Pub Date : 2026-01-22DOI: 10.22331/q-2026-01-22-1981
Joel Rajakumar, James D. Watson
Sampling from Gibbs states – states corresponding to system in thermal equilibrium – has recently been shown to be a task for which quantum computers are expected to achieve super-polynomial speed-up compared to classical computers, provided the locality of the Hamiltonian increases with the system size [1]. We extend these results to show that this quantum advantage still occurs for Gibbs states of Hamiltonians with O(1)-local interactions at constant temperature by showing classical hardness-of-sampling and demonstrating such Gibbs states can be prepared efficiently using a quantum computer. In particular, we show hardness-of-sampling is maintained even for 5-local Hamiltonians on a 3D lattice. We additionally show that the hardness-of-sampling is robust when we are only able to make imperfect measurements.
{"title":"Gibbs Sampling gives Quantum Advantage at Constant Temperatures with O(1)-Local Hamiltonians","authors":"Joel Rajakumar, James D. Watson","doi":"10.22331/q-2026-01-22-1981","DOIUrl":"https://doi.org/10.22331/q-2026-01-22-1981","url":null,"abstract":"Sampling from Gibbs states – states corresponding to system in thermal equilibrium – has recently been shown to be a task for which quantum computers are expected to achieve super-polynomial speed-up compared to classical computers, provided the locality of the Hamiltonian increases with the system size [1]. We extend these results to show that this quantum advantage still occurs for Gibbs states of Hamiltonians with O(1)-local interactions at constant temperature by showing classical hardness-of-sampling and demonstrating such Gibbs states can be prepared efficiently using a quantum computer. In particular, we show hardness-of-sampling is maintained even for 5-local Hamiltonians on a 3D lattice. We additionally show that the hardness-of-sampling is robust when we are only able to make imperfect measurements.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"36 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146021925","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-22DOI: 10.22331/q-2026-01-22-1984
Felix Burt, Kuan-Cheng Chen, Kin K. Leung
Executing quantum algorithms over distributed quantum systems requires quantum circuits to be divided into sub-circuits which communicate via entanglement-based teleportation. Naively mapping circuits to qubits over multiple quantum processing units (QPUs) results in large communication overhead, increasing both execution time and noise. This can be minimised by optimising the assignment of qubits to QPUs and the methods used for covering non-local operations. Formulations that are general enough to capture the spectrum of teleportation possibilities lead to complex problem instances which can be difficult to solve effectively. This highlights a need to exploit the wide range of heuristic techniques used in the graph partitioning literature. This paper formalises and extends existing constructions for graphical quantum circuit partitioning and designs a new objective function that captures further possibilities for non-local operations via $textit{nested state teleportation}$. We adapt the well-known Fiduccia-Mattheyses heuristic to the constraints and problem objective and explore multilevel techniques that coarsen hypergraphs and partition at multiple levels of granularity. We find that this reduces runtime and improves solution quality of standard partitioning. We place these techniques within a larger framework, through which we can extract full distributed quantum circuits including teleportation instructions. We compare the entanglement requirements and runtimes with state-of-the-art methods, finding that we achieve the lowest entanglement costs in most cases. Averaging over a wide range of circuits, we reduce the entanglement requirements by 35% compared with the next best-performing method. We also find that our techniques can scale to much larger circuit sizes than competing methods, provided the number of partitions is not too large.
在分布式量子系统上执行量子算法需要将量子电路划分为子电路，这些子电路通过基于纠缠的隐形传态进行通信。天真地将电路映射到多个量子处理单元（qpu）上的量子比特会导致巨大的通信开销，增加执行时间和噪声。这可以通过优化量子比特到qpu的分配和用于覆盖非局部操作的方法来最小化。那些足以捕捉到瞬间移动可能性的通用公式会导致难以有效解决的复杂问题实例。这突出了利用图划分文献中广泛使用的启发式技术的需要。本文形式化并扩展了图形量子电路划分的现有结构，并设计了一个新的目标函数，通过$textit{nested state teleportation}$捕获非局部操作的进一步可能性。我们将著名的Fiduccia-Mattheyses启发式方法应用于约束和问题目标，并探索了在多个粒度级别上粗化超图和划分的多层技术。我们发现这减少了运行时间并提高了标准分区的解决方案质量。我们将这些技术放在一个更大的框架中，通过这个框架，我们可以提取包括隐形传态指令在内的完整分布式量子电路。我们将缠结需求和运行时间与最先进的方法进行比较，发现我们在大多数情况下实现了最低的缠结成本。在广泛的电路范围内进行平均，我们将纠缠要求减少了35% compared with the next best-performing method. We also find that our techniques can scale to much larger circuit sizes than competing methods, provided the number of partitions is not too large.
{"title":"A Multilevel Framework for Partitioning Quantum Circuits","authors":"Felix Burt, Kuan-Cheng Chen, Kin K. Leung","doi":"10.22331/q-2026-01-22-1984","DOIUrl":"https://doi.org/10.22331/q-2026-01-22-1984","url":null,"abstract":"Executing quantum algorithms over distributed quantum systems requires quantum circuits to be divided into sub-circuits which communicate via entanglement-based teleportation. Naively mapping circuits to qubits over multiple quantum processing units (QPUs) results in large communication overhead, increasing both execution time and noise. This can be minimised by optimising the assignment of qubits to QPUs and the methods used for covering non-local operations. Formulations that are general enough to capture the spectrum of teleportation possibilities lead to complex problem instances which can be difficult to solve effectively. This highlights a need to exploit the wide range of heuristic techniques used in the graph partitioning literature. This paper formalises and extends existing constructions for graphical quantum circuit partitioning and designs a new objective function that captures further possibilities for non-local operations via $textit{nested state teleportation}$. We adapt the well-known Fiduccia-Mattheyses heuristic to the constraints and problem objective and explore multilevel techniques that coarsen hypergraphs and partition at multiple levels of granularity. We find that this reduces runtime and improves solution quality of standard partitioning. We place these techniques within a larger framework, through which we can extract full distributed quantum circuits including teleportation instructions. We compare the entanglement requirements and runtimes with state-of-the-art methods, finding that we achieve the lowest entanglement costs in most cases. Averaging over a wide range of circuits, we reduce the entanglement requirements by 35% compared with the next best-performing method. We also find that our techniques can scale to much larger circuit sizes than competing methods, provided the number of partitions is not too large.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"93 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146021927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-22DOI: 10.22331/q-2026-01-22-1982
Martin Stefanak, Vaclav Potocek, Iskender Yalcinkaya, Aurel Gabris, Igor Jex
Interplay between quantum interference and classical randomness can enhance performance of various quantum information tasks. In the present paper we analyze recurrence phenomena in the discrete-time quantum stochastic walk on a line, which is a quantum stochastic process that interpolates between quantum and classical walk dynamics. Surprisingly, we find that introducing classical randomness can reduce the recurrence probability – despite the fact that the classical random walk returns with certainty – and we identify the conditions under which this intriguing phenomenon occurs. Numerical evaluation of the first-return generating function allows us to investigate the asymptotics of the return probability as the step number approaches infinity. This provides strong evidence that the suppression of recurrence probability is not a transient effect but a robust feature of the underlying quantum-classical interplay in the asymptotic limit. Our results show that for certain tasks discrete-time quantum stochastic walks outperform both classical random walks and unitary quantum walks.
{"title":"Recurrence in discrete-time quantum stochastic walks","authors":"Martin Stefanak, Vaclav Potocek, Iskender Yalcinkaya, Aurel Gabris, Igor Jex","doi":"10.22331/q-2026-01-22-1982","DOIUrl":"https://doi.org/10.22331/q-2026-01-22-1982","url":null,"abstract":"Interplay between quantum interference and classical randomness can enhance performance of various quantum information tasks. In the present paper we analyze recurrence phenomena in the discrete-time quantum stochastic walk on a line, which is a quantum stochastic process that interpolates between quantum and classical walk dynamics. Surprisingly, we find that introducing classical randomness can reduce the recurrence probability – despite the fact that the classical random walk returns with certainty – and we identify the conditions under which this intriguing phenomenon occurs. Numerical evaluation of the first-return generating function allows us to investigate the asymptotics of the return probability as the step number approaches infinity. This provides strong evidence that the suppression of recurrence probability is not a transient effect but a robust feature of the underlying quantum-classical interplay in the asymptotic limit. Our results show that for certain tasks discrete-time quantum stochastic walks outperform both classical random walks and unitary quantum walks.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"43 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146021950","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-22DOI: 10.22331/q-2026-01-22-1980
Mohammed Barhoush, Louis Salvail
Signing quantum messages has long been considered impossible even under computational assumptions. In this work, we challenge this notion and provide three innovative approaches to sign quantum messages that are the first to ensure authenticity with public verifiability. Our contributions can be summarized as follows: 1) We introduce the concept of time-dependent (TD) signatures, where the signature of a quantum message depends on the time of signing and the verification process depends on the time of the signature reception. We construct this primitive assuming the existence of post-quantum secure one-way functions (pq-OWFs) and time-lock puzzles (TLPs). 2) By utilizing verification keys that evolve over time, we eliminate the need for TLPs in our construction. This leads to TD signatures from pq-OWFs with dynamic verification keys. 3) We then consider the bounded quantum storage model, where adversaries are limited with respect to their quantum memories. We show that quantum messages can be signed with information-theoretic security in this model. Moreover, we leverage TD signatures to achieve the following objectives, relying solely on pq-OWFs: (a) We design a public key encryption scheme featuring authenticated quantum public keys that resist adversarial tampering. (b) We present a novel TD public-key quantum money scheme.
{"title":"How to Sign Quantum Messages","authors":"Mohammed Barhoush, Louis Salvail","doi":"10.22331/q-2026-01-22-1980","DOIUrl":"https://doi.org/10.22331/q-2026-01-22-1980","url":null,"abstract":"Signing quantum messages has long been considered impossible even under computational assumptions. In this work, we challenge this notion and provide three innovative approaches to sign quantum messages that are the first to ensure authenticity with public verifiability. Our contributions can be summarized as follows:<br/> 1) We introduce the concept of time-dependent (TD) signatures, where the signature of a quantum message depends on the time of signing and the verification process depends on the time of the signature reception. We construct this primitive assuming the existence of post-quantum secure one-way functions (pq-OWFs) and time-lock puzzles (TLPs).<br/> 2) By utilizing verification keys that evolve over time, we eliminate the need for TLPs in our construction. This leads to TD signatures from pq-OWFs with dynamic verification keys.<br/> 3) We then consider the bounded quantum storage model, where adversaries are limited with respect to their quantum memories. We show that quantum messages can be signed with information-theoretic security in this model.<br/> Moreover, we leverage TD signatures to achieve the following objectives, relying solely on pq-OWFs: (a) We design a public key encryption scheme featuring authenticated quantum public keys that resist adversarial tampering. (b) We present a novel TD public-key quantum money scheme.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"269 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146021949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-22DOI: 10.22331/q-2026-01-22-1983
Zeno Bacciconi, Giulia Piccitto, Alessandro Maria Verga, Giuseppe Falci, Elisabetta Paladino, Giuliano Chiriacò
We study the properties of photons in a cryogenic cavity, made by cryo-cooled mirrors surrounded by a room temperature environment. We model such a system as a multimode cavity coupled to two thermal reservoirs at different temperatures. Using a Lindblad master equation approach, we derive the photon distribution and the statistical properties of the cavity modes, finding an overall non-thermal state described by a mode-dependent effective temperature. We also calculate the dissipation rates arising from the interaction of the cavity field with the external environment and the mirrors, relating such rates to measurable macroscopic quantities. These results provide a simple theory to calculate the dissipative properties and the effective temperature of a cavity coupled to different thermal reservoirs, offering potential pathways for engineering dissipations and photon statistics in cavity settings.
{"title":"Dissipation and non-thermal states in cryogenic cavities","authors":"Zeno Bacciconi, Giulia Piccitto, Alessandro Maria Verga, Giuseppe Falci, Elisabetta Paladino, Giuliano Chiriacò","doi":"10.22331/q-2026-01-22-1983","DOIUrl":"https://doi.org/10.22331/q-2026-01-22-1983","url":null,"abstract":"We study the properties of photons in a cryogenic cavity, made by cryo-cooled mirrors surrounded by a room temperature environment. We model such a system as a multimode cavity coupled to two thermal reservoirs at different temperatures. Using a Lindblad master equation approach, we derive the photon distribution and the statistical properties of the cavity modes, finding an overall non-thermal state described by a mode-dependent effective temperature. We also calculate the dissipation rates arising from the interaction of the cavity field with the external environment and the mirrors, relating such rates to measurable macroscopic quantities. These results provide a simple theory to calculate the dissipative properties and the effective temperature of a cavity coupled to different thermal reservoirs, offering potential pathways for engineering dissipations and photon statistics in cavity settings.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"142 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146021951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-21DOI: 10.22331/q-2026-01-21-1978
Timothée Hoffreumon, Ognyan Oreshkov
Transformations of transformations, also called higher-order transformations, is a natural concept in information processing, which has recently attracted significant interest in the study of quantum causal relations. In this work, a framework for characterizing higher-order quantum transformations which relies on the use of superoperator projectors is presented. More precisely, working with projectors in the Choi-Jamiołkowski picture is shown to provide a handy way of defining the characterization constraints on any class of higher-order transformations. The algebraic properties of these projectors are furthermore shown to obey rules similar to $textit{multiplicative additive linear logic (MALL)}$, providing an intuitive way of comparing any two classes through their projectors. The main novelty of this work is the introduction to the algebra of the 'prec' connector. It is used for the characterization of maps that are no signaling from input to output or the other way around. This allows to assess the possible signaling structure of any transformation characterized within the projective framework. The properties of the prec are moreover shown to yield a normal form for projective expressions. This hints towards a general way to compare different classes of higher-order transformations.
变换的变换，也称为高阶变换，是信息处理中的一个自然概念，近年来引起了量子因果关系研究的极大兴趣。在这项工作中，提出了一个表征依赖于使用超算子投影的高阶量子变换的框架。更准确地说，使用Choi-Jamiołkowski图中的投影仪提供了一种方便的方法来定义任何高阶变换类的特征约束。这些投影仪的代数性质进一步证明遵循类似于$textit{multiplicative additive linear logic (MALL)}$的规则，提供了一种直观的方法来通过它们的投影仪比较任何两个类。这项工作的主要新颖之处在于引入了“prec”连接器的代数。它用于描述从输入到输出或其他方式没有信号的映射。这允许评估在投影框架内表征的任何转换的可能的信号结构。此外，我们还证明了该公式的性质，从而得出了射影表达式的标准形式。这暗示了一种比较不同高阶变换类的通用方法。
{"title":"Projective characterization of higher-order quantum transformations","authors":"Timothée Hoffreumon, Ognyan Oreshkov","doi":"10.22331/q-2026-01-21-1978","DOIUrl":"https://doi.org/10.22331/q-2026-01-21-1978","url":null,"abstract":"Transformations of transformations, also called higher-order transformations, is a natural concept in information processing, which has recently attracted significant interest in the study of quantum causal relations. In this work, a framework for characterizing higher-order quantum transformations which relies on the use of superoperator projectors is presented. More precisely, working with projectors in the Choi-Jamiołkowski picture is shown to provide a handy way of defining the characterization constraints on any class of higher-order transformations. The algebraic properties of these projectors are furthermore shown to obey rules similar to $textit{multiplicative additive linear logic (MALL)}$, providing an intuitive way of comparing any two classes through their projectors. The main novelty of this work is the introduction to the algebra of the 'prec' connector. It is used for the characterization of maps that are no signaling from input to output or the other way around. This allows to assess the possible signaling structure of any transformation characterized within the projective framework. The properties of the prec are moreover shown to yield a normal form for projective expressions. This hints towards a general way to compare different classes of higher-order transformations.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"28 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146006017","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-21DOI: 10.22331/q-2026-01-21-1979
Andreas Bluhm, Matthias C. Caro, Aadil Oufkir
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 local were known. We investigate Hamiltonian locality testing as a property testing problem, where the task is to determine whether an unknown $n$-qubit Hamiltonian $H$ is $k$-local or $varepsilon$-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 $tilde{Omega}(2^n)$ many time evolution queries and an expected total evolution time of $tilde{Omega}(2^n / varepsilon)$, and even coherent testers need $Omega(2^{n/2})$ many queries and $Omega(2^{n/2}/varepsilon)$ 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.
{"title":"Hamiltonian Property Testing","authors":"Andreas Bluhm, Matthias C. Caro, Aadil Oufkir","doi":"10.22331/q-2026-01-21-1979","DOIUrl":"https://doi.org/10.22331/q-2026-01-21-1979","url":null,"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 local were known. We investigate Hamiltonian locality testing as a property testing problem, where the task is to determine whether an unknown $n$-qubit Hamiltonian $H$ is $k$-local or $varepsilon$-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 $tilde{Omega}(2^n)$ many time evolution queries and an expected total evolution time of $tilde{Omega}(2^n / varepsilon)$, and even coherent testers need $Omega(2^{n/2})$ many queries and $Omega(2^{n/2}/varepsilon)$ 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.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"6 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146006018","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-21DOI: 10.22331/q-2026-01-21-1977
Konrad Szymański, Lina Vandré, Otfried Gühne
Cluster states and graph states in general offer a useful model of the stabilizer formalism and a path toward the development of measurement-based quantum computation. Their defining structure – the stabilizer group – encodes all possible correlations that can be observed during measurement. The measurement outcomes which are consistent with the stabilizer structure make error correction possible. Here, we leverage both properties to design feasible families of states that can be used as robust building blocks of quantum computation. This procedure reduces the effect of experimentally relevant noise models on the extraction of smaller entangled states from the larger noisy graph state. In particular, we study the extraction of Bell pairs from linearly extended graph states – this has the immediate consequence for state teleportation across the graph. We show that robust entanglement can be extracted by proper design of the linear graph with only a minimal overhead of the physical qubits. This scenario is relevant to systems in which the entanglement can be created between neighboring sites. The results shown in this work provide a mathematical framework for noise reduction in measurement-based quantum computation. With proper connectivity structures, the effect of noise can be minimized for a large class of realistic noise processes.
{"title":"Useful entanglement can be extracted from noisy graph states","authors":"Konrad Szymański, Lina Vandré, Otfried Gühne","doi":"10.22331/q-2026-01-21-1977","DOIUrl":"https://doi.org/10.22331/q-2026-01-21-1977","url":null,"abstract":"Cluster states and graph states in general offer a useful model of the stabilizer formalism and a path toward the development of measurement-based quantum computation. Their defining structure – the stabilizer group – encodes all possible correlations that can be observed during measurement. The measurement outcomes which are consistent with the stabilizer structure make error correction possible. Here, we leverage both properties to design feasible families of states that can be used as robust building blocks of quantum computation. This procedure reduces the effect of experimentally relevant noise models on the extraction of smaller entangled states from the larger noisy graph state. In particular, we study the extraction of Bell pairs from linearly extended graph states – this has the immediate consequence for state teleportation across the graph. We show that robust entanglement can be extracted by proper design of the linear graph with only a minimal overhead of the physical qubits. This scenario is relevant to systems in which the entanglement can be created between neighboring sites. The results shown in this work provide a mathematical framework for noise reduction in measurement-based quantum computation. With proper connectivity structures, the effect of noise can be minimized for a large class of realistic noise processes.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"53 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146006016","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-20DOI: 10.22331/q-2026-01-20-1975
Martijn Brehm, Jordi Weggemans
For many problems, quantum algorithms promise speedups over their classical counterparts. However, these results predominantly rely on asymptotic worst-case analysis, which overlooks significant overheads due to error correction and the fact that real-world instances often contain exploitable structure. In this work, we employ the hybrid benchmarking method to evaluate the potential of quantum Backtracking and Grover's algorithm against the 2023 SAT competition main track winner in solving random $k$-SAT instances with tunable structure, designed to represent industry-like scenarios, using both $T$-depth and $T$-count as cost metrics to estimate quantum run times. Our findings reproduce the results of Campbell, Khurana, and Montanaro (Quantum '19) in the unstructured case using hybrid benchmarking. However, we offer a more sobering perspective in practically relevant regimes: almost all quantum speedups vanish, even asymptotically, when minimal structure is introduced or when $T$-count is considered instead of $T$-depth. Moreover, when the requirement is for the algorithm to find a solution within a single day, we find that only Grover's algorithm has the potential to outperform classical algorithms, but only in a very limited regime and only when using $T$-depth. We also discuss how more sophisticated heuristics could restore the asymptotic scaling advantage for quantum backtracking, but our findings suggest that the potential for practical quantum speedups in more structured $k$-SAT solving will remain limited.
{"title":"Assessing fault-tolerant quantum advantage for $k$-SAT with structure","authors":"Martijn Brehm, Jordi Weggemans","doi":"10.22331/q-2026-01-20-1975","DOIUrl":"https://doi.org/10.22331/q-2026-01-20-1975","url":null,"abstract":"For many problems, quantum algorithms promise speedups over their classical counterparts. However, these results predominantly rely on asymptotic worst-case analysis, which overlooks significant overheads due to error correction and the fact that real-world instances often contain exploitable structure. In this work, we employ the hybrid benchmarking method to evaluate the potential of quantum Backtracking and Grover's algorithm against the 2023 SAT competition main track winner in solving random $k$-SAT instances with tunable structure, designed to represent industry-like scenarios, using both $T$-depth and $T$-count as cost metrics to estimate quantum run times. Our findings reproduce the results of Campbell, Khurana, and Montanaro (Quantum '19) in the unstructured case using hybrid benchmarking. However, we offer a more sobering perspective in practically relevant regimes: almost all quantum speedups vanish, even asymptotically, when minimal structure is introduced or when $T$-count is considered instead of $T$-depth. Moreover, when the requirement is for the algorithm to find a solution within a single day, we find that only Grover's algorithm has the potential to outperform classical algorithms, but only in a very limited regime and only when using $T$-depth. We also discuss how more sophisticated heuristics could restore the asymptotic scaling advantage for quantum backtracking, but our findings suggest that the potential for practical quantum speedups in more structured $k$-SAT solving will remain limited.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"3 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146006026","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-20DOI: 10.22331/q-2026-01-20-1976
Eric R. Anschuetz, Xun Gao
Recent theoretical results in quantum machine learning have demonstrated a general trade-off between the expressive power of quantum neural networks (QNNs) and their trainability; as a corollary of these results, practical exponential separations in expressive power over classical machine learning models are believed to be infeasible as such QNNs take a time to train that is exponential in the model size. We here circumvent these negative results by constructing a hierarchy of efficiently trainable QNNs that exhibit unconditionally provable, polynomial memory separations of arbitrary constant degree over classical neural networks—including state-of-the-art models, such as Transformers—in performing a classical sequence modeling task. This construction is also computationally efficient, as each unit cell of the introduced class of QNNs only has constant gate complexity. We show that contextuality—informally, a quantitative notion of semantic ambiguity—is the source of the expressivity separation, suggesting that other learning tasks with this property may be a natural setting for the use of quantum learning algorithms.
{"title":"Arbitrary Polynomial Separations in Trainable Quantum Machine Learning","authors":"Eric R. Anschuetz, Xun Gao","doi":"10.22331/q-2026-01-20-1976","DOIUrl":"https://doi.org/10.22331/q-2026-01-20-1976","url":null,"abstract":"Recent theoretical results in quantum machine learning have demonstrated a general trade-off between the expressive power of quantum neural networks (QNNs) and their trainability; as a corollary of these results, practical exponential separations in expressive power over classical machine learning models are believed to be infeasible as such QNNs take a time to train that is exponential in the model size. We here circumvent these negative results by constructing a hierarchy of efficiently trainable QNNs that exhibit unconditionally provable, polynomial memory separations of arbitrary constant degree over classical neural networks—including state-of-the-art models, such as Transformers—in performing a classical sequence modeling task. This construction is also computationally efficient, as each unit cell of the introduced class of QNNs only has constant gate complexity. We show that contextuality—informally, a quantitative notion of semantic ambiguity—is the source of the expressivity separation, suggesting that other learning tasks with this property may be a natural setting for the use of quantum learning algorithms.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"64 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146006027","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：