, we develop the resource theory of quantum secret key. Operating under the assumption that entangled states with zero distillable key do not exist, we define the key cost of a quantum state, channel, and device. We study its properties through the lens of a quantity that we call the key of formation. The main result of our paper is that the regularized key of formation equals the key cost of a quantum state. The core protocol underlying this result is privacy dilution, which converts states containing ideal privacy into ones with diluted privacy. Additionally, our main result follows by proving that the key of formation is an entanglement monotone with appealing mathematical properties. We further focus on mixed-state analogues of pure quantum states in the domain of privacy, and we prove that a number of entanglement measures are equal to each other for these states, similar to the case of pure entangled states. The privacy cost in the single-shot regime exhibits a yield-cost relation, and basic results for quantum channels and devices are also provided.
84.
Rodrigo Coelho, Luís Santos, André Sequeira
Data Re-Uploading in Quantum Variational Q-Learning Poster
2023.
@Poster{P2531,
title = {Data Re-Uploading in Quantum Variational Q-Learning},
author = {Rodrigo Coelho and Luís Santos and André Sequeira},
year = {2023},
date = {2023-01-01},
keywords = {},
pubstate = {published},
tppubtype = {Poster}
}
85.
João F. Doriguello
Decoding probabilistic syndrome measurement and the role of entropy Poster
2023.
@Poster{P6744,
title = {Decoding probabilistic syndrome measurement and the role of entropy},
author = {João F. Doriguello},
year = {2023},
date = {2023-01-01},
howpublished = {Poster},
keywords = {},
pubstate = {published},
tppubtype = {Poster}
}
86.
Yun Shang, Xiao Shi
Density peak clustering using tensor networks Poster
2023.
@Poster{P5443,
title = {Density peak clustering using tensor networks},
author = {Yun Shang and Xiao Shi},
year = {2023},
date = {2023-01-01},
howpublished = {Poster},
keywords = {},
pubstate = {published},
tppubtype = {Poster}
}
87.
Vaibhab Chimalgi, Bihalan Bhattacharya, Suchetana Goswami, Samyadeb Bhattacharya
Detecting entanglement harnessing Lindblad structure Poster
2023.
@Poster{P3290,
title = {Detecting entanglement harnessing Lindblad structure},
author = {Vaibhab Chimalgi and Bihalan Bhattacharya and Suchetana Goswami and Samyadeb Bhattacharya},
year = {2023},
date = {2023-01-01},
howpublished = {Poster},
keywords = {},
pubstate = {published},
tppubtype = {Poster}
}
88.
Zhenhuan Liu, Yifan Tang, Hao Dai, Pengyu Liu, Shu Chen, Xiongfeng Ma
Detecting Entanglement in Quantum Many-Body Systems via Permutation Moments Poster
2023.
@Poster{P9126,
title = {Detecting Entanglement in Quantum Many-Body Systems via Permutation Moments},
author = {Zhenhuan Liu and Yifan Tang and Hao Dai and Pengyu Liu and Shu Chen and Xiongfeng Ma},
year = {2023},
date = {2023-01-01},
howpublished = {Poster},
keywords = {},
pubstate = {published},
tppubtype = {Poster}
}
89.
Srijita Kundu, Ernest Y. -Z. Tan
Device-independent uncloneable encryption Poster
2023.
@Poster{P2136,
title = {Device-independent uncloneable encryption},
author = {Srijita Kundu and Ernest Y. -Z. Tan},
year = {2023},
date = {2023-01-01},
howpublished = {Poster},
keywords = {},
pubstate = {published},
tppubtype = {Poster}
}
90.
Alexis R. Legon, Ernesto Medina
Dilemma breaking in quantum games by joint probabilities approach Poster
2023.
Abstract | Links:
@Poster{P758,
title = {Dilemma breaking in quantum games by joint probabilities approach},
author = {Alexis R. Legon and Ernesto Medina},
url = {https://www.nature.com/articles/s41598-022-17072-8},
year = {2023},
date = {2023-01-01},
abstract = {Classical games are fundamentally modified in the quantum realm, due to non-locality and entanglement, which overlook some of the crucial features of the classical problem that define a dilemma [1,2]. Therefore, we analyze how the dilemma can be diverted and even
completely eliminated by players using quantum strategies from the point of view of joint probabilities [3], based on the fact that quantum games are characterized by the nature of their joint probabilities; if these are factorable, it is a classical game, otherwise, it is a quantum game. In this way, in this work, we extend the focus of the
non-factorizable joint probabilities when obtaining expressions that do not allow determining Nash equilibria in games [4]. Likewise, we introduce entropy as a definition of game information, in which the game is considered as an information channel, by incorporating it into the game strategies, we obtain equilibria that eliminate dilemmas. In addition to obtaining better performance than channels information channels, such as the Flip channel. We also connect the potential of
the formalism of quantum games with the transmission of quantum information in noisy channels quantum and recent considerations of the connection between the mechanisms of thermalization in the
statistical mechanics, the many-body problem, and cooperative games considered here in the quantum regime. Being this the first work in which the information is used in the strategies of the game in order to solve the dilemmas of these.
References
[1] Eisert, J., Wilkens, M. & Lewenstein, M., Phys. Rev. Lett. 83, 3077–3080 (1999)
[2] Eisert, J. & Wilkens, M., J. Mod. Opt. 47, 2453–2556 (2000)
[3] Iqbal, A., Chappell, J. M. & Abbott, D., R. Soc. Open Sci. 3, 150477 (2016) [4] Legón, A.R., Medina, E., Sci Rep 12, 13470 (2022)},
howpublished = {Poster},
keywords = {},
pubstate = {published},
tppubtype = {Poster}
}
Classical games are fundamentally modified in the quantum realm, due to non-locality and entanglement, which overlook some of the crucial features of the classical problem that define a dilemma [1,2]. Therefore, we analyze how the dilemma can be diverted and even
completely eliminated by players using quantum strategies from the point of view of joint probabilities [3], based on the fact that quantum games are characterized by the nature of their joint probabilities; if these are factorable, it is a classical game, otherwise, it is a quantum game. In this way, in this work, we extend the focus of the
non-factorizable joint probabilities when obtaining expressions that do not allow determining Nash equilibria in games [4]. Likewise, we introduce entropy as a definition of game information, in which the game is considered as an information channel, by incorporating it into the game strategies, we obtain equilibria that eliminate dilemmas. In addition to obtaining better performance than channels information channels, such as the Flip channel. We also connect the potential of
the formalism of quantum games with the transmission of quantum information in noisy channels quantum and recent considerations of the connection between the mechanisms of thermalization in the
statistical mechanics, the many-body problem, and cooperative games considered here in the quantum regime. Being this the first work in which the information is used in the strategies of the game in order to solve the dilemmas of these.
References
[1] Eisert, J., Wilkens, M. & Lewenstein, M., Phys. Rev. Lett. 83, 3077–3080 (1999)
[2] Eisert, J. & Wilkens, M., J. Mod. Opt. 47, 2453–2556 (2000)
[3] Iqbal, A., Chappell, J. M. & Abbott, D., R. Soc. Open Sci. 3, 150477 (2016) [4] Legón, A.R., Medina, E., Sci Rep 12, 13470 (2022)
completely eliminated by players using quantum strategies from the point of view of joint probabilities [3], based on the fact that quantum games are characterized by the nature of their joint probabilities; if these are factorable, it is a classical game, otherwise, it is a quantum game. In this way, in this work, we extend the focus of the
non-factorizable joint probabilities when obtaining expressions that do not allow determining Nash equilibria in games [4]. Likewise, we introduce entropy as a definition of game information, in which the game is considered as an information channel, by incorporating it into the game strategies, we obtain equilibria that eliminate dilemmas. In addition to obtaining better performance than channels information channels, such as the Flip channel. We also connect the potential of
the formalism of quantum games with the transmission of quantum information in noisy channels quantum and recent considerations of the connection between the mechanisms of thermalization in the
statistical mechanics, the many-body problem, and cooperative games considered here in the quantum regime. Being this the first work in which the information is used in the strategies of the game in order to solve the dilemmas of these.
References
[1] Eisert, J., Wilkens, M. & Lewenstein, M., Phys. Rev. Lett. 83, 3077–3080 (1999)
[2] Eisert, J. & Wilkens, M., J. Mod. Opt. 47, 2453–2556 (2000)
[3] Iqbal, A., Chappell, J. M. & Abbott, D., R. Soc. Open Sci. 3, 150477 (2016) [4] Legón, A.R., Medina, E., Sci Rep 12, 13470 (2022)
91.
Scott Aaronson, Jason Pollack
Discrete Bulk Reconstruction Poster
2023.
@Poster{P4645,
title = {Discrete Bulk Reconstruction},
author = {Scott Aaronson and Jason Pollack},
year = {2023},
date = {2023-01-01},
howpublished = {Poster},
keywords = {},
pubstate = {published},
tppubtype = {Poster}
}
92.
Shradhanjali Sahu
Discrete Modulation Continuous Variable Quantum Key Distribution in Multiple-Input Multiple-Output Settings Poster
2023.
@Poster{P8386,
title = {Discrete Modulation Continuous Variable Quantum Key Distribution in Multiple-Input Multiple-Output Settings},
author = {Shradhanjali Sahu},
year = {2023},
date = {2023-01-01},
keywords = {},
pubstate = {published},
tppubtype = {Poster}
}
93.
Tim Möbus, Andreas Bluhm, Matthias C. Caro, Albert H. Werner, Cambyse Rouzé
Dissipation-enabled bosonic Hamiltonian learning via new information-propagation bounds Talk
2024.
@Talk{T24_176,
title = {Dissipation-enabled bosonic Hamiltonian learning via new information-propagation bounds},
author = {Tim Möbus and Andreas Bluhm and Matthias C. Caro and Albert H. Werner and Cambyse Rouzé},
year = {2024},
date = {2024-01-01},
abstract = {Reliable quantum technology requires knowledge of the dynamics governing the underlying system. This problem of characterizing and benchmarking quantum devices or experiments in continuous time is referred to as the Hamiltonian learning problem. In contrast to multi-qubit systems, learning guarantees for the dynamics of bosonic systems have hitherto remained mostly unexplored. For m-mode Hamiltonians given as polynomials in annihilation and creation operators with modes arranged on a lattice, we establish a simple moment criterion in terms of the particle number operator which ensures that learning strategies from the finite-dimensional setting extend to the bosonic setting, requiring only coherent states and heterodyne detection on the experimental side. We then propose an enhanced procedure based on added dissipation that even works if the Hamiltonian time evolution violates this moment criterion: With high success probability it learns all coefficients of the Hamiltonian to accuracy ε using a total evolution time of O(ε−2 log(m)). Our protocol involves the experimentally reachable resources of projected coherent state preparation, dissipative regularization akin to recent quantum error correction schemes involving cat qubits stabilized by a nonlinear multi-photon driven dissipation process, and heterodyne measurements. As a crucial step in our analysis, we establish our moment criterion and a new Lieb-Robinson type bound for the evolution generated by an arbitrary bosonic Hamiltonian of bounded degree in the annihilation and creation operators combined with photon-driven dissipation. Our work demonstrates that a broad class of bosonic Hamiltonians can be efficiently learned from simple quantum experiments, and our bosonic Lieb-Robinson bound may independently serve as a versatile tool for studying evolutions on continuous variable systems.},
keywords = {},
pubstate = {published},
tppubtype = {Talk}
}
Reliable quantum technology requires knowledge of the dynamics governing the underlying system. This problem of characterizing and benchmarking quantum devices or experiments in continuous time is referred to as the Hamiltonian learning problem. In contrast to multi-qubit systems, learning guarantees for the dynamics of bosonic systems have hitherto remained mostly unexplored. For m-mode Hamiltonians given as polynomials in annihilation and creation operators with modes arranged on a lattice, we establish a simple moment criterion in terms of the particle number operator which ensures that learning strategies from the finite-dimensional setting extend to the bosonic setting, requiring only coherent states and heterodyne detection on the experimental side. We then propose an enhanced procedure based on added dissipation that even works if the Hamiltonian time evolution violates this moment criterion: With high success probability it learns all coefficients of the Hamiltonian to accuracy ε using a total evolution time of O(ε−2 log(m)). Our protocol involves the experimentally reachable resources of projected coherent state preparation, dissipative regularization akin to recent quantum error correction schemes involving cat qubits stabilized by a nonlinear multi-photon driven dissipation process, and heterodyne measurements. As a crucial step in our analysis, we establish our moment criterion and a new Lieb-Robinson type bound for the evolution generated by an arbitrary bosonic Hamiltonian of bounded degree in the annihilation and creation operators combined with photon-driven dissipation. Our work demonstrates that a broad class of bosonic Hamiltonians can be efficiently learned from simple quantum experiments, and our bosonic Lieb-Robinson bound may independently serve as a versatile tool for studying evolutions on continuous variable systems.
94.
Farzin Salek, Andreas Winter
Distillation of Secret Key and GHZ States from Multipartite Mixed States Poster
2023.
Abstract | Links:
@Poster{P1171,
title = {Distillation of Secret Key and GHZ States from Multipartite Mixed States},
author = {Farzin Salek and Andreas Winter},
url = {https://ieeexplore.ieee.org/document/9834630},
year = {2023},
date = {2023-01-01},
abstract = {We consider two related problems of extracting correlation from a given multipartite mixed quantum state: the first is the distillation of a conference key when the state is shared between a number of legal players and an eavesdropper; the eavesdropper, apart from starting off with this quantum side information, also observes the public communication between the players. The second is the distillation of Greenberger-Horne-Zeilinger (GHZ) states by means of LOCC from the given mixed state. These problem settings extend our previous paper [FS & AW, IEEE Trans. Inf. Theory 68(2):976-988, 2022], and we generalise its results: using a quantum version of the task of communication for omniscience, we derive a novel lower bound on the distillable secret key from any multipartite quantum state by means of a so-called non-interacting communication protocol. Secondly, by making the secret key distillation protocol coherent, we derive novel lower bounds on the distillation rate of GHZ states.},
howpublished = {Poster},
keywords = {},
pubstate = {published},
tppubtype = {Poster}
}
We consider two related problems of extracting correlation from a given multipartite mixed quantum state: the first is the distillation of a conference key when the state is shared between a number of legal players and an eavesdropper; the eavesdropper, apart from starting off with this quantum side information, also observes the public communication between the players. The second is the distillation of Greenberger-Horne-Zeilinger (GHZ) states by means of LOCC from the given mixed state. These problem settings extend our previous paper [FS & AW, IEEE Trans. Inf. Theory 68(2):976-988, 2022], and we generalise its results: using a quantum version of the task of communication for omniscience, we derive a novel lower bound on the distillable secret key from any multipartite quantum state by means of a so-called non-interacting communication protocol. Secondly, by making the secret key distillation protocol coherent, we derive novel lower bounds on the distillation rate of GHZ states.
95.
François Le Gall, Masayuki Miyamoto, Harumichi Nishimura
Distributed Merlin-Arthur Synthesis of Quantum States and Its Applications Workshop
2023.
@Workshop{T4427,
title = {Distributed Merlin-Arthur Synthesis of Quantum States and Its Applications},
author = {François Le Gall and Masayuki Miyamoto and Harumichi Nishimura},
year = {2023},
date = {2023-01-01},
abstract = {The generation and verification of quantum states are fundamental tasks for quantum information processing that have recently been investigated by Irani, Natarajan, Nirkhe, Rao and Yuen [CCC 2022], Rosenthal and Yuen [ITCS 2022], Metger and Yuen [QIP 2023] under the term emphstate synthesis. This paper studies this concept from the viewpoint of quantum distributed computing, and especially distributed quantum Merlin-Arthur (dQMA) protocols. We first introduce a novel task, on a line, called state generation with distributed inputs (SGDI). In this task, the goal is to generate the quantum state $Uketpsi$ at the rightmost node of the line, where $ketpsi$ is a quantum state given at the leftmost node and $U$ is an unitary matrix whose description is distributed over the nodes of the line. We give a dQMA protocol for SGDI and utilize this protocol to construct a dQMA protocol for the Set Equality problem studied by Naor, Parter and Yogev [SODA 2020], and complement our protocol by showing classical lower bounds for this problem. Our second contribution is a dQMA protocol, based on a recent work by Zhu and Hayashi [Physical Review A, 2019], to create EPR-pairs between adjacent nodes of a network without quantum communication. As an application of this dQMA protocol, we prove a general result showing how to convert any dQMA protocol on an arbitrary network into another dQMA protocol where the verification stage does not require any quantum communication.},
howpublished = {Talk},
keywords = {},
pubstate = {published},
tppubtype = {Workshop}
}
The generation and verification of quantum states are fundamental tasks for quantum information processing that have recently been investigated by Irani, Natarajan, Nirkhe, Rao and Yuen [CCC 2022], Rosenthal and Yuen [ITCS 2022], Metger and Yuen [QIP 2023] under the term emphstate synthesis. This paper studies this concept from the viewpoint of quantum distributed computing, and especially distributed quantum Merlin-Arthur (dQMA) protocols. We first introduce a novel task, on a line, called state generation with distributed inputs (SGDI). In this task, the goal is to generate the quantum state $Uketpsi$ at the rightmost node of the line, where $ketpsi$ is a quantum state given at the leftmost node and $U$ is an unitary matrix whose description is distributed over the nodes of the line. We give a dQMA protocol for SGDI and utilize this protocol to construct a dQMA protocol for the Set Equality problem studied by Naor, Parter and Yogev [SODA 2020], and complement our protocol by showing classical lower bounds for this problem. Our second contribution is a dQMA protocol, based on a recent work by Zhu and Hayashi [Physical Review A, 2019], to create EPR-pairs between adjacent nodes of a network without quantum communication. As an application of this dQMA protocol, we prove a general result showing how to convert any dQMA protocol on an arbitrary network into another dQMA protocol where the verification stage does not require any quantum communication.
96.
Marco Erba, Paolo Perinotti, Davide Rolino, Alessandro Tosini
Disturbance does not imply complementarity Poster
2023.
Abstract | Links:
@Poster{P2358,
title = {Disturbance does not imply complementarity},
author = {Marco Erba and Paolo Perinotti and Davide Rolino and Alessandro Tosini},
url = {https://arxiv.org/abs/2305.16931 https://tqc-conference.org/wp-content/uploads/cfdb7_uploads/1688121953-poster-2358.pdf},
year = {2023},
date = {2023-01-01},
abstract = {Among the strangest properties of quantum mechanics there is certainly the fact that acting on a quantum system disturbs it. This phenomenon has always been at the center of an extremely active line of research, and only recently, thanks to quantum information analysis tools, we have begun to understand it more deeply. In our work we continued the characterization of this property by demonstrating that this disturbance action is logically independent from the property of complementarity, i.e. the existence of couples of observables that is impossible to measure simultaneously. To do this we have built two different toy theories, called Minimal Classical Theory and Minimal Strongly-causal Bilocal Classical Theory within the framework of operational probabilistic theories, which posses the former property, but not the latter.},
howpublished = {Poster},
keywords = {},
pubstate = {published},
tppubtype = {Poster}
}
Among the strangest properties of quantum mechanics there is certainly the fact that acting on a quantum system disturbs it. This phenomenon has always been at the center of an extremely active line of research, and only recently, thanks to quantum information analysis tools, we have begun to understand it more deeply. In our work we continued the characterization of this property by demonstrating that this disturbance action is logically independent from the property of complementarity, i.e. the existence of couples of observables that is impossible to measure simultaneously. To do this we have built two different toy theories, called Minimal Classical Theory and Minimal Strongly-causal Bilocal Classical Theory within the framework of operational probabilistic theories, which posses the former property, but not the latter.
97.
Chien-Hung Cho, Dominic W. Berry, Min-Hsiu Hsieh
Doubling the order of approximation via the randomized product formula Workshop
2023.
Abstract | Links:
@Workshop{T4057,
title = {Doubling the order of approximation via the randomized product formula},
author = {Chien-Hung Cho and Dominic W. Berry and Min-Hsiu Hsieh},
url = {https://arxiv.org/abs/2210.11281},
year = {2023},
date = {2023-01-01},
abstract = {Randomization has been applied to Hamiltonian simulation in a number of ways to improve the accuracy or efficiency of product formulas. Deterministic product formulas are often constructed in a symmetric way to provide accuracy of even order 2k. We show that by applying randomized corrections, it is possible to more than double the order to 4k + 1 (corresponding to a doubling of the order of the error). In practice, applying the corrections in a quantum algorithm requires some structure to the Hamiltonian, for example the Pauli strings as are used in the simulation of quantum chemistry.},
howpublished = {Talk},
keywords = {},
pubstate = {published},
tppubtype = {Workshop}
}
Randomization has been applied to Hamiltonian simulation in a number of ways to improve the accuracy or efficiency of product formulas. Deterministic product formulas are often constructed in a symmetric way to provide accuracy of even order 2k. We show that by applying randomized corrections, it is possible to more than double the order to 4k + 1 (corresponding to a doubling of the order of the error). In practice, applying the corrections in a quantum algorithm requires some structure to the Hamiltonian, for example the Pauli strings as are used in the simulation of quantum chemistry.
98.
Xiaogang Li, Chao Zheng, Jiancun Gao, Guilu Long
Dynamics simulation and numerical analysis of arbitrary time-dependent PT -symmetric system based on density operators Poster
2023.
@Poster{P6688,
title = {Dynamics simulation and numerical analysis of arbitrary time-dependent PT -symmetric system based on density operators},
author = {Xiaogang Li and Chao Zheng and Jiancun Gao and Guilu Long},
year = {2023},
date = {2023-01-01},
howpublished = {Poster},
keywords = {},
pubstate = {published},
tppubtype = {Poster}
}
99.
Giuseppe Catalano, Giacomo De Palma, Marco Fanizza, Vittorio Giovannetti
Efficiency Analysis of Continuous Variable Quantum Communication Lines in the Presence of Fluctuating Parameters Poster
2023.
Abstract | Links:
@Poster{P1954,
title = {Efficiency Analysis of Continuous Variable Quantum Communication Lines in the Presence of Fluctuating Parameters},
author = {Giuseppe Catalano and Giacomo De Palma and Marco Fanizza and Vittorio Giovannetti},
url = {https://arxiv.org/pdf/quant-ph/0304020.pdf https://arxiv.org/pdf/quant-ph/9912067.pdf},
year = {2023},
date = {2023-01-01},
abstract = {In the context of Quantum Communication theory, a lossy channel is a quantum channel that can describe a wide variety of scenarios that cause an attenuation of the input signal, such as the transmission in an optical fiber or free-space communication. From the mathematical point of view, a lossy channel is described as an interaction, mediated by a beam-splitter with fixed transmissivity, between the input state and the environment state, which is the vacuum state.
In some realistic situations, as the transmission of photons through the atmosphere, the noise that affects the quantum carrier cannot be described by a single lossy channel, because of the fluctuations in the loss parameter. Therefore, it is better to model these scenarios considering an ensemble of lossy channels.
The classical capacity of a quantum channel is the asymptotic rate of transmission of classical information, sent from a sender to a receiver, when the quantum system that carries the information is subject to the noise described by the quantum channel. If sender and receiver share an unlimited amount of entanglement that can be used to improve the communication, one can define the entanglement-assisted classical capacity. In this work, we studied some families of channels, that are convex combinations of two different lossy channels and, in order to describe such a convex combination, we used an ancillary qubit that selects one or the other channel. We found that, for those channels, there exist quantum states with a better communication performance with respect to the thermal state with the same energy; this is surprising because it is known that a thermal state is the best choice for a single lossy channel. However, using the methods developed in this work, it is possible to model even more general scenarios, in order to improve the quantum communication performance of more realistic noises.},
howpublished = {Poster},
keywords = {},
pubstate = {published},
tppubtype = {Poster}
}
In the context of Quantum Communication theory, a lossy channel is a quantum channel that can describe a wide variety of scenarios that cause an attenuation of the input signal, such as the transmission in an optical fiber or free-space communication. From the mathematical point of view, a lossy channel is described as an interaction, mediated by a beam-splitter with fixed transmissivity, between the input state and the environment state, which is the vacuum state.
In some realistic situations, as the transmission of photons through the atmosphere, the noise that affects the quantum carrier cannot be described by a single lossy channel, because of the fluctuations in the loss parameter. Therefore, it is better to model these scenarios considering an ensemble of lossy channels.
The classical capacity of a quantum channel is the asymptotic rate of transmission of classical information, sent from a sender to a receiver, when the quantum system that carries the information is subject to the noise described by the quantum channel. If sender and receiver share an unlimited amount of entanglement that can be used to improve the communication, one can define the entanglement-assisted classical capacity. In this work, we studied some families of channels, that are convex combinations of two different lossy channels and, in order to describe such a convex combination, we used an ancillary qubit that selects one or the other channel. We found that, for those channels, there exist quantum states with a better communication performance with respect to the thermal state with the same energy; this is surprising because it is known that a thermal state is the best choice for a single lossy channel. However, using the methods developed in this work, it is possible to model even more general scenarios, in order to improve the quantum communication performance of more realistic noises.
In some realistic situations, as the transmission of photons through the atmosphere, the noise that affects the quantum carrier cannot be described by a single lossy channel, because of the fluctuations in the loss parameter. Therefore, it is better to model these scenarios considering an ensemble of lossy channels.
The classical capacity of a quantum channel is the asymptotic rate of transmission of classical information, sent from a sender to a receiver, when the quantum system that carries the information is subject to the noise described by the quantum channel. If sender and receiver share an unlimited amount of entanglement that can be used to improve the communication, one can define the entanglement-assisted classical capacity. In this work, we studied some families of channels, that are convex combinations of two different lossy channels and, in order to describe such a convex combination, we used an ancillary qubit that selects one or the other channel. We found that, for those channels, there exist quantum states with a better communication performance with respect to the thermal state with the same energy; this is surprising because it is known that a thermal state is the best choice for a single lossy channel. However, using the methods developed in this work, it is possible to model even more general scenarios, in order to improve the quantum communication performance of more realistic noises.
100.
Yusuke Kimura, Hidetoshi Nishimori
Efficiency-guaranteed protocol of simulated quantum annealing Poster
2023.
@Poster{P7842,
title = {Efficiency-guaranteed protocol of simulated quantum annealing},
author = {Yusuke Kimura and Hidetoshi Nishimori},
year = {2023},
date = {2023-01-01},
howpublished = {Poster},
keywords = {},
pubstate = {published},
tppubtype = {Poster}
}
101.
Adam Wills, Min-Hsiu Hsieh, Sergii Strelchuk
Efficient Algorithms for All Port-Based Teleportation Protocols Talk
2024.
@Talk{T24_137,
title = {Efficient Algorithms for All Port-Based Teleportation Protocols},
author = {Adam Wills and Min-Hsiu Hsieh and Sergii Strelchuk},
year = {2024},
date = {2024-01-01},
abstract = {We resolve the long-standing open problem of implementing port-based teleportation (PBT) efficiently in all regimes: both probabilistically and deterministically, either with maximally entangled resource state or an optimised resource state. Compared to previous PBT implementations, which are restricted to the deterministic setting, we are able to demonstrate an exponential improvement in the number of ancillas required, as well as polynomial improvements in the gate complexity (albeit in separate protocols). The framework we introduce to implement PBT is flexible enough to be generalisable to other cases of the pretty good measurement, which is useful in the case that the approach via Petz recovery is inefficient.},
keywords = {},
pubstate = {published},
tppubtype = {Talk}
}
We resolve the long-standing open problem of implementing port-based teleportation (PBT) efficiently in all regimes: both probabilistically and deterministically, either with maximally entangled resource state or an optimised resource state. Compared to previous PBT implementations, which are restricted to the deterministic setting, we are able to demonstrate an exponential improvement in the number of ancillas required, as well as polynomial improvements in the gate complexity (albeit in separate protocols). The framework we introduce to implement PBT is flexible enough to be generalisable to other cases of the pretty good measurement, which is useful in the case that the approach via Petz recovery is inefficient.
102.
Masahito Hayashi, Yuxiang Yang
Efficient algorithms for quantum information bottleneck Poster
2023.
@Poster{P2657,
title = {Efficient algorithms for quantum information bottleneck},
author = {Masahito Hayashi and Yuxiang Yang},
year = {2023},
date = {2023-01-01},
howpublished = {Poster},
keywords = {},
pubstate = {published},
tppubtype = {Poster}
}
103.
Qi-Ming Ding
Efficient estimation of multipartite quantum coherence Poster
2023.
@Poster{P112,
title = {Efficient estimation of multipartite quantum coherence},
author = {Qi-Ming Ding},
year = {2023},
date = {2023-01-01},
howpublished = {Poster},
keywords = {},
pubstate = {published},
tppubtype = {Poster}
}
104.
Daniel McNulty, Filip Maciejewski, Susane Calegari, Joanna Majsak, Michał Oszmaniec
Efficient Joint Measurement Schemes for Estimating Non-Commuting Observables in Quantum Systems Poster
2023.
@Poster{P1151,
title = {Efficient Joint Measurement Schemes for Estimating Non-Commuting Observables in Quantum Systems},
author = {Daniel McNulty and Filip Maciejewski and Susane Calegari and Joanna Majsak and Michał Oszmaniec},
year = {2023},
date = {2023-01-01},
howpublished = {Poster},
keywords = {},
pubstate = {published},
tppubtype = {Poster}
}
105.
Emilio Onorati, Cambyse Rouze, Daniel Stilck Franca, James Watson
Efficient learning of ground & thermal states within phases of matter Workshop
2023.
Abstract | Links:
@Workshop{T7940,
title = {Efficient learning of ground & thermal states within phases of matter},
author = {Emilio Onorati and Cambyse Rouze and Daniel Stilck Franca and James Watson},
url = {http://arxiv.org/abs/2301.12946},
year = {2023},
date = {2023-01-01},
abstract = {We consider two related tasks: (a) estimating a parameterisation of a given Gibbs state and expectation values of Lipschitz observables on this state; and (b) learning the expectation values of local observables within a thermal or quantum phase of matter. In both cases, we wish to minimise the number of samples we use to learn these properties to a given precision.
For the first task, we develop new techniques to learn parameterisations of classes of systems, including quantum Gibbs states of non-commuting Hamiltonians with exponential decay of correlations and the approximate Markov property. We show it is possible to infer the expectation values of all extensive properties of the state from a number of copies that not only scales polylogarithmically with the system size, but polynomially in the observable's locality – an exponential improvement. This set of properties includes expected values of quasi-local observables and entropies. For the second task, we develop efficient algorithms for learning observables in a phase of matter of a quantum system. By exploiting the locality of the Hamiltonian, we show that M local observables can be learned with probability 1−δ to precision ϵ with using only N=O(log(Mδ)epolylog(ϵ−1)) samples – an exponential improvement on the precision over previous bounds. Our results apply to both families of ground states of Hamiltonians displaying local topological quantum order, and thermal phases of matter with exponential decay of correlations. In addition, our sample complexity applies to the worse case setting whereas previous results only applied on average. Furthermore, we develop tools of independent interest, such as robust shadow tomography algorithms, Gibbs approximations to ground states, and generalisations of transportation cost inequalities for Gibbs states.},
howpublished = {Talk},
keywords = {},
pubstate = {published},
tppubtype = {Workshop}
}
We consider two related tasks: (a) estimating a parameterisation of a given Gibbs state and expectation values of Lipschitz observables on this state; and (b) learning the expectation values of local observables within a thermal or quantum phase of matter. In both cases, we wish to minimise the number of samples we use to learn these properties to a given precision.
For the first task, we develop new techniques to learn parameterisations of classes of systems, including quantum Gibbs states of non-commuting Hamiltonians with exponential decay of correlations and the approximate Markov property. We show it is possible to infer the expectation values of all extensive properties of the state from a number of copies that not only scales polylogarithmically with the system size, but polynomially in the observable's locality – an exponential improvement. This set of properties includes expected values of quasi-local observables and entropies. For the second task, we develop efficient algorithms for learning observables in a phase of matter of a quantum system. By exploiting the locality of the Hamiltonian, we show that M local observables can be learned with probability 1−δ to precision ϵ with using only N=O(log(Mδ)epolylog(ϵ−1)) samples – an exponential improvement on the precision over previous bounds. Our results apply to both families of ground states of Hamiltonians displaying local topological quantum order, and thermal phases of matter with exponential decay of correlations. In addition, our sample complexity applies to the worse case setting whereas previous results only applied on average. Furthermore, we develop tools of independent interest, such as robust shadow tomography algorithms, Gibbs approximations to ground states, and generalisations of transportation cost inequalities for Gibbs states.
For the first task, we develop new techniques to learn parameterisations of classes of systems, including quantum Gibbs states of non-commuting Hamiltonians with exponential decay of correlations and the approximate Markov property. We show it is possible to infer the expectation values of all extensive properties of the state from a number of copies that not only scales polylogarithmically with the system size, but polynomially in the observable's locality – an exponential improvement. This set of properties includes expected values of quasi-local observables and entropies. For the second task, we develop efficient algorithms for learning observables in a phase of matter of a quantum system. By exploiting the locality of the Hamiltonian, we show that M local observables can be learned with probability 1−δ to precision ϵ with using only N=O(log(Mδ)epolylog(ϵ−1)) samples – an exponential improvement on the precision over previous bounds. Our results apply to both families of ground states of Hamiltonians displaying local topological quantum order, and thermal phases of matter with exponential decay of correlations. In addition, our sample complexity applies to the worse case setting whereas previous results only applied on average. Furthermore, we develop tools of independent interest, such as robust shadow tomography algorithms, Gibbs approximations to ground states, and generalisations of transportation cost inequalities for Gibbs states.
106.
Wenhao He, Tongyang Li, Xiantao Li, Zecheng Li, Chunhao Wang, Ke Wang
Efficient Optimal Control of Open Quantum Systems Talk
2024.
@Talk{T24_423,
title = {Efficient Optimal Control of Open Quantum Systems},
author = {Wenhao He and Tongyang Li and Xiantao Li and Zecheng Li and Chunhao Wang and Ke Wang},
year = {2024},
date = {2024-01-01},
abstract = {The optimal control problem for open quantum systems can be formulated as a time- dependent Lindbladian that is parameterized by a number of time-dependent control variables. Given an observable and an initial state, the goal is to tune the control variables so that the expected value of some observable with respect to the final state is maximized. In this paper, we present algorithms for solving this optimal control problem efficiently, i.e., having a poly-logarithmic dependency on the system dimension, which is exponentially faster than best-known classical algorithms. Our algorithms are hybrid, consisting of both quantum and classical components. The quantum procedure simulates time-dependent Lindblad evolution that drives the initial state to the final state, and it also provides access to the gradients of the objective function via quantum gradient estimation. The classical procedure uses the gradient information to update the control variables. At the technical level, we provide the first (to the best of our knowledge) simulation al- gorithm for time-dependent Lindbladians with an ℓ1-norm dependence. As an alternative, we also present a simulation algorithm in the interaction picture to improve the algorithm for the cases where the time-independent component of a Lindbladian dominates the time-dependent part. On the classical side, we heavily adapt the state-of-the-art classical optimization analysis to interface with the quantum part of our algorithms. Both the quantum simulation techniques and the classical optimization analyses might be of independent interest},
keywords = {},
pubstate = {published},
tppubtype = {Talk}
}
The optimal control problem for open quantum systems can be formulated as a time- dependent Lindbladian that is parameterized by a number of time-dependent control variables. Given an observable and an initial state, the goal is to tune the control variables so that the expected value of some observable with respect to the final state is maximized. In this paper, we present algorithms for solving this optimal control problem efficiently, i.e., having a poly-logarithmic dependency on the system dimension, which is exponentially faster than best-known classical algorithms. Our algorithms are hybrid, consisting of both quantum and classical components. The quantum procedure simulates time-dependent Lindblad evolution that drives the initial state to the final state, and it also provides access to the gradients of the objective function via quantum gradient estimation. The classical procedure uses the gradient information to update the control variables. At the technical level, we provide the first (to the best of our knowledge) simulation al- gorithm for time-dependent Lindbladians with an ℓ1-norm dependence. As an alternative, we also present a simulation algorithm in the interaction picture to improve the algorithm for the cases where the time-independent component of a Lindbladian dominates the time-dependent part. On the classical side, we heavily adapt the state-of-the-art classical optimization analysis to interface with the quantum part of our algorithms. Both the quantum simulation techniques and the classical optimization analyses might be of independent interest
107.
Xiantao Li, Chunhao Wang
Efficient Quantum Algorithms for Quantum Optimal Control Poster
2023.
@Poster{P3928,
title = {Efficient Quantum Algorithms for Quantum Optimal Control},
author = {Xiantao Li and Chunhao Wang},
year = {2023},
date = {2023-01-01},
howpublished = {Poster},
keywords = {},
pubstate = {published},
tppubtype = {Poster}
}
108.
Dmitry Grinko, Adam Burchardt, Maris Ozols
Efficient quantum circuits for port-based teleportation Talk
2024.
@Talk{T24_403,
title = {Efficient quantum circuits for port-based teleportation},
author = {Dmitry Grinko and Adam Burchardt and Maris Ozols},
year = {2024},
date = {2024-01-01},
abstract = {Port-based teleportation (PBT) is a variant of quantum teleportation that, unlike the canonical protocol by Bennett et al., does not require a correction operation on the teleported state. Since its introduction by Ishizaka and Hiroshima in 2008, no efficient implementation of PBT was known. We close this long-standing gap using methods from representation theory, in particular, recent results on representations of partially transposed permutation matrix algebras and mixed quantum Schur transform. We describe efficient quantum circuits for probabilistic and deterministic PBT protocols on n ports of arbitrary local dimension, both for EPR and optimized resource states. We provide two constructions based on different encodings of the so-called Gelfand-Tsetlin basis for n qudits: a standard encoding that achieves O(n) time and O(n log(n)) space complexity, and a Yamanouchi encoding that achieves O(n^2) time and O(log(n)) space complexity, both for constant local dimension and target error. We also describe efficient circuits for preparing the optimal resource states.},
keywords = {},
pubstate = {published},
tppubtype = {Talk}
}
Port-based teleportation (PBT) is a variant of quantum teleportation that, unlike the canonical protocol by Bennett et al., does not require a correction operation on the teleported state. Since its introduction by Ishizaka and Hiroshima in 2008, no efficient implementation of PBT was known. We close this long-standing gap using methods from representation theory, in particular, recent results on representations of partially transposed permutation matrix algebras and mixed quantum Schur transform. We describe efficient quantum circuits for probabilistic and deterministic PBT protocols on n ports of arbitrary local dimension, both for EPR and optimized resource states. We provide two constructions based on different encodings of the so-called Gelfand-Tsetlin basis for n qudits: a standard encoding that achieves O(n) time and O(n log(n)) space complexity, and a Yamanouchi encoding that achieves O(n^2) time and O(log(n)) space complexity, both for constant local dimension and target error. We also describe efficient circuits for preparing the optimal resource states.
109.
Dominic Berry, Nicholas Rubin, Ahmed Elnabawy, Gabriele Ahlers, Eugene DePrince, Joonho Lee, Christian Gogolin, Ryan Babbush
Efficient Quantum Simulation of Solid-State Materials via Pseudopotentials Talk
2024.
@Talk{T24_131,
title = {Efficient Quantum Simulation of Solid-State Materials via Pseudopotentials},
author = {Dominic Berry and Nicholas Rubin and Ahmed Elnabawy and Gabriele Ahlers and Eugene DePrince and Joonho Lee and Christian Gogolin and Ryan Babbush},
year = {2024},
date = {2024-01-01},
abstract = {First-quantized plane-wave representations provide a very promising approach for quantum algorithms for solid state materials. Pseudopotentials provide a method of further reducing the complexity by avoiding the need to simulate highly localized core orbitals. The complicated functional form of pseudopotentials constitutes a major challenge for the design of quantum algorithms. In this work we provide new techniques to efficiently implement pseudopotentials in quantum algorithms, with orders of magnitude improvement in complexity. Our methods include a high-accuracy QROM interpolation of the exponential function, combined with QROM for the pseudopotential parameters and coherent arithmetic. Moreover, we generalize prior methods to enable the simulation of materials defined by non-cubic unit cells. Finally, we combine these techniques to estimate the resources for block encoding required for simulating commercially relevant instances of heterogeneous catalysis.},
keywords = {},
pubstate = {published},
tppubtype = {Talk}
}
First-quantized plane-wave representations provide a very promising approach for quantum algorithms for solid state materials. Pseudopotentials provide a method of further reducing the complexity by avoiding the need to simulate highly localized core orbitals. The complicated functional form of pseudopotentials constitutes a major challenge for the design of quantum algorithms. In this work we provide new techniques to efficiently implement pseudopotentials in quantum algorithms, with orders of magnitude improvement in complexity. Our methods include a high-accuracy QROM interpolation of the exponential function, combined with QROM for the pseudopotential parameters and coherent arithmetic. Moreover, we generalize prior methods to enable the simulation of materials defined by non-cubic unit cells. Finally, we combine these techniques to estimate the resources for block encoding required for simulating commercially relevant instances of heterogeneous catalysis.
110.
Quynh Nguyen
Efficient qudit circuits for the mixed Schur transform and applications Poster
2023.
@Poster{P3587,
title = {Efficient qudit circuits for the mixed Schur transform and applications},
author = {Quynh Nguyen},
year = {2023},
date = {2023-01-01},
howpublished = {Poster},
keywords = {},
pubstate = {published},
tppubtype = {Poster}
}
111.
Nadine Meister, Christopher Pattison, John Preskill
Efficient soft-output decoders for the surface code Talk
2024.
@Talk{T24_393,
title = {Efficient soft-output decoders for the surface code},
author = {Nadine Meister and Christopher Pattison and John Preskill},
year = {2024},
date = {2024-01-01},
abstract = {Decoders that provide an estimate of the probability of a logical failure conditioned on the error syndrome ("soft-output decoders") can reduce the overhead cost of fault-tolerant quantum memory and computation. In this work we construct efficient soft-output decoders for the surface code derived from the Minimum-Weight Perfect Matching and Union-Find decoders. We show that soft-output decoding can improve the performance of a "hierarchical code," a concatenated scheme in which the inner code is the surface code, and the outer code is a high-rate quantum low-density parity-check code. Alternatively, the soft-output decoding can improve the reliability of fault-tolerant circuit sampling by flagging those runs that should be discarded because the probability of a logical error is intolerably large.},
keywords = {},
pubstate = {published},
tppubtype = {Talk}
}
Decoders that provide an estimate of the probability of a logical failure conditioned on the error syndrome ("soft-output decoders") can reduce the overhead cost of fault-tolerant quantum memory and computation. In this work we construct efficient soft-output decoders for the surface code derived from the Minimum-Weight Perfect Matching and Union-Find decoders. We show that soft-output decoding can improve the performance of a "hierarchical code," a concatenated scheme in which the inner code is the surface code, and the outer code is a high-rate quantum low-density parity-check code. Alternatively, the soft-output decoding can improve the reliability of fault-tolerant circuit sampling by flagging those runs that should be discarded because the probability of a logical error is intolerably large.
112.
Scott Aaronson, Sabee Grewal
Efficient Tomography of Non-Interacting Fermion States Conference
2023.
@Conference{T8570,
title = {Efficient Tomography of Non-Interacting Fermion States},
author = {Scott Aaronson and Sabee Grewal},
year = {2023},
date = {2023-01-01},
urldate = {2023-01-01},
abstract = {We give an efficient algorithm that learns a non-interacting fermion state, given copies of the state. For a system of $n$ non-interacting fermions and $m$ modes, we show that $O(m^3 n^2 łog(1/delta) / eps^4)$ copies of the input state and $O(m^4 n^2 łog(1/delta)/ eps^4)$ time are sufficient to learn the state to trace distance at most $eps$ with probability at least $1 - delta$. Our algorithm empirically estimates one-mode correlations in $O(m)$ different measurement bases and uses them to reconstruct a succinct description of the entire state efficiently.},
howpublished = {Talk and Proceedings},
keywords = {},
pubstate = {published},
tppubtype = {Conference}
}
We give an efficient algorithm that learns a non-interacting fermion state, given copies of the state. For a system of $n$ non-interacting fermions and $m$ modes, we show that $O(m^3 n^2 łog(1/delta) / eps^4)$ copies of the input state and $O(m^4 n^2 łog(1/delta)/ eps^4)$ time are sufficient to learn the state to trace distance at most $eps$ with probability at least $1 - delta$. Our algorithm empirically estimates one-mode correlations in $O(m)$ different measurement bases and uses them to reconstruct a succinct description of the entire state efficiently.
113.
Benoit Seron, Leonardo Novo, Alex Arkhipov, Nicolas Cerf
Efficient validation of Boson Sampling from binned photon-number distributions Poster
2023.
@Poster{P3284,
title = {Efficient validation of Boson Sampling from binned photon-number distributions},
author = {Benoit Seron and Leonardo Novo and Alex Arkhipov and Nicolas Cerf},
year = {2023},
date = {2023-01-01},
keywords = {},
pubstate = {published},
tppubtype = {Poster}
}
114.
Joseph Cunningham, Jérémie Roland
Eigenpath traversal by Poisson-distributed phase randomisation Talk
2024.
@Talk{T24_194,
title = {Eigenpath traversal by Poisson-distributed phase randomisation},
author = {Joseph Cunningham and Jérémie Roland},
year = {2024},
date = {2024-01-01},
abstract = {We present a framework for quantum computation, similar to Adiabatic Quantum Computation (AQC), that is based on the quantum Zeno effect. By performing randomised dephasing operations at intervals determined by a Poisson process, we are able to track the eigenspace associated to a particular eigenvalue. We derive a simple differential equation for the fidelity leading to general theorems bounding the time complexity of a whole class of algorithms. We also use eigenstate filtering to optimise the scaling of the complexity in the error tolerance ε. In many cases the bounds given by our general theorems are optimal, giving a time complexity of O(1/Δ) with Δ the minimum of the gap. This allows us to prove optimal results using very general features of problems, minimising the amount of problem-specific insight necessary. As two applications of our framework we obtain optimal scaling for the Grover problem (i.e. O(N^1/2) where N is the database size) and the Quantum Linear System Problem (i.e. O(κłog(1/ε)) where κ is the condition number and ε the error tolerance) by direct applications of our theorems.},
keywords = {},
pubstate = {published},
tppubtype = {Talk}
}
We present a framework for quantum computation, similar to Adiabatic Quantum Computation (AQC), that is based on the quantum Zeno effect. By performing randomised dephasing operations at intervals determined by a Poisson process, we are able to track the eigenspace associated to a particular eigenvalue. We derive a simple differential equation for the fidelity leading to general theorems bounding the time complexity of a whole class of algorithms. We also use eigenstate filtering to optimise the scaling of the complexity in the error tolerance ε. In many cases the bounds given by our general theorems are optimal, giving a time complexity of O(1/Δ) with Δ the minimum of the gap. This allows us to prove optimal results using very general features of problems, minimising the amount of problem-specific insight necessary. As two applications of our framework we obtain optimal scaling for the Grover problem (i.e. O(N^1/2) where N is the database size) and the Quantum Linear System Problem (i.e. O(κłog(1/ε)) where κ is the condition number and ε the error tolerance) by direct applications of our theorems.
115.
Stephen Piddock, Simon Apers
Elfs, trees and quantum walks Workshop
2023.
Abstract | Links:
@Workshop{T5309,
title = {Elfs, trees and quantum walks},
author = {Stephen Piddock and Simon Apers},
url = {https://arxiv.org/abs/2211.16379},
year = {2023},
date = {2023-01-01},
abstract = {We study an elementary Markov process on graphs based on electric flow sampling (elfs). The elfs process repeatedly samples from an electric flow on a graph. While the sinks of the flow are fixed, the source is updated using the electric flow sample, and the process ends when it hits a sink vertex.
We argue that this process naturally connects to many key quantities of interest. E.g., we describe a random walk coupling which implies that the elfs process has the same arrival distribution as a random walk. We also analyze the electric hitting time, which is the expected time before the process hits a sink vertex. As our main technical contribution, we show that the electric hitting time on trees is logarithmic in the graph size and weights. The initial motivation behind the elfs process is that quantum walks can sample from electric flows, and they can hence implement this process very naturally. This yields a quantum walk algorithm for sampling from the random walk arrival distribution, which has widespread applications. It complements the existing line of quantum walk search algorithms which only return an element from the sink, but yield no insight in the distribution of the returned element. By our bound on the electric hitting time on trees, the quantum walk algorithm on trees requires quadratically fewer steps than the random walk hitting time, up to polylog factors.},
howpublished = {Talk},
keywords = {},
pubstate = {published},
tppubtype = {Workshop}
}
We study an elementary Markov process on graphs based on electric flow sampling (elfs). The elfs process repeatedly samples from an electric flow on a graph. While the sinks of the flow are fixed, the source is updated using the electric flow sample, and the process ends when it hits a sink vertex.
We argue that this process naturally connects to many key quantities of interest. E.g., we describe a random walk coupling which implies that the elfs process has the same arrival distribution as a random walk. We also analyze the electric hitting time, which is the expected time before the process hits a sink vertex. As our main technical contribution, we show that the electric hitting time on trees is logarithmic in the graph size and weights. The initial motivation behind the elfs process is that quantum walks can sample from electric flows, and they can hence implement this process very naturally. This yields a quantum walk algorithm for sampling from the random walk arrival distribution, which has widespread applications. It complements the existing line of quantum walk search algorithms which only return an element from the sink, but yield no insight in the distribution of the returned element. By our bound on the electric hitting time on trees, the quantum walk algorithm on trees requires quadratically fewer steps than the random walk hitting time, up to polylog factors.
We argue that this process naturally connects to many key quantities of interest. E.g., we describe a random walk coupling which implies that the elfs process has the same arrival distribution as a random walk. We also analyze the electric hitting time, which is the expected time before the process hits a sink vertex. As our main technical contribution, we show that the electric hitting time on trees is logarithmic in the graph size and weights. The initial motivation behind the elfs process is that quantum walks can sample from electric flows, and they can hence implement this process very naturally. This yields a quantum walk algorithm for sampling from the random walk arrival distribution, which has widespread applications. It complements the existing line of quantum walk search algorithms which only return an element from the sink, but yield no insight in the distribution of the returned element. By our bound on the electric hitting time on trees, the quantum walk algorithm on trees requires quadratically fewer steps than the random walk hitting time, up to polylog factors.
116.
V. Vilasini, Renato Renner
Embedding cyclic causal structures in acyclic spacetimes: no-go results for process matrices Poster
2023.
@Poster{P3482,
title = {Embedding cyclic causal structures in acyclic spacetimes: no-go results for process matrices},
author = {V. Vilasini and Renato Renner},
year = {2023},
date = {2023-01-01},
howpublished = {Poster},
keywords = {},
pubstate = {published},
tppubtype = {Poster}
}
117.
Alexander Dalzell, B. David Clader, Grant Salton, Mario Berta, Cedric Yen-Yu Lin, David Bader, Nikitas Stamatopoulos, Martin Schuetz, Fernando Brandao, Helmut Katzgraber, William Zeng
End-to-end analysis for quantum interior point methods with improved block-encodings Poster
2023.
@Poster{P5394,
title = {End-to-end analysis for quantum interior point methods with improved block-encodings},
author = {Alexander Dalzell and B. David Clader and Grant Salton and Mario Berta and Cedric Yen-Yu Lin and David Bader and Nikitas Stamatopoulos and Martin Schuetz and Fernando Brandao and Helmut Katzgraber and William Zeng},
year = {2023},
date = {2023-01-01},
howpublished = {Poster},
keywords = {},
pubstate = {published},
tppubtype = {Poster}
}
118.
Gerard Anglès Munné, Valentin Kasper, Felix Huber
Engineering holography with stabilizer graph codes Poster
2023.
@Poster{P4664,
title = {Engineering holography with stabilizer graph codes},
author = {Gerard Anglès Munné and Valentin Kasper and Felix Huber},
year = {2023},
date = {2023-01-01},
howpublished = {Poster},
keywords = {},
pubstate = {published},
tppubtype = {Poster}
}
119.
Albert Rico, Felix Huber
Entanglement detection with trace polynomials Poster
2023.
@Poster{P746,
title = {Entanglement detection with trace polynomials},
author = {Albert Rico and Felix Huber},
year = {2023},
date = {2023-01-01},
keywords = {},
pubstate = {published},
tppubtype = {Poster}
}
120.
Som Kanjilal, Vivek Pandey, Arun Kumar Pati
Entanglement meter: estimation of entanglement with single copy in interferometer Poster
2023.
@Poster{P3798,
title = {Entanglement meter: estimation of entanglement with single copy in interferometer},
author = {Som Kanjilal and Vivek Pandey and Arun Kumar Pati},
url = {https://tqc-conference.org/wp-content/uploads/cfdb7_uploads/1688117290-poster-Estimation_of_entanglement_with_single_copy_inerferometer.pdf},
year = {2023},
date = {2023-01-01},
keywords = {},
pubstate = {published},
tppubtype = {Poster}
}
