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.
Itai Arad, Raz Firanko, Rahul Jain
An area law for the maximally-mixed ground state in arbitrarily degenerate systems with good AGSP Talk
2024.
Abstract | Tags: Intersection of quantum information and condensed-matter theory, Quantum complexity theory
@Talk{T24_417,
title = {An area law for the maximally-mixed ground state in arbitrarily degenerate systems with good AGSP},
author = {Itai Arad and Raz Firanko and Rahul Jain},
year = {2024},
date = {2024-01-01},
abstract = {We show an area law in the mutual information for the maximally-mixed state Ω in the ground space of general Hamiltonians, which is independent of the underlying ground space degeneracy. Our result assumes the existence of a `good' approximation to the ground state projector (a good AGSP), a crucial ingredient in former area-law proofs. Such approximations have been explicitly derived for 1D gapped local Hamiltonians and 2D frustration-free and locally-gapped local Hamiltonians. As a corollary, we show that in 1D gapped local Hamiltonians, for any $eps>0$ and any bi-partition $Lcup L^c$ of the system, beginalign* I^eps_max(L:L^c)_Ømega łe bigO łog (|L|) + łog(1/eps), endalign* where $|L|$ represents the number of sites in $L$ and $I^eps_max(L:L^c)_Ømega$ represents the $eps$-emphsmoothed maximum mutual information with respect to the $L:L^c$ partition in Ω. From this bound we then conclude $I(L:L^c)_Ømega łe bigOłog(|L|)$ – an area law for the mutual information in 1D systems with a logarithmic correction. In addition, we show that Ω can be approximated up to an $eps$ in trace norm with a state of Schmidt rank of at most $poly(|L|/eps)$. Similar corollaries are derived for the mutual information of 2D frustration-free locally-gapped local Hamiltonians.},
keywords = {Intersection of quantum information and condensed-matter theory, Quantum complexity theory},
pubstate = {published},
tppubtype = {Talk}
}
We show an area law in the mutual information for the maximally-mixed state Ω in the ground space of general Hamiltonians, which is independent of the underlying ground space degeneracy. Our result assumes the existence of a `good' approximation to the ground state projector (a good AGSP), a crucial ingredient in former area-law proofs. Such approximations have been explicitly derived for 1D gapped local Hamiltonians and 2D frustration-free and locally-gapped local Hamiltonians. As a corollary, we show that in 1D gapped local Hamiltonians, for any $eps>0$ and any bi-partition $Lcup L^c$ of the system, beginalign* I^eps_max(L:L^c)_Ømega łe bigO łog (|L|) + łog(1/eps), endalign* where $|L|$ represents the number of sites in $L$ and $I^eps_max(L:L^c)_Ømega$ represents the $eps$-emphsmoothed maximum mutual information with respect to the $L:L^c$ partition in Ω. From this bound we then conclude $I(L:L^c)_Ømega łe bigOłog(|L|)$ – an area law for the mutual information in 1D systems with a logarithmic correction. In addition, we show that Ω can be approximated up to an $eps$ in trace norm with a state of Schmidt rank of at most $poly(|L|/eps)$. Similar corollaries are derived for the mutual information of 2D frustration-free locally-gapped local Hamiltonians.
2.
Eunou Lee, Ojas Parekh
An improved Quantum Max Cut approximation via Maximum Matching Talk
2024.
Abstract | Tags: Intersection of quantum information and condensed-matter theory, Quantum algorithms
@Talk{T24_62,
title = {An improved Quantum Max Cut approximation via Maximum Matching},
author = {Eunou Lee and Ojas Parekh},
year = {2024},
date = {2024-01-01},
abstract = {Finding a high (or low) energy state of a given quantum Hamiltonian is a potential area to gain a provable and practical quantum advantage. A line of recent studies focuses on Quantum Max Cut, where one is asked to find a high energy state of a given antiferromagnetic Heisenberg Hamiltonian. In this work, we present a classical approximation algorithm for Quantum Max Cut that achieves an approximation ratio of 0.595, outperforming the previous best algorithms of Lee (0.562, generic input graph) and King (0.582, triangle-free input graph). The algorithm is based on finding the maximum weighted matching of an input graph and outputs a product of at most 2-qubit states, which is simpler than the fully entangled output states of the previous best algorithms},
keywords = {Intersection of quantum information and condensed-matter theory, Quantum algorithms},
pubstate = {published},
tppubtype = {Talk}
}
Finding a high (or low) energy state of a given quantum Hamiltonian is a potential area to gain a provable and practical quantum advantage. A line of recent studies focuses on Quantum Max Cut, where one is asked to find a high energy state of a given antiferromagnetic Heisenberg Hamiltonian. In this work, we present a classical approximation algorithm for Quantum Max Cut that achieves an approximation ratio of 0.595, outperforming the previous best algorithms of Lee (0.562, generic input graph) and King (0.582, triangle-free input graph). The algorithm is based on finding the maximum weighted matching of an input graph and outputs a product of at most 2-qubit states, which is simpler than the fully entangled output states of the previous best algorithms
3.
Jun Takahashi, Chaithanya Rayudu, Cunlu Zhou, Robbie King, Kevin Thompson, Ojas Parekh
An SU(2)-symmetric Semidefinite Programming Hierarchy for Quantum Max Cut Talk
2024.
Abstract | Tags: Intersection of quantum information and condensed-matter theory, Quantum complexity theory, Simulation of quantum systems
@Talk{T24_437,
title = {An SU(2)-symmetric Semidefinite Programming Hierarchy for Quantum Max Cut},
author = {Jun Takahashi and Chaithanya Rayudu and Cunlu Zhou and Robbie King and Kevin Thompson and Ojas Parekh},
year = {2024},
date = {2024-01-01},
abstract = {Understanding and approximating extremal energy states of local Hamiltonians is a central problem in quantum physics and complexity theory. Recent work has focused on developing approximation algorithms for local Hamiltonians, and in particular the ``Quantum Max Cut'' (QMaxCut) problem, which is closely related to the antiferromagnetic Heisenberg model. In this work, we introduce a family of semidefinite programming (SDP) relaxations based on the Navascues-Pironio-Acin (NPA) hierarchy which is tailored for QMaxCut by taking into account its SU(2) symmetry. We show that the hierarchy converges to the optimal QMaxCut value at a finite level, which is based on a characterization of the algebra of SWAP operators. We give several analytic proofs and computational results showing exactness/inexactness of our hierarchy at the lowest level on several important families of graphs. We also discuss relationships between SDP approaches for QMaxCut and frustration-freeness in condensed matter physics and numerically demonstrate that the SDP-solvability practically becomes an efficiently-computable generalization of frustration-freeness. Furthermore, by numerical demonstration we show the potential of SDP algorithms to perform as an approximate method to compute physical quantities and capture physical features of some Heisenberg-type statistical mechanics models even away from the frustration-free regions.},
keywords = {Intersection of quantum information and condensed-matter theory, Quantum complexity theory, Simulation of quantum systems},
pubstate = {published},
tppubtype = {Talk}
}
Understanding and approximating extremal energy states of local Hamiltonians is a central problem in quantum physics and complexity theory. Recent work has focused on developing approximation algorithms for local Hamiltonians, and in particular the ``Quantum Max Cut'' (QMaxCut) problem, which is closely related to the antiferromagnetic Heisenberg model. In this work, we introduce a family of semidefinite programming (SDP) relaxations based on the Navascues-Pironio-Acin (NPA) hierarchy which is tailored for QMaxCut by taking into account its SU(2) symmetry. We show that the hierarchy converges to the optimal QMaxCut value at a finite level, which is based on a characterization of the algebra of SWAP operators. We give several analytic proofs and computational results showing exactness/inexactness of our hierarchy at the lowest level on several important families of graphs. We also discuss relationships between SDP approaches for QMaxCut and frustration-freeness in condensed matter physics and numerically demonstrate that the SDP-solvability practically becomes an efficiently-computable generalization of frustration-freeness. Furthermore, by numerical demonstration we show the potential of SDP algorithms to perform as an approximate method to compute physical quantities and capture physical features of some Heisenberg-type statistical mechanics models even away from the frustration-free regions.
4.
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.
5.
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.
6.
Andreas Bauer
Fault-tolerant circuits from twisted quantum doubles – Quantum error correction beyond stabilizer and Clifford Talk
2024.
Abstract | Tags: Intersection of quantum information and condensed-matter theory, Quantum error correction and fault-tolerant quantum computing
@Talk{T24_407,
title = {Fault-tolerant circuits from twisted quantum doubles – Quantum error correction beyond stabilizer and Clifford},
author = {Andreas Bauer},
year = {2024},
date = {2024-01-01},
abstract = {We propose a family of explicit fault-tolerant geometrically local circuits realizing any abelian non-chiral topological phase. These circuits are constructed by relating them to discrete fixed-point path integrals, specifically the abelian Dijkgraaf-Witten state sum on a 3-dimensional cellulation, which is a spacetime representation of the twisted quantum double model. The resulting circuits are based on the well-known syndrome extraction circuit of the (qudit) toric code with $8$ controlled-$X$ gates per spacetime unit cell, into which we insert non-Pauli phase gates that implement the ``twist''. The overhead compared to the toric code is moderate, in contrast to the few known constructions for twisted abelian phases. The simplest example is a fault-tolerant circuit for the double-semion phase, which consists of $12$ controlled-$S$ gates in addition to the $8$ controlled-$X$ gates per spacetime unit cell. We also show that other architectures for the qudit toric code phase, like measurement-based topological quantum computation, or Floquet codes, can be equipped with phase gates implementing the twist. As a further result, we prove fault tolerance for a very general class of topological circuits that we call 1-form symmetric fixed-point circuits, which includes the circuits in this paper as well as the standard toric code, subsystem toric codes, measurement-based topological quantum computation, or the (CSS) honeycomb Floquet code. The noise model we use includes arbitrary local noise, including weakly correlated noise and non-Pauli noise, for which explicit fault-tolerance proofs might not exist in the literature to date. In the appendix we present a simple combinatorial procedure to define formulas for higher cup products on arbitrary cellulation, which might be interesting in its own right for the study of twisted gauge theory.},
keywords = {Intersection of quantum information and condensed-matter theory, Quantum error correction and fault-tolerant quantum computing},
pubstate = {published},
tppubtype = {Talk}
}
We propose a family of explicit fault-tolerant geometrically local circuits realizing any abelian non-chiral topological phase. These circuits are constructed by relating them to discrete fixed-point path integrals, specifically the abelian Dijkgraaf-Witten state sum on a 3-dimensional cellulation, which is a spacetime representation of the twisted quantum double model. The resulting circuits are based on the well-known syndrome extraction circuit of the (qudit) toric code with $8$ controlled-$X$ gates per spacetime unit cell, into which we insert non-Pauli phase gates that implement the ``twist''. The overhead compared to the toric code is moderate, in contrast to the few known constructions for twisted abelian phases. The simplest example is a fault-tolerant circuit for the double-semion phase, which consists of $12$ controlled-$S$ gates in addition to the $8$ controlled-$X$ gates per spacetime unit cell. We also show that other architectures for the qudit toric code phase, like measurement-based topological quantum computation, or Floquet codes, can be equipped with phase gates implementing the twist. As a further result, we prove fault tolerance for a very general class of topological circuits that we call 1-form symmetric fixed-point circuits, which includes the circuits in this paper as well as the standard toric code, subsystem toric codes, measurement-based topological quantum computation, or the (CSS) honeycomb Floquet code. The noise model we use includes arbitrary local noise, including weakly correlated noise and non-Pauli noise, for which explicit fault-tolerance proofs might not exist in the literature to date. In the appendix we present a simple combinatorial procedure to define formulas for higher cup products on arbitrary cellulation, which might be interesting in its own right for the study of twisted gauge theory.
7.
Shivan Mittal, Nicholas Hunter-Jones
Local random quantum circuits form approximate designs on arbitrary architectures Talk
2024.
Abstract | Tags: Intersection of quantum information and condensed-matter theory, Models of quantum computation, Quantum information theory
@Talk{T24_309,
title = {Local random quantum circuits form approximate designs on arbitrary architectures},
author = {Shivan Mittal and Nicholas Hunter-Jones},
year = {2024},
date = {2024-01-01},
abstract = {We consider random quantum circuits (RQC) on arbitrary connected graphs whose edges determine the allowed 2-qudit interactions. Prior work has established that such $n$-qudit circuits with local dimension $q$ on 1D, complete, and $D$-dimensional graphs form approximate unitary designs, that is, they generate unitaries from distributions close to the Haar measure on the unitary group $U(q^n)$ after polynomially many gates. Here, we extend those results by proving that RQCs comprised of $O(poly(n,k))$ gates on a wide class of graphs form approximate unitary $k$-designs. We prove that RQCs on graphs with spanning trees of bounded degree and height form $k$-designs after $O(|E|n rm poly(k))$ gates, where $|E|$ is the number of edges in the graph. Furthermore, we identify larger classes of graphs for which RQCs generate approximate designs in polynomial circuit size. For $k łeq 4$, we show that RQCs on graphs of certain maximum degrees form designs after $O(|E|n)$ gates, providing explicit constants. We determine our circuit size bounds from the spectral gaps of local Hamiltonians. To that end, we extend the finite-size (or Knabe) method for bounding gaps of frustration-free Hamiltonians on regular graphs to arbitrary connected graphs. We further introduce a new method based on the Detectability Lemma for determining the spectral gaps of Hamiltonians on arbitrary graphs. Our methods have wider applicability as the first method provides a succinct alternative proof of [Commun. Math. Phys. 291, 257 (2009)] and the second method proves that RQCs on any connected architecture form approximate designs in quasi-polynomial circuit size.},
keywords = {Intersection of quantum information and condensed-matter theory, Models of quantum computation, Quantum information theory},
pubstate = {published},
tppubtype = {Talk}
}
We consider random quantum circuits (RQC) on arbitrary connected graphs whose edges determine the allowed 2-qudit interactions. Prior work has established that such $n$-qudit circuits with local dimension $q$ on 1D, complete, and $D$-dimensional graphs form approximate unitary designs, that is, they generate unitaries from distributions close to the Haar measure on the unitary group $U(q^n)$ after polynomially many gates. Here, we extend those results by proving that RQCs comprised of $O(poly(n,k))$ gates on a wide class of graphs form approximate unitary $k$-designs. We prove that RQCs on graphs with spanning trees of bounded degree and height form $k$-designs after $O(|E|n rm poly(k))$ gates, where $|E|$ is the number of edges in the graph. Furthermore, we identify larger classes of graphs for which RQCs generate approximate designs in polynomial circuit size. For $k łeq 4$, we show that RQCs on graphs of certain maximum degrees form designs after $O(|E|n)$ gates, providing explicit constants. We determine our circuit size bounds from the spectral gaps of local Hamiltonians. To that end, we extend the finite-size (or Knabe) method for bounding gaps of frustration-free Hamiltonians on regular graphs to arbitrary connected graphs. We further introduce a new method based on the Detectability Lemma for determining the spectral gaps of Hamiltonians on arbitrary graphs. Our methods have wider applicability as the first method provides a succinct alternative proof of [Commun. Math. Phys. 291, 257 (2009)] and the second method proves that RQCs on any connected architecture form approximate designs in quasi-polynomial circuit size.
8.
Daniel Malz, Georgios Styliaris, Zhi-Yuan Wei, J. Ignacio Cirac
Preparation of Matrix Product States with Log-Depth Quantum Circuits Talk
2024.
Abstract | Tags: Intersection of quantum information and condensed-matter theory, Quantum algorithms, Quantum information theory
@Talk{T24_79,
title = {Preparation of Matrix Product States with Log-Depth Quantum Circuits},
author = {Daniel Malz and Georgios Styliaris and Zhi-Yuan Wei and J. Ignacio Cirac},
year = {2024},
date = {2024-01-01},
abstract = {We consider the preparation of matrix product states (MPS) on quantum devices via quantum circuits of local gates. We first prove that faithfully preparing translation-invariant normal MPS of $N$ sites requires a circuit depth $T=Ømega(łog N)$. We then introduce an algorithm based on the renormalization-group transformation to prepare normal MPS with an error ε in depth $T=O(łog (N/epsilon))$, which is optimal. We also show that measurement and feedback leads to an exponential speedup of the algorithm, to $T=O(łogłog (N/epsilon))$. Measurements also allow one to prepare arbitrary translation-invariant MPS, including long-range non-normal ones, in the same depth. Finally, the algorithm naturally extends to inhomogeneous MPS.},
keywords = {Intersection of quantum information and condensed-matter theory, Quantum algorithms, Quantum information theory},
pubstate = {published},
tppubtype = {Talk}
}
We consider the preparation of matrix product states (MPS) on quantum devices via quantum circuits of local gates. We first prove that faithfully preparing translation-invariant normal MPS of $N$ sites requires a circuit depth $T=Ømega(łog N)$. We then introduce an algorithm based on the renormalization-group transformation to prepare normal MPS with an error ε in depth $T=O(łog (N/epsilon))$, which is optimal. We also show that measurement and feedback leads to an exponential speedup of the algorithm, to $T=O(łogłog (N/epsilon))$. Measurements also allow one to prepare arbitrary translation-invariant MPS, including long-range non-normal ones, in the same depth. Finally, the algorithm naturally extends to inhomogeneous MPS.
