Pub Date : 2025-12-02DOI: 10.22331/q-2025-12-02-1921
Julia Liebert, Federico Castillo, Jean-Philippe Labbé, Tomasz Maciazek, Christian Schilling
The Pauli exclusion principle is fundamental to understanding electronic quantum systems. It namely constrains the expected occupancies $n_i$ of orbitals $varphi_i$ according to $0 leq n_i leq 2$. In this work, we first refine the underlying one-body $N$-representability problem by taking into account simultaneously spin symmetries and a potential degree of mixedness $boldsymbol w$ of the $N$-electron quantum state. We then derive a comprehensive solution to this problem by using basic tools from representation theory, convex analysis and discrete geometry. Specifically, we show that the set of admissible orbital one-body reduced density matrices is fully characterized by linear spectral constraints on the natural orbital occupation numbers, defining a convex polytope $Sigma_{N,S}(boldsymbol w) subset [0,2]^d$. These constraints are independent of $M$ and the number $d$ of orbitals, while their dependence on $N, S$ is linear, and we can thus calculate them for arbitrary system sizes and spin quantum numbers. Our results provide a crucial missing cornerstone for ensemble density (matrix) functional theory.
{"title":"Solving one-body ensemble N-representability problems with spin","authors":"Julia Liebert, Federico Castillo, Jean-Philippe Labbé, Tomasz Maciazek, Christian Schilling","doi":"10.22331/q-2025-12-02-1921","DOIUrl":"https://doi.org/10.22331/q-2025-12-02-1921","url":null,"abstract":"The Pauli exclusion principle is fundamental to understanding electronic quantum systems. It namely constrains the expected occupancies $n_i$ of orbitals $varphi_i$ according to $0 leq n_i leq 2$. In this work, we first refine the underlying one-body $N$-representability problem by taking into account simultaneously spin symmetries and a potential degree of mixedness $boldsymbol w$ of the $N$-electron quantum state. We then derive a comprehensive solution to this problem by using basic tools from representation theory, convex analysis and discrete geometry. Specifically, we show that the set of admissible orbital one-body reduced density matrices is fully characterized by linear spectral constraints on the natural orbital occupation numbers, defining a convex polytope $Sigma_{N,S}(boldsymbol w) subset [0,2]^d$. These constraints are independent of $M$ and the number $d$ of orbitals, while their dependence on $N, S$ is linear, and we can thus calculate them for arbitrary system sizes and spin quantum numbers. Our results provide a crucial missing cornerstone for ensemble density (matrix) functional theory.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"198200 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145651596","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 : 2025-12-02DOI: 10.22331/q-2025-12-02-1926
Matthew Amy, Lucas Shigeru Stinchcombe
Implementations of Roetteler's shifted bent function algorithm have in recent years been used to test and benchmark both classical simulation algorithms and quantum hardware. These circuits have many favorable properties, including a tunable amount of non-Clifford resources and a deterministic output, and moreover do not belong to any class of quantum circuits that is known to be efficiently simulable. We show that this family of circuits can in fact be simulated in polynomial time via symbolic path integrals. We do so by endowing symbolic sums with a confluent rewriting system and show that this rewriting system suffices to reduce the circuit's path integral to the hidden shift in polynomial time. We hence resolve an open conjecture about the efficient simulability of this class of circuits.
{"title":"Polynomial-Time Classical Simulation of Hidden Shift Circuits via Confluent Rewriting of Symbolic Sums","authors":"Matthew Amy, Lucas Shigeru Stinchcombe","doi":"10.22331/q-2025-12-02-1926","DOIUrl":"https://doi.org/10.22331/q-2025-12-02-1926","url":null,"abstract":"Implementations of Roetteler's shifted bent function algorithm have in recent years been used to test and benchmark both classical simulation algorithms and quantum hardware. These circuits have many favorable properties, including a tunable amount of non-Clifford resources and a deterministic output, and moreover do not belong to any class of quantum circuits that is known to be efficiently simulable. We show that this family of circuits can in fact be simulated in polynomial time via symbolic path integrals. We do so by endowing symbolic sums with a confluent rewriting system and show that this rewriting system suffices to reduce the circuit's path integral to the hidden shift in polynomial time. We hence resolve an open conjecture about the efficient simulability of this class of circuits.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"26 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145651600","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 : 2025-12-02DOI: 10.22331/q-2025-12-02-1924
Cahit Kargi, Angsar Manatuly, Lukas M. Sieberer, Juan Pablo Dehollain, Fabio Henriques, Tobias Olsacher, Philipp Hauke, Markus Heyl, Peter Zoller, Nathan K. Langford
Digital quantum simulation (DQS) is one of the most promising paths for achieving first useful real-world applications for quantum processors. Yet even assuming rapid progress in device engineering and development of fault-tolerant quantum processors, algorithmic resource optimisation will long remain crucial to exploit their full power. Currently, Trotterisation provides state-of-the-art resource scaling. And recent theoretical studies of Trotterised Ising models suggest that even better performance than expected may be possible up to a distinct breakdown threshold in empirical performance. Here, we study multiple paradigmatic DQS models with experimentally realisable Trotterisations, and evidence the universality of a range of Trotterisation performance behaviours, including not only the threshold, but also new features in the pre-threshold regime that is most important for practical applications. In each model, we observe a distinct Trotterisation threshold shared across widely varying performance signatures; we further show that an onset of quantum chaotic dynamics causes the performance breakdown and is directly induced by digitisation errors. In the important pre-threshold regime, we are able to identify new distinct regimes displaying qualitatively different quasiperiodic performance behaviours, and show analytic behaviour for properly defined operational Trotter errors. Our results rely crucially on diverse new analytical tools, and provide a previously missing unified picture of Trotterisation behaviour across local observables, the global quantum state, and the full Trotterised unitary. This work provides new insights and tools for addressing important questions about the algorithm performance and underlying theoretical principles of sufficiently complex Trotterisation-based DQS, that will help in extracting maximum simulation power from future quantum processors.
{"title":"Quantum Chaos and Universal Trotterisation Behaviours in Digital Quantum Simulations","authors":"Cahit Kargi, Angsar Manatuly, Lukas M. Sieberer, Juan Pablo Dehollain, Fabio Henriques, Tobias Olsacher, Philipp Hauke, Markus Heyl, Peter Zoller, Nathan K. Langford","doi":"10.22331/q-2025-12-02-1924","DOIUrl":"https://doi.org/10.22331/q-2025-12-02-1924","url":null,"abstract":"Digital quantum simulation (DQS) is one of the most promising paths for achieving first useful real-world applications for quantum processors. Yet even assuming rapid progress in device engineering and development of fault-tolerant quantum processors, algorithmic resource optimisation will long remain crucial to exploit their full power. Currently, Trotterisation provides state-of-the-art resource scaling. And recent theoretical studies of Trotterised Ising models suggest that even better performance than expected may be possible up to a distinct breakdown threshold in empirical performance. Here, we study multiple paradigmatic DQS models with experimentally realisable Trotterisations, and evidence the universality of a range of Trotterisation performance behaviours, including not only the threshold, but also new features in the pre-threshold regime that is most important for practical applications. In each model, we observe a distinct Trotterisation threshold shared across widely varying performance signatures; we further show that an onset of quantum chaotic dynamics causes the performance breakdown and is directly induced by digitisation errors. In the important pre-threshold regime, we are able to identify new distinct regimes displaying qualitatively different quasiperiodic performance behaviours, and show analytic behaviour for properly defined operational Trotter errors. Our results rely crucially on diverse new analytical tools, and provide a previously missing unified picture of Trotterisation behaviour across local observables, the global quantum state, and the full Trotterised unitary. This work provides new insights and tools for addressing important questions about the algorithm performance and underlying theoretical principles of sufficiently complex Trotterisation-based DQS, that will help in extracting maximum simulation power from future quantum processors.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"20 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145651599","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 : 2025-12-02DOI: 10.22331/q-2025-12-02-1927
Mateusz Meller, Vendel Szeremi, Oliver Thomson Brown
Recent advances in quantum computing have brought us closer to realizing the potential of this transformative technology. While significant strides have been made in quantum error correction, many challenges persist, particularly in the realm of noise and scalability. Analogue quantum computing schemes, such as Analogue Hamiltonian Simulation and Quantum Annealing, offer a promising approach to address these limitations. By operating at a higher level of abstraction, these schemes can simplify the development of large-scale quantum algorithms. To fully harness the power of quantum computers, they must be seamlessly integrated with traditional high-performance computing (HPC) systems. While substantial research has focused on the integration of circuit-based quantum computers with HPC, the integration of analogue quantum computers remains relatively unexplored. This paper aims to bridge this gap by contributing in the following way: Comprehensive Survey: We conduct a comprehensive survey of existing quantum software tools with analogue capabilities. Readiness Assessment: We introduce a classification and rating system to assess the readiness of these tools for HPC integration. Gap Identification and Recommendations: We identify critical gaps in the landscape of analogue quantum programming models and propose actionable recommendations for future research and development.
{"title":"Programming tools for Analogue Quantum Computing in the High-Performance Computing Context – A Review","authors":"Mateusz Meller, Vendel Szeremi, Oliver Thomson Brown","doi":"10.22331/q-2025-12-02-1927","DOIUrl":"https://doi.org/10.22331/q-2025-12-02-1927","url":null,"abstract":"Recent advances in quantum computing have brought us closer to realizing the potential of this transformative technology. While significant strides have been made in quantum error correction, many challenges persist, particularly in the realm of noise and scalability. Analogue quantum computing schemes, such as Analogue Hamiltonian Simulation and Quantum Annealing, offer a promising approach to address these limitations. By operating at a higher level of abstraction, these schemes can simplify the development of large-scale quantum algorithms. To fully harness the power of quantum computers, they must be seamlessly integrated with traditional high-performance computing (HPC) systems. While substantial research has focused on the integration of circuit-based quantum computers with HPC, the integration of analogue quantum computers remains relatively unexplored. This paper aims to bridge this gap by contributing in the following way:<br/> Comprehensive Survey: We conduct a comprehensive survey of existing quantum software tools with analogue capabilities.<br/> Readiness Assessment: We introduce a classification and rating system to assess the readiness of these tools for HPC integration.<br/> Gap Identification and Recommendations: We identify critical gaps in the landscape of analogue quantum programming models and propose actionable recommendations for future research and development.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"7 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145651607","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 : 2025-11-27DOI: 10.22331/q-2025-11-27-1920
Min Ye, Nicolas Delfosse
We propose a model for quantum computing with long chains of trapped ions and we design quantum error correction schemes for this model. The main components of a quantum error correction scheme are the quantum code and a quantum circuit called the syndrome extraction circuit, which is executed to perform error correction with this code. In this work, we design syndrome extraction circuits tailored to our ion chain model, a syndrome extraction tuning protocol to optimize these circuits, and we construct new quantum codes that outperform the state-of-the-art for chains of about $50$ qubits. To establish a baseline under the ion chain model, we simulate the performance of surface codes and bivariate bicycle (BB) codes equipped with our optimized syndrome extraction circuits. Then, we propose a new variant of BB codes defined by weight-five measurements, that we refer to as BB5 codes and we identify BB5 codes that achieve a better minimum distance than any BB codes with the same number of logical qubits and data qubits, such as a $[[48, 4, 7]]$ BB5 code. For a physical error rate of $10^{-3}$, the $[[48, 4, 7]]$ BB5 code achieves a logical error rate per logical qubit of $5 cdot 10^{-5}$, which is four times smaller than the best BB code in our baseline family. It also achieves the same logical error rate per logical qubit as the distance-7 surface code but using four times fewer physical qubits per logical qubit.
{"title":"Quantum error correction for long chains of trapped ions","authors":"Min Ye, Nicolas Delfosse","doi":"10.22331/q-2025-11-27-1920","DOIUrl":"https://doi.org/10.22331/q-2025-11-27-1920","url":null,"abstract":"We propose a model for quantum computing with long chains of trapped ions and we design quantum error correction schemes for this model. The main components of a quantum error correction scheme are the quantum code and a quantum circuit called the syndrome extraction circuit, which is executed to perform error correction with this code. In this work, we design syndrome extraction circuits tailored to our ion chain model, a syndrome extraction tuning protocol to optimize these circuits, and we construct new quantum codes that outperform the state-of-the-art for chains of about $50$ qubits. To establish a baseline under the ion chain model, we simulate the performance of surface codes and bivariate bicycle (BB) codes equipped with our optimized syndrome extraction circuits. Then, we propose a new variant of BB codes defined by weight-five measurements, that we refer to as BB5 codes and we identify BB5 codes that achieve a better minimum distance than any BB codes with the same number of logical qubits and data qubits, such as a $[[48, 4, 7]]$ BB5 code. For a physical error rate of $10^{-3}$, the $[[48, 4, 7]]$ BB5 code achieves a logical error rate per logical qubit of $5 cdot 10^{-5}$, which is four times smaller than the best BB code in our baseline family. It also achieves the same logical error rate per logical qubit as the distance-7 surface code but using four times fewer physical qubits per logical qubit.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"118 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145609764","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 : 2025-11-20DOI: 10.22331/q-2025-11-20-1917
Hongrui Chen, Bowen Li, Jianfeng Lu, Lexing Ying
We study a qDRIFT-type randomized method to simulate Lindblad dynamics by decomposing its generator into an ensemble of Lindbladians, $mathcal{L} = sum_{a in mathcal{A}} mathcal{L}_a$, where each $mathcal{L}_a$ comprises a simple Hamiltonian and a single jump operator. Assuming an efficient quantum simulation is available for the Lindblad evolution $e^{tmathcal{L}_a}$, we implement $e^{tmathcal{L}_a}$ for a randomly sampled $mathcal{L}_a$ at each time step according to a probability distribution $mu$ over the ensemble ${mathcal{L}_a}_{a in mathcal{A}}$. This randomized strategy reduces the quantum cost of simulating Lindblad dynamics, particularly in quantum many-body systems with a large or even infinite number of jump operators. Our contributions are two-fold. First, we provide a detailed convergence analysis of the proposed randomized method, covering both average and typical algorithmic realizations. This analysis extends the known results for the random product formula from closed systems to open systems, ensuring rigorous performance guarantees. Second, based on the random product approximation, we derive a new quantum Gibbs sampler algorithm that utilizes jump operators sampled from a Clifford-random circuit. This generator (i) can be efficiently implemented using our randomized algorithm, and (ii) exhibits a spectral gap lower bound that depends on the spectrum of the Hamiltonian. Our results present a new instance of a class of Hamiltonians for which the thermal states can be efficiently prepared using a quantum Gibbs sampling algorithm.
我们研究了一种qdrift类型的随机方法，通过将其生成器分解为Lindbladians的集合$mathcal{L} = sum_{a in mathcal{A}} mathcal{L}_a$来模拟lindbladiad动力学，其中每个$mathcal{L}_a$包含一个简单的哈密顿算子和一个跳跃算子。假设对于Lindblad进化$e^{tmathcal{L}_a}$有一个有效的量子模拟，我们根据集合${mathcal{L}_a}_{a in mathcal{A}}$上的概率分布$mu$对每个时间步随机采样$mathcal{L}_a$实现$e^{tmathcal{L}_a}$。这种随机化策略降低了模拟Lindblad动力学的量子成本，特别是在具有大量甚至无限数量跳跃算子的量子多体系统中。我们的贡献是双重的。首先，我们对所提出的随机化方法进行了详细的收敛分析，涵盖了平均和典型的算法实现。这种分析将已知的随机乘积公式的结果从封闭系统扩展到开放系统，确保了严格的性能保证。其次，基于随机积近似，我们推导了一种新的量子Gibbs采样器算法，该算法利用从Clifford-random电路中采样的跳变算子。该生成器(i)可以使用我们的随机化算法有效地实现，并且（ii）表现出依赖于哈密顿谱的谱隙下界。我们的结果提供了一类哈密顿量的新实例，它可以用量子吉布斯采样算法有效地制备热态。
{"title":"A Randomized Method for Simulating Lindblad Equations and Thermal State Preparation","authors":"Hongrui Chen, Bowen Li, Jianfeng Lu, Lexing Ying","doi":"10.22331/q-2025-11-20-1917","DOIUrl":"https://doi.org/10.22331/q-2025-11-20-1917","url":null,"abstract":"We study a qDRIFT-type randomized method to simulate Lindblad dynamics by decomposing its generator into an ensemble of Lindbladians, $mathcal{L} = sum_{a in mathcal{A}} mathcal{L}_a$, where each $mathcal{L}_a$ comprises a simple Hamiltonian and a single jump operator. Assuming an efficient quantum simulation is available for the Lindblad evolution $e^{tmathcal{L}_a}$, we implement $e^{tmathcal{L}_a}$ for a randomly sampled $mathcal{L}_a$ at each time step according to a probability distribution $mu$ over the ensemble ${mathcal{L}_a}_{a in mathcal{A}}$. This randomized strategy reduces the quantum cost of simulating Lindblad dynamics, particularly in quantum many-body systems with a large or even infinite number of jump operators.<br/> Our contributions are two-fold. First, we provide a detailed convergence analysis of the proposed randomized method, covering both average and typical algorithmic realizations. This analysis extends the known results for the random product formula from closed systems to open systems, ensuring rigorous performance guarantees. Second, based on the random product approximation, we derive a new quantum Gibbs sampler algorithm that utilizes jump operators sampled from a Clifford-random circuit. This generator (i) can be efficiently implemented using our randomized algorithm, and (ii) exhibits a spectral gap lower bound that depends on the spectrum of the Hamiltonian. Our results present a new instance of a class of Hamiltonians for which the thermal states can be efficiently prepared using a quantum Gibbs sampling algorithm.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"158 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145554224","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 : 2025-11-20DOI: 10.22331/q-2025-11-20-1916
Zuzana Gavorová
To better understand quantum computation we can search for its limits or no-gos, especially if analogous limits do not appear in classical computation. Classical computation easily implements and extensively employs the addition of two bit strings, so here we study 'quantum addition': the superposition of two quantum states. We prove the impossibility of superposing two unknown states, no matter how many samples of each state are available. The proof uses topology; a quantum algorithm of any sample complexity corresponds to a continuous function, but the function required by the superposition task cannot be continuous by topological arguments. Our result for the first time quantifies the approximation error and the sample complexity $N$ of the superposition task, and it is tight. We present a trivial algorithm with a large approximation error and $N=1$, and the matching impossibility of any smaller approximation error for any $N$. Consequently, our results limit state tomography as a useful subroutine for the superposition. State tomography is useful only in a model that tolerates randomness in the superposed state. The optimal protocol in this random model remains open.
{"title":"Topologically driven no-superposing theorem with a tight error bound","authors":"Zuzana Gavorová","doi":"10.22331/q-2025-11-20-1916","DOIUrl":"https://doi.org/10.22331/q-2025-11-20-1916","url":null,"abstract":"To better understand quantum computation we can search for its limits or no-gos, especially if analogous limits do not appear in classical computation. Classical computation easily implements and extensively employs the addition of two bit strings, so here we study 'quantum addition': the superposition of two quantum states. We prove the impossibility of superposing two unknown states, no matter how many samples of each state are available. The proof uses topology; a quantum algorithm of any sample complexity corresponds to a continuous function, but the function required by the superposition task cannot be continuous by topological arguments. Our result for the first time quantifies the approximation error and the sample complexity $N$ of the superposition task, and it is tight. We present a trivial algorithm with a large approximation error and $N=1$, and the matching impossibility of any smaller approximation error for any $N$. Consequently, our results limit state tomography as a useful subroutine for the superposition. State tomography is useful only in a model that tolerates randomness in the superposed state. The optimal protocol in this random model remains open.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"135 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145554225","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 : 2025-11-20DOI: 10.22331/q-2025-11-20-1918
Felix Huber, Nikolai Wyderka
The spectral variant of the quantum marginal problem asks: Given prescribed spectra for a set of overlapping quantum marginals, does there exist a compatible joint state? The main idea of this work is a symmetry-reduced semidefinite programming hierarchy that detects when no such joint state exists. The hierarchy is complete, in the sense that it detects every incompatible set of spectra. The refutations it provides are dimension-free, certifying incompatibility in all local dimensions. The hierarchy also applies to the sums of Hermitian matrices problem, the compatibility of local unitary invariants, for certifying vanishing Kronecker coefficients, and to optimize over equivariant state polynomials.
{"title":"Refuting spectral compatibility of quantum marginals","authors":"Felix Huber, Nikolai Wyderka","doi":"10.22331/q-2025-11-20-1918","DOIUrl":"https://doi.org/10.22331/q-2025-11-20-1918","url":null,"abstract":"The spectral variant of the quantum marginal problem asks: Given prescribed spectra for a set of overlapping quantum marginals, does there exist a compatible joint state? The main idea of this work is a symmetry-reduced semidefinite programming hierarchy that detects when no such joint state exists. The hierarchy is complete, in the sense that it detects every incompatible set of spectra. The refutations it provides are dimension-free, certifying incompatibility in all local dimensions. The hierarchy also applies to the sums of Hermitian matrices problem, the compatibility of local unitary invariants, for certifying vanishing Kronecker coefficients, and to optimize over equivariant state polynomials.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"208 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145560525","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 : 2025-11-20DOI: 10.22331/q-2025-11-20-1919
Jordi Pérez-Guijarro, Alba Pagès-Zamora, Javier R. Fonollosa
Sequential methods for quantum hypothesis testing offer significant advantages over fixed-length approaches, which rely on a predefined number of state copies. Despite their potential, these methods remain underexplored for unambiguous discrimination. In this work, we derive performance bounds for such methods when applied to the discrimination of a set of pure states. The performance is evaluated based on the expected number of copies required. We establish a lower bound applicable to any sequential method and an upper bound on the optimal sequential method. The upper bound is derived using a novel and simple non-adaptive method. Importantly, the gap between these bounds is minimal, scaling logarithmically with the number of distinct states.
{"title":"Bounds in Sequential Unambiguous Discrimination of Multiple Pure Quantum States","authors":"Jordi Pérez-Guijarro, Alba Pagès-Zamora, Javier R. Fonollosa","doi":"10.22331/q-2025-11-20-1919","DOIUrl":"https://doi.org/10.22331/q-2025-11-20-1919","url":null,"abstract":"Sequential methods for quantum hypothesis testing offer significant advantages over fixed-length approaches, which rely on a predefined number of state copies. Despite their potential, these methods remain underexplored for unambiguous discrimination. In this work, we derive performance bounds for such methods when applied to the discrimination of a set of pure states. The performance is evaluated based on the expected number of copies required. We establish a lower bound applicable to any sequential method and an upper bound on the optimal sequential method. The upper bound is derived using a novel and simple non-adaptive method. Importantly, the gap between these bounds is minimal, scaling logarithmically with the number of distinct states.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"141 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145560526","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 : 2025-11-17DOI: 10.22331/q-2025-11-17-1912
Jeet Shah, Christopher Fechisin, Yu-Xin Wang, Joseph T. Iosue, James D. Watson, Yan-Qi Wang, Brayden Ware, Alexey V. Gorshkov, Cheng-Ju Lin
Recent experimental progress in controlling open quantum systems enables the pursuit of mixed-state nonequilibrium quantum phases. We investigate whether open quantum systems hosting mixed-state symmetry-protected topological states as steady states retain this property under symmetric perturbations. Focusing on the $textit{decohered cluster state}$ – a mixed-state symmetry-protected topological state protected by a combined strong and weak symmetry – we construct a parent Lindbladian that hosts it as a steady state. This Lindbladian can be mapped onto exactly solvable reaction-diffusion dynamics, even in the presence of certain perturbations, allowing us to solve the parent Lindbladian in detail and reveal previously-unknown steady states. Using both analytical and numerical methods, we find that typical symmetric perturbations cause strong-to-weak spontaneous symmetry breaking at arbitrarily small perturbations, destabilize the steady-state mixed-state symmetry-protected topological order. However, when perturbations introduce only weak symmetry defects, the steady-state mixed-state symmetry-protected topological order remains stable. Additionally, we construct a quantum channel which replicates the essential physics of the Lindbladian and can be efficiently simulated using only Clifford gates, Pauli measurements, and feedback.
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