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.
{"title":"Instability of steady-state mixed-state symmetry-protected topological order to strong-to-weak spontaneous symmetry breaking","authors":"Jeet Shah, Christopher Fechisin, Yu-Xin Wang, Joseph T. Iosue, James D. Watson, Yan-Qi Wang, Brayden Ware, Alexey V. Gorshkov, Cheng-Ju Lin","doi":"10.22331/q-2025-11-17-1912","DOIUrl":"https://doi.org/10.22331/q-2025-11-17-1912","url":null,"abstract":"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.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"08 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145532115","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-2025-11-17-1913
Robert Lin
In this work, we develop a graphical calculus for multi-qudit computations with generalized Clifford algebras, building off the algebraic framework developed in our prior work. We build our graphical calculus out of a fixed set of graphical primitives defined by algebraic expressions constructed out of elements of a given generalized Clifford algebra, a graphical primitive corresponding to the ground state, and also graphical primitives corresponding to projections onto the ground state of each qudit. We establish many properties of the graphical calculus using purely algebraic methods, including a novel algebraic proof of a Yang-Baxter equation and a construction of a corresponding braid group representation. Our algebraic proof, which applies to arbitrary qudit dimension, also enables a resolution of an open problem of Cobanera and Ortiz on the construction of self-dual braid group representations for even qudit dimension. We also derive several new identities for the braid elements, which are key to our proofs. Furthermore, we demonstrate that in many cases, the verification of involved vector identities can be reduced to the combinatorial application of two basic vector identities. Additionally, in terms of quantum computation, we demonstrate that it is feasible to envision implementing the braid operators for quantum computation, by showing that they are 2-local operators. In fact, these braid elements are almost Clifford gates, for they normalize the generalized Pauli group up to an extra factor $zeta$, which is an appropriate square root of a primitive root of unity.
{"title":"A Graphical Calculus for Quantum Computing with Multiple Qudits using Generalized Clifford Algebras","authors":"Robert Lin","doi":"10.22331/q-2025-11-17-1913","DOIUrl":"https://doi.org/10.22331/q-2025-11-17-1913","url":null,"abstract":"In this work, we develop a graphical calculus for multi-qudit computations with generalized Clifford algebras, building off the algebraic framework developed in our prior work. We build our graphical calculus out of a fixed set of graphical primitives defined by algebraic expressions constructed out of elements of a given generalized Clifford algebra, a graphical primitive corresponding to the ground state, and also graphical primitives corresponding to projections onto the ground state of each qudit. We establish many properties of the graphical calculus using purely algebraic methods, including a novel algebraic proof of a Yang-Baxter equation and a construction of a corresponding braid group representation. Our algebraic proof, which applies to arbitrary qudit dimension, also enables a resolution of an open problem of Cobanera and Ortiz on the construction of self-dual braid group representations for even qudit dimension. We also derive several new identities for the braid elements, which are key to our proofs. Furthermore, we demonstrate that in many cases, the verification of involved vector identities can be reduced to the combinatorial application of two basic vector identities. Additionally, in terms of quantum computation, we demonstrate that it is feasible to envision implementing the braid operators for quantum computation, by showing that they are 2-local operators. In fact, these braid elements are almost Clifford gates, for they normalize the generalized Pauli group up to an extra factor $zeta$, which is an appropriate square root of a primitive root of unity.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"120 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145535911","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-2025-11-17-1914
Daniel McNulty, Susane Calegari, Michał Oszmaniec
An important class of fermionic observables, relevant in tasks such as fermionic partial tomography and estimating energy levels of chemical Hamiltonians, are the binary measurements obtained from the product of anti-commuting Majorana operators. In this work, we investigate efficient estimation strategies of these observables based on a joint measurement which, after classical post-processing, yields all sufficiently unsharp (noisy) Majorana observables of even-degree. By exploiting the symmetry properties of the Majorana observables, as described by the braid group, we show that the incompatibility robustness, i.e., the minimal classical noise necessary for joint measurability, relates to the spectral properties of the Sachdev-Ye-Kitaev (SYK) model. In particular, we show that for an $n$ mode fermionic system, the incompatibility robustness of all degree-$2k$ Majorana observables satisfies $Theta(n^{-k/2})$ for $kleq 5$. Furthermore, we present a joint measurement scheme achieving the asymptotically optimal noise, implemented by a small number of fermionic Gaussian unitaries and sampling from the set of all Majorana monomials. Our joint measurement, which can be performed via a randomization over projective measurements, provides rigorous performance guarantees for estimating fermionic observables comparable with fermionic classical shadows.
{"title":"Optimal Fermionic Joint Measurements for Estimating Non-Commuting Majorana Observables","authors":"Daniel McNulty, Susane Calegari, Michał Oszmaniec","doi":"10.22331/q-2025-11-17-1914","DOIUrl":"https://doi.org/10.22331/q-2025-11-17-1914","url":null,"abstract":"An important class of fermionic observables, relevant in tasks such as fermionic partial tomography and estimating energy levels of chemical Hamiltonians, are the binary measurements obtained from the product of anti-commuting Majorana operators. In this work, we investigate efficient estimation strategies of these observables based on a joint measurement which, after classical post-processing, yields all sufficiently unsharp (noisy) Majorana observables of even-degree. By exploiting the symmetry properties of the Majorana observables, as described by the braid group, we show that the incompatibility robustness, i.e., the minimal classical noise necessary for joint measurability, relates to the spectral properties of the Sachdev-Ye-Kitaev (SYK) model. In particular, we show that for an $n$ mode fermionic system, the incompatibility robustness of all degree-$2k$ Majorana observables satisfies $Theta(n^{-k/2})$ for $kleq 5$. Furthermore, we present a joint measurement scheme achieving the asymptotically optimal noise, implemented by a small number of fermionic Gaussian unitaries and sampling from the set of all Majorana monomials. Our joint measurement, which can be performed via a randomization over projective measurements, provides rigorous performance guarantees for estimating fermionic observables comparable with fermionic classical shadows.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"178 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145535912","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-2025-11-17-1915
Samo Novák, David D. Roberts, Alexander Makarovskiy, Raúl García-Patrón, William R. Clements
Loop-based boson samplers interfere photons in the time degree of freedom using a sequence of delay lines. Since they require few hardware components while also allowing for long-range entanglement, they are strong candidates for demonstrating quantum advantage beyond the reach of classical emulation. We propose a method to exploit this loop-based structure to more efficiently classically sample from such systems. Our algorithm exploits a causal-cone argument to decompose the circuit into smaller effective components that can each be simulated sequentially by calling a state vector simulator as a subroutine. To quantify the complexity of our approach, we develop a new lattice path formalism that allows us to efficiently characterize the state space that must be tracked during the simulation. In addition, we develop a heuristic method that allows us to predict the expected average and worst-case memory requirements of running these simulations. We use these methods to compare the simulation complexity of different families of loop-based interferometers, allowing us to quantify the potential for quantum advantage of single-photon Boson Sampling in loop-based architectures.
{"title":"Boundaries for quantum advantage with single photons and loop-based time-bin interferometers","authors":"Samo Novák, David D. Roberts, Alexander Makarovskiy, Raúl García-Patrón, William R. Clements","doi":"10.22331/q-2025-11-17-1915","DOIUrl":"https://doi.org/10.22331/q-2025-11-17-1915","url":null,"abstract":"Loop-based boson samplers interfere photons in the time degree of freedom using a sequence of delay lines. Since they require few hardware components while also allowing for long-range entanglement, they are strong candidates for demonstrating quantum advantage beyond the reach of classical emulation. We propose a method to exploit this loop-based structure to more efficiently classically sample from such systems. Our algorithm exploits a causal-cone argument to decompose the circuit into smaller effective components that can each be simulated sequentially by calling a state vector simulator as a subroutine. To quantify the complexity of our approach, we develop a new lattice path formalism that allows us to efficiently characterize the state space that must be tracked during the simulation. In addition, we develop a heuristic method that allows us to predict the expected average and worst-case memory requirements of running these simulations. We use these methods to compare the simulation complexity of different families of loop-based interferometers, allowing us to quantify the potential for quantum advantage of single-photon Boson Sampling in loop-based architectures.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"174 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145535913","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-2025-11-17-1911
Aniruddha Sen, Kenneth Goodenough, Don Towsley
Quantum networks are important for quantum communication, enabling tasks such as quantum teleportation, quantum key distribution, quantum sensing, and quantum error correction, often utilizing graph states, a specific class of multipartite entangled states that can be represented by graphs. We propose a novel approach for distributing graph states across a quantum network. We show that the distribution of graph states can be characterized by a system of subgraph complementations, which we also relate to the minimum rank of the underlying graph and the degree of entanglement quantified by the Schmidt-rank of the quantum state. We analyze resource usage for our algorithm and show that it improves on the number of qubits, bits for classical communication, and EPR pairs utilized, as compared to prior work. In fact, the number of local operations and resource consumption for our approach scales linearly in the number of vertices. This produces a quadratic improvement in completion time for several classes of graph states represented by dense graphs, which translates into an exponential improvement by allowing parallelization of gate operations. This leads to improved fidelities in the presence of noisy operations, as we show through simulation in the presence of noisy operations. We classify common classes of graph states, along with their optimal distribution time using subgraph complementations. We find a sequence of subgraph complementation operations to distribute an arbitrary graph state which we conjecture is close to the optimal sequence, and establish upper bounds on distribution time along with providing approximate greedy algorithms.
{"title":"Multipartite Entanglement Distribution in Quantum Networks using Subgraph Complementations","authors":"Aniruddha Sen, Kenneth Goodenough, Don Towsley","doi":"10.22331/q-2025-11-17-1911","DOIUrl":"https://doi.org/10.22331/q-2025-11-17-1911","url":null,"abstract":"Quantum networks are important for quantum communication, enabling tasks such as quantum teleportation, quantum key distribution, quantum sensing, and quantum error correction, often utilizing graph states, a specific class of multipartite entangled states that can be represented by graphs. We propose a novel approach for distributing graph states across a quantum network. We show that the distribution of graph states can be characterized by a system of subgraph complementations, which we also relate to the minimum rank of the underlying graph and the degree of entanglement quantified by the Schmidt-rank of the quantum state. We analyze resource usage for our algorithm and show that it improves on the number of qubits, bits for classical communication, and EPR pairs utilized, as compared to prior work. In fact, the number of local operations and resource consumption for our approach scales linearly in the number of vertices. This produces a quadratic improvement in completion time for several classes of graph states represented by dense graphs, which translates into an exponential improvement by allowing parallelization of gate operations. This leads to improved fidelities in the presence of noisy operations, as we show through simulation in the presence of noisy operations. We classify common classes of graph states, along with their optimal distribution time using subgraph complementations. We find a sequence of subgraph complementation operations to distribute an arbitrary graph state which we conjecture is close to the optimal sequence, and establish upper bounds on distribution time along with providing approximate greedy algorithms.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"13 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145532101","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 : 2025-11-14DOI: 10.22331/q-2025-11-14-1909
Pegah Mohammadipour, Xiantao Li
Zero-noise extrapolation (ZNE) is a widely used quantum error mitigation technique that artificially amplifies circuit noise and then extrapolates the results to the noise-free circuit. A common ZNE approach is Richardson extrapolation, which relies on polynomial interpolation. Despite its simplicity, efficient implementations of Richardson extrapolation face several challenges, including approximation errors from the non-polynomial behavior of noise channels, overfitting due to polynomial interpolation, and exponentially amplified measurement noise. This paper provides a comprehensive analysis of these challenges, presenting bias and variance bounds that quantify approximation errors. Additionally, for any precision $varepsilon$, our results offer an estimate of the necessary sample complexity. We further extend the analysis to polynomial least squares-based extrapolation, which mitigates measurement noise and avoids overfitting. Finally, we propose a strategy for simultaneously mitigating circuit and algorithmic errors in the Trotter-Suzuki algorithm by jointly scaling the time step size and the noise level. This strategy provides a practical tool to enhance the reliability of near-term quantum computations. We support our theoretical findings with numerical experiments.
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