The Programme Committee of TQC 2024 selected 92 out of 460 submissions for a contributed talk (20% acceptance rate).
You may find the contributed talks here.
The list of accepted posters will be published on the 2nd of May, after the poster notification date. The conference schedule will be published in July.
Note on the list: The talks are listed in alphabetical order of title. Later they will be listed by day of presentation. The topic tags were self-selected by the authors upon submission, given the options provided by the PC chairs.
1.
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.
Abstract | Tags: Intersection of quantum information and condensed-matter theory, Quantum estimation and measurement, Quantum information theory
@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 = {Intersection of quantum information and condensed-matter theory, Quantum estimation and measurement, Quantum information theory},
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.
2.
Tim Möbus, Andreas Bluhm, Matthias C. Caro, Albert H. Werner, Cambyse Rouzé
Dissipation-enabled bosonic Hamiltonian learning via new information-propagation bounds Talk
2024.
Abstract | Tags: Intersection of quantum information and condensed-matter theory, Quantum estimation and measurement
@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 = {Intersection of quantum information and condensed-matter theory, Quantum estimation and measurement},
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.
3.
Dmitry Grinko, Adam Burchardt, Maris Ozols
Efficient quantum circuits for port-based teleportation Talk
2024.
Abstract | Tags: Other, Quantum algorithms, Quantum communication, Quantum estimation and measurement, Quantum information theory
@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 = {Other, Quantum algorithms, Quantum communication, Quantum estimation and measurement, Quantum information theory},
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.
4.
Robbie King, Kianna Wan, Jarrod McClean
Exponential learning advantages with conjugate states and minimal quantum memory Talk
2024.
Abstract | Tags: Intersection of quantum information and machine learning, Quantum algorithms, Quantum estimation and measurement
@Talk{T24_274,
title = {Exponential learning advantages with conjugate states and minimal quantum memory},
author = {Robbie King and Kianna Wan and Jarrod McClean},
year = {2024},
date = {2024-01-01},
abstract = {The ability of quantum computers to directly manipulate and analyze quantum states stored in quantum memory allows them to learn about aspects of our physical world that would otherwise be invisible given a modest number of measurements. Here we investigate a new learning resource which could be available to quantum computers in the future – measurements on the unknown state accompanied by its complex conjugate ρ⊗ρ*. For a certain shadow tomography task, we surprisingly find that measurements on only copies of ρ⊗ρ* can be exponentially more powerful than measurements on ρ⊗K, even for large K. This expands the class of exponential advantages using only a constant overhead quantum memory, or minimal quantum memory, and we provide a number of examples where the state ρ* is naturally available in both computational and physical applications. In addition, we precisely quantify the power of classical shadows on single copies under a generalized Clifford ensemble and give a class of quantities that can be efficiently learned. The learning task we study in both the single copy and quantum memory is physically natural and corresponds to real-space observables with a limit of bosonic modes, where it achieves an exponential improvement in detecting certain signals under a noisy background. In addition to quantifying a fundamentally new and powerful resource in quantum learning, we believe the advantage may find applications in improving quantum simulation, learning from quantum sensors, and uncovering new physical phenomena.},
keywords = {Intersection of quantum information and machine learning, Quantum algorithms, Quantum estimation and measurement},
pubstate = {published},
tppubtype = {Talk}
}
The ability of quantum computers to directly manipulate and analyze quantum states stored in quantum memory allows them to learn about aspects of our physical world that would otherwise be invisible given a modest number of measurements. Here we investigate a new learning resource which could be available to quantum computers in the future – measurements on the unknown state accompanied by its complex conjugate ρ⊗ρ*. For a certain shadow tomography task, we surprisingly find that measurements on only copies of ρ⊗ρ* can be exponentially more powerful than measurements on ρ⊗K, even for large K. This expands the class of exponential advantages using only a constant overhead quantum memory, or minimal quantum memory, and we provide a number of examples where the state ρ* is naturally available in both computational and physical applications. In addition, we precisely quantify the power of classical shadows on single copies under a generalized Clifford ensemble and give a class of quantities that can be efficiently learned. The learning task we study in both the single copy and quantum memory is physically natural and corresponds to real-space observables with a limit of bosonic modes, where it achieves an exponential improvement in detecting certain signals under a noisy background. In addition to quantifying a fundamentally new and powerful resource in quantum learning, we believe the advantage may find applications in improving quantum simulation, learning from quantum sensors, and uncovering new physical phenomena.
5.
Andreas Bluhm, Matthias C. Caro, Aadil Oufkir
Hamiltonian Property Testing Talk
2024.
Abstract | Tags: Intersection of quantum information and machine learning, Quantum estimation and measurement
@Talk{T24_182,
title = {Hamiltonian Property Testing},
author = {Andreas Bluhm and Matthias C. Caro and Aadil Oufkir},
year = {2024},
date = {2024-01-01},
abstract = {Locality is a fundamental feature of many physical time evolutions. Assumptions on locality and related structural properties also underlie recently proposed procedures for learning an unknown Hamiltonian from access to the induced time evolution. However, no protocols to rigorously test whether an unknown Hamiltonian is in fact local were known. We investigate Hamiltonian locality testing as a property testing problem, where the task is to determine whether an unknown Hamiltonian $H$ is $k$-local or ε-far from all $k$-local Hamiltonians, given access to the time evolution along $H$. First, we emphasize the importance of the chosen distance measure: With respect to the operator norm, a worst-case distance measure, incoherent quantum locality testers require $TildeØmega(2^n)$ many time evolution queries and an expected total evolution time of $TildeØmega(2^n/ε)$, and even coherent testers need $Ømega(2^n/2)$ many queries and $Ømega(2^n/2/ε)$ total evolution time. In contrast, when distances are measured according to the normalized Frobenius norm, corresponding to an average-case distance, we give a sample-, time-, and computationally efficient incoherent Hamiltonian locality testing algorithm based on randomized measurements. In fact, our procedure can be used to simultaneously test a wide class of Hamiltonian properties beyond locality. Finally, we prove that learning a general Hamiltonian remains exponentially hard with this average-case distance, thereby establishing an exponential separation between Hamiltonian testing and learning. Our work initiates the study of property testing for quantum Hamiltonians, demonstrating that a broad class of Hamiltonian properties is efficiently testable even with limited quantum capabilities, and positioning Hamiltonian testing as an independent area of research alongside Hamiltonian learning.},
keywords = {Intersection of quantum information and machine learning, Quantum estimation and measurement},
pubstate = {published},
tppubtype = {Talk}
}
Locality is a fundamental feature of many physical time evolutions. Assumptions on locality and related structural properties also underlie recently proposed procedures for learning an unknown Hamiltonian from access to the induced time evolution. However, no protocols to rigorously test whether an unknown Hamiltonian is in fact local were known. We investigate Hamiltonian locality testing as a property testing problem, where the task is to determine whether an unknown Hamiltonian $H$ is $k$-local or ε-far from all $k$-local Hamiltonians, given access to the time evolution along $H$. First, we emphasize the importance of the chosen distance measure: With respect to the operator norm, a worst-case distance measure, incoherent quantum locality testers require $TildeØmega(2^n)$ many time evolution queries and an expected total evolution time of $TildeØmega(2^n/ε)$, and even coherent testers need $Ømega(2^n/2)$ many queries and $Ømega(2^n/2/ε)$ total evolution time. In contrast, when distances are measured according to the normalized Frobenius norm, corresponding to an average-case distance, we give a sample-, time-, and computationally efficient incoherent Hamiltonian locality testing algorithm based on randomized measurements. In fact, our procedure can be used to simultaneously test a wide class of Hamiltonian properties beyond locality. Finally, we prove that learning a general Hamiltonian remains exponentially hard with this average-case distance, thereby establishing an exponential separation between Hamiltonian testing and learning. Our work initiates the study of property testing for quantum Hamiltonians, demonstrating that a broad class of Hamiltonian properties is efficiently testable even with limited quantum capabilities, and positioning Hamiltonian testing as an independent area of research alongside Hamiltonian learning.
6.
Sisi Zhou
Limits of noisy quantum metrology with restricted quantum controls Talk
2024.
Abstract | Tags: Quantum estimation and measurement, Quantum information theory
@Talk{T24_81,
title = {Limits of noisy quantum metrology with restricted quantum controls},
author = {Sisi Zhou},
year = {2024},
date = {2024-01-01},
abstract = {The Heisenberg limit (HL) and the standard quantum limit (SQL) are two quantum metrological limits, which describe the scalings of estimation precision $Delta hatþeta$ of an unknown parameter θ with respect to $n$, the number of one-parameter quantum channels applied. It was known that the HL ($Delta hatþeta propto 1/n$) is achievable using quantum error correction (QEC) strategies when the ``Hamiltonian-not-in-Kraus-span'' (HNKS) condition is satisfied; and when HNKS is violated, the SQL ($Delta hatþeta propto 1/n^1/2$) is optimal and can be achieved with $n$ repetitive measurements. However, it is unknown whether such limits are still achievable using restricted quantum devices where the required QEC operations are not available—e.g., finite-size devices where only unitary controls are available or where noiseless ancilla is not available. In this work, we identify various new noisy metrological limits for estimating one-parameter qubit channels in different settings with restricted controls. The HL is proven to be unattainbale in these cases, indicating the necessity of QEC in achieving the HL. Furthermore, we find a necessary and sufficient condition for qubit channels to attain the SQL, called the ``rotation-generators-not-in-Kraus-span'' (RGNKS) condition. When RGNKS is satisfied, the SQL is achievable using only unitary controls and a single measurement. When RGNKS is violated, the estimation precision (in most cases) has a constant floor when repetitive measurements are not allowed. Demonstration of this separation in metrological powers is within reach of current quantum technologies.},
keywords = {Quantum estimation and measurement, Quantum information theory},
pubstate = {published},
tppubtype = {Talk}
}
The Heisenberg limit (HL) and the standard quantum limit (SQL) are two quantum metrological limits, which describe the scalings of estimation precision $Delta hatþeta$ of an unknown parameter θ with respect to $n$, the number of one-parameter quantum channels applied. It was known that the HL ($Delta hatþeta propto 1/n$) is achievable using quantum error correction (QEC) strategies when the ``Hamiltonian-not-in-Kraus-span'' (HNKS) condition is satisfied; and when HNKS is violated, the SQL ($Delta hatþeta propto 1/n^1/2$) is optimal and can be achieved with $n$ repetitive measurements. However, it is unknown whether such limits are still achievable using restricted quantum devices where the required QEC operations are not available—e.g., finite-size devices where only unitary controls are available or where noiseless ancilla is not available. In this work, we identify various new noisy metrological limits for estimating one-parameter qubit channels in different settings with restricted controls. The HL is proven to be unattainbale in these cases, indicating the necessity of QEC in achieving the HL. Furthermore, we find a necessary and sufficient condition for qubit channels to attain the SQL, called the ``rotation-generators-not-in-Kraus-span'' (RGNKS) condition. When RGNKS is satisfied, the SQL is achievable using only unitary controls and a single measurement. When RGNKS is violated, the estimation precision (in most cases) has a constant floor when repetitive measurements are not allowed. Demonstration of this separation in metrological powers is within reach of current quantum technologies.
7.
Harry Buhrman, Dmitry Grinko, Philip Verduyn Lunel, Jordi Weggemans
Permutation tests for quantum state identity Talk
2024.
Abstract | Tags: Other, Quantum estimation and measurement, Quantum information theory
@Talk{T24_400,
title = {Permutation tests for quantum state identity},
author = {Harry Buhrman and Dmitry Grinko and Philip Verduyn Lunel and Jordi Weggemans},
year = {2024},
date = {2024-01-01},
abstract = {The quantum analogue of the equality function, known as the quantum state identity problem, is the task of deciding whether n unknown quantum states are equal or unequal, given the promise that all states are either pairwise orthogonal or identical. Under the one-sided error requirement, it is known that the permutation test is optimal for this task, and for two input states this coincides with the well-known Swap test. Until now, the optimal measurement in the general two-sided error regime was unknown. Under more specific promises, the problem can be solved approximately or even optimally with simpler tests, such as the circle test. This work attempts to capture the underlying structure of (fine-grained formulations of) the quantum state identity problem. Using tools from semi-definite programming and representation theory, we (i) give an optimal test for any input distribution without the one-sided error requirement by writing the problem as an SDP, giving the exact solutions to the primal and dual programs and showing that the two values coincide; (ii) propose a general G-test which uses an arbitrary subgroup G of S_n, giving an analytic expression of the performance of the specific test, and (iii) give an approximation of the permutation test using only a classical permutation and n-1 Swap tests.},
keywords = {Other, Quantum estimation and measurement, Quantum information theory},
pubstate = {published},
tppubtype = {Talk}
}
The quantum analogue of the equality function, known as the quantum state identity problem, is the task of deciding whether n unknown quantum states are equal or unequal, given the promise that all states are either pairwise orthogonal or identical. Under the one-sided error requirement, it is known that the permutation test is optimal for this task, and for two input states this coincides with the well-known Swap test. Until now, the optimal measurement in the general two-sided error regime was unknown. Under more specific promises, the problem can be solved approximately or even optimally with simpler tests, such as the circle test. This work attempts to capture the underlying structure of (fine-grained formulations of) the quantum state identity problem. Using tools from semi-definite programming and representation theory, we (i) give an optimal test for any input distribution without the one-sided error requirement by writing the problem as an SDP, giving the exact solutions to the primal and dual programs and showing that the two values coincide; (ii) propose a general G-test which uses an arbitrary subgroup G of S_n, giving an analytic expression of the performance of the specific test, and (iii) give an approximation of the permutation test using only a classical permutation and n-1 Swap tests.
8.
Tobias Haug, Kishor Bharti, Dax Koh
Pseudorandom unitaries are neither real nor sparse nor noise-robust Talk
2024.
Abstract | Tags: Quantum complexity theory, Quantum cryptography, Quantum estimation and measurement, Quantum information theory
@Talk{T24_71,
title = {Pseudorandom unitaries are neither real nor sparse nor noise-robust},
author = {Tobias Haug and Kishor Bharti and Dax Koh},
year = {2024},
date = {2024-01-01},
abstract = {Pseudorandom quantum states (PRSs) and pseudorandom unitaries (PRUs) possess the dual nature of being efficiently constructible while appearing completely random to any efficient quantum algorithm. In this study, we establish fundamental bounds on pseudorandomness. We show that PRSs and PRUs exist only when the probability that an error occurs is negligible, ruling out their generation on noisy intermediate-scale and early fault-tolerant quantum computers. Additionally, we derive lower bounds on the imaginarity and coherence of PRSs and PRUs, rule out the existence of sparse or real PRUs. We also show that the notions of PRS, PRUs and pseudorandom scramblers (PRSSs) are distinct in terms of resource requirements. We introduce the concept of pseudoresources, where states which contain a low amount of a given resource masquerade as high-resource states. We define pseudocoherence, pseudopurity and pseudoimaginarity, and identify three distinct types of pseudoresources in terms of their masquerading capabilities. Our work also establishes rigorous bounds on the efficiency of property testing, demonstrating the exponential complexity in distinguishing real quantum states from imaginary ones, in contrast to the efficient measurability of unitary imaginarity. Lastly, we show that the transformation from a complex to a real model of quantum computation is inefficient, in contrast to the reverse process, which is efficient. Our results establish fundamental limits on property testing and provide valuable insights into quantum pseudorandomness.},
keywords = {Quantum complexity theory, Quantum cryptography, Quantum estimation and measurement, Quantum information theory},
pubstate = {published},
tppubtype = {Talk}
}
Pseudorandom quantum states (PRSs) and pseudorandom unitaries (PRUs) possess the dual nature of being efficiently constructible while appearing completely random to any efficient quantum algorithm. In this study, we establish fundamental bounds on pseudorandomness. We show that PRSs and PRUs exist only when the probability that an error occurs is negligible, ruling out their generation on noisy intermediate-scale and early fault-tolerant quantum computers. Additionally, we derive lower bounds on the imaginarity and coherence of PRSs and PRUs, rule out the existence of sparse or real PRUs. We also show that the notions of PRS, PRUs and pseudorandom scramblers (PRSSs) are distinct in terms of resource requirements. We introduce the concept of pseudoresources, where states which contain a low amount of a given resource masquerade as high-resource states. We define pseudocoherence, pseudopurity and pseudoimaginarity, and identify three distinct types of pseudoresources in terms of their masquerading capabilities. Our work also establishes rigorous bounds on the efficiency of property testing, demonstrating the exponential complexity in distinguishing real quantum states from imaginary ones, in contrast to the efficient measurability of unitary imaginarity. Lastly, we show that the transformation from a complex to a real model of quantum computation is inefficient, in contrast to the reverse process, which is efficient. Our results establish fundamental limits on property testing and provide valuable insights into quantum pseudorandomness.
9.
Alexander Volberg, Haonan Zhang, Ohad Klein, Joseph Slote
Quantum Bohnenblust–Hille inequalities and applications to learning low-degree quantum observables Talk
2024.
Abstract | Tags: Intersection of quantum information and machine learning, Quantum algorithms, Quantum estimation and measurement
@Talk{T24_425,
title = {Quantum Bohnenblust–Hille inequalities and applications to learning low-degree quantum observables},
author = {Alexander Volberg and Haonan Zhang and Ohad Klein and Joseph Slote},
year = {2024},
date = {2024-01-01},
abstract = {Analysis on the Boolean hypercube −1,1^n, particularly Fourier analysis, has played a crucial role in many areas of mathematics and computer science, including learning algorithms. In view of the success and importance of quantum algorithms, it is natural to transfer classical learning results to the quantum realm. In this contribution, we extend the recent progress on learning low-degree functions and quantum operators to the setting of general qudit systems, as well as develop novel Fourier-analytic tools for studying (generalized) Pauli decompositions of Hermitian operators. These tools also allow us to deduce new results in quantum Boolean analysis and approximate theory, such as the junta-type theorem and dimension-free discrete Remez-type inequalities.},
keywords = {Intersection of quantum information and machine learning, Quantum algorithms, Quantum estimation and measurement},
pubstate = {published},
tppubtype = {Talk}
}
Analysis on the Boolean hypercube −1,1^n, particularly Fourier analysis, has played a crucial role in many areas of mathematics and computer science, including learning algorithms. In view of the success and importance of quantum algorithms, it is natural to transfer classical learning results to the quantum realm. In this contribution, we extend the recent progress on learning low-degree functions and quantum operators to the setting of general qudit systems, as well as develop novel Fourier-analytic tools for studying (generalized) Pauli decompositions of Hermitian operators. These tools also allow us to deduce new results in quantum Boolean analysis and approximate theory, such as the junta-type theorem and dimension-free discrete Remez-type inequalities.
10.
Connor Clayton, Yulong Dong, Murphy Yuezhen Niu, Shi Jie Samuel Tan
Signal-Processing Phase Estimation against Time-dependent Errors Talk
2024.
Abstract | Tags: Quantum estimation and measurement
@Talk{T24_444,
title = {Signal-Processing Phase Estimation against Time-dependent Errors},
author = {Connor Clayton and Yulong Dong and Murphy Yuezhen Niu and Shi Jie Samuel Tan},
year = {2024},
date = {2024-01-01},
abstract = {Harnessing quantum effects in metrology, such as entanglement and coherence, enables enhanced sensitivity in measuring parameters. Despite this, decoherence and time-dependent errors can uNdermine Heisenberg-limited amplification. To navigate these challenges in realistic experiments for phase estimation of a two-level unitary gate, we introduce a suite of quantum metrology algorithms. These algorithms capitalize on the universality of quantum signal transformation to decouple two interdependent phase parameters into largely orthogonal ones, ensuring that time-dependent errors in one do not compromise the accuracy of learning the other. Our approach combines provably optimal classical estimation with nearly optimal quantum circuit design, achieving unparalleled accuracy of 10−4 radians in standard deviation for estimating extremely small angles in superconducting qubit experiments with low-depth (< 10) circuits. This accuracy surpasses existing alternatives by two orders of magnitude and is adaptable to ion trap gates. We prove both theoretically and numerically the optimality of our algorithm against time-dependent phase error in φ. Remarkably, in the low circuit depth limit, our method’s estimation variance on the time-sensitive parameter φ scales faster than the asymptotic Heisenberg limit as a function of depth, Var(φˆ) ∼ 1/d4. Crucially, our method’s efficacy is rigorously affirmed through an analysis against the quantum Fisher information. This analysis underpins our protocol’s ability to achieve unmatched precision, leveraging quantum resources more effectively than has been possible before.},
keywords = {Quantum estimation and measurement},
pubstate = {published},
tppubtype = {Talk}
}
Harnessing quantum effects in metrology, such as entanglement and coherence, enables enhanced sensitivity in measuring parameters. Despite this, decoherence and time-dependent errors can uNdermine Heisenberg-limited amplification. To navigate these challenges in realistic experiments for phase estimation of a two-level unitary gate, we introduce a suite of quantum metrology algorithms. These algorithms capitalize on the universality of quantum signal transformation to decouple two interdependent phase parameters into largely orthogonal ones, ensuring that time-dependent errors in one do not compromise the accuracy of learning the other. Our approach combines provably optimal classical estimation with nearly optimal quantum circuit design, achieving unparalleled accuracy of 10−4 radians in standard deviation for estimating extremely small angles in superconducting qubit experiments with low-depth (< 10) circuits. This accuracy surpasses existing alternatives by two orders of magnitude and is adaptable to ion trap gates. We prove both theoretically and numerically the optimality of our algorithm against time-dependent phase error in φ. Remarkably, in the low circuit depth limit, our method’s estimation variance on the time-sensitive parameter φ scales faster than the asymptotic Heisenberg limit as a function of depth, Var(φˆ) ∼ 1/d4. Crucially, our method’s efficacy is rigorously affirmed through an analysis against the quantum Fisher information. This analysis underpins our protocol’s ability to achieve unmatched precision, leveraging quantum resources more effectively than has been possible before.
