Quantum最新文献_第4页

Decoding quantum color codes with MaxSAT 用 MaxSAT 解码量子色码

IF 6.4 2区物理与天体物理

Quantum Pub Date : 2024-10-23 DOI: 10.22331/q-2024-10-23-1506

Lucas Berent, Lukas Burgholzer, Peter-Jan H.S. Derks, Jens Eisert, Robert Wille

{"title":"Decoding quantum color codes with MaxSAT","authors":"Lucas Berent, Lukas Burgholzer, Peter-Jan H.S. Derks, Jens Eisert, Robert Wille","doi":"10.22331/q-2024-10-23-1506","DOIUrl":"https://doi.org/10.22331/q-2024-10-23-1506","url":null,"abstract":"In classical computing, error-correcting codes are well established and are ubiquitous both in theory and practical applications. For quantum computing, error-correction is essential as well, but harder to realize, coming along with substantial resource overheads and being concomitant with needs for substantial classical computing. Quantum error-correcting codes play a central role on the avenue towards fault-tolerant quantum computation beyond presumed near-term applications. Among those, color codes constitute a particularly important class of quantum codes that have gained interest in recent years due to favourable properties over other codes. As in classical computing, $decoding$ is the problem of inferring an operation to restore an uncorrupted state from a corrupted one and is central in the development of fault-tolerant quantum devices. In this work, we show how the decoding problem for color codes can be reduced to a slight variation of the well-known $texttt{LightsOut}$ puzzle. We propose a novel decoder for quantum color codes using a formulation as a MaxSAT problem based on this analogy. Furthermore, we optimize the MaxSAT construction and show numerically that the decoding performance of the proposed decoder achieves state-of-the-art decoding performance on color codes. The implementation of the decoder as well as tools to automatically conduct numerical experiments are publicly available as part of the $textit{Munich Quantum Toolkit}$ (MQT) on GitHub.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"1 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142487366","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}

引用次数: 0

Random Natural Gradient 随机自然渐变

IF 6.4 2区物理与天体物理

Quantum Pub Date : 2024-10-22 DOI: 10.22331/q-2024-10-22-1503

Ioannis Kolotouros, Petros Wallden

{"title":"Random Natural Gradient","authors":"Ioannis Kolotouros, Petros Wallden","doi":"10.22331/q-2024-10-22-1503","DOIUrl":"https://doi.org/10.22331/q-2024-10-22-1503","url":null,"abstract":"Hybrid quantum-classical algorithms appear to be the most promising approach for near-term quantum applications. An important bottleneck is the classical optimization loop, where the multiple local minima and the emergence of barren plateaux make these approaches less appealing. To improve the optimization the Quantum Natural Gradient (QNG) method [15] was introduced – a method that uses information about the local geometry of the quantum state-space. While the QNG-based optimization is promising, in each step it requires more quantum resources, since to compute the QNG one requires $O(m^2)$ quantum state preparations, where $m$ is the number of parameters in the parameterized circuit. In this work we propose two methods that reduce the resources/state preparations required for QNG, while keeping the advantages and performance of the QNG-based optimization. Specifically, we first introduce the Random Natural Gradient (RNG) that uses random measurements and the classical Fisher information matrix (as opposed to the quantum Fisher information used in QNG). The essential quantum resources reduce to linear $O(m)$ and thus offer a quadratic \"speed-up\", while in our numerical simulations it matches QNG in terms of accuracy. We give some theoretical arguments for RNG and then benchmark the method with the QNG on both classical and quantum problems. Secondly, inspired by stochastic-coordinate methods, we propose a novel approximation to the QNG which we call Stochastic-Coordinate Quantum Natural Gradient that optimizes only a small (randomly sampled) fraction of the total parameters at each iteration. This method also performs equally well in our benchmarks, while it uses fewer resources than the QNG.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"88 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142486843","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}

引用次数: 0

Efficient Parameter Optimisation for Quantum Kernel Alignment: A Sub-sampling Approach in Variational Training 量子核配准的高效参数优化：变分训练中的子采样方法

IF 6.4 2区物理与天体物理

Quantum Pub Date : 2024-10-18 DOI: 10.22331/q-2024-10-18-1502

M. Emre Sahin, Benjamin C. B. Symons, Pushpak Pati, Fayyaz Minhas, Declan Millar, Maria Gabrani, Stefano Mensa, Jan Lukas Robertus

引用次数: 0

Quantum Locally Testable Code with Constant Soundness 具有恒健性的量子局部可测试代码

IF 6.4 2区物理与天体物理

Quantum Pub Date : 2024-10-18 DOI: 10.22331/q-2024-10-18-1501

Andrew Cross, Zhiyang He, Anand Natarajan, Mario Szegedy, Guanyu Zhu

引用次数: 0

Quantum lozenge tiling and entanglement phase transition 量子菱形瓦与纠缠相变

IF 6.4 2区物理与天体物理

Quantum Pub Date : 2024-10-10 DOI: 10.22331/q-2024-10-10-1497

Zhao Zhang, Israel Klich

{"title":"Quantum lozenge tiling and entanglement phase transition","authors":"Zhao Zhang, Israel Klich","doi":"10.22331/q-2024-10-10-1497","DOIUrl":"https://doi.org/10.22331/q-2024-10-10-1497","url":null,"abstract":"While volume violation of area law has been exhibited in several quantum spin chains, the construction of a corresponding ground state in higher dimensions, entangled in more than one direction, has been an open problem. Here we construct a 2D frustration-free Hamiltonian with maximal violation of the area law. We do so by building a quantum model of random surfaces with color degree of freedom that can be viewed as a collection of colored Dyck paths. The Hamiltonian may be viewed as a 2D generalization of the Fredkin spin chain. It relates all the colored random surface configurations subject to a Dirichlet boundary condition and hard wall constraint from below to one another, and the ground state is therefore a superposition of all such classical states and non-degenerate. Its entanglement entropy between subsystems undergoes a quantum phase transition as the deformation parameter is tuned. The area- and volume-law phases are similar to the one-dimensional model, while the critical point scales with the linear size of the system $L$ as $Llog L$. Further it is conjectured that similar models with entanglement phase transitions can be built in higher dimensions with even softer area law violations at the critical point.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"65 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142398001","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}

引用次数: 0

Branching States as The Emergent Structure of a Quantum Universe 作为量子宇宙新兴结构的分支状态

IF 6.4 2区物理与天体物理

Quantum Pub Date : 2024-10-10 DOI: 10.22331/q-2024-10-10-1494

Akram Touil, Fabio Anza, Sebastian Deffner, James P. Crutchfield

引用次数: 0

Resource Efficient Boolean Function Solver on Quantum Computer 量子计算机上的资源高效布尔函数求解器

IF 6.4 2区物理与天体物理

Quantum Pub Date : 2024-10-10 DOI: 10.22331/q-2024-10-10-1500

Xiang Li, Hanxiang Shen, Weiguo Gao, Yingzhou Li

引用次数: 0

Implementing any Linear Combination of Unitaries on Intermediate-term Quantum Computers 在中期量子计算机上实现任意单元线性组合

IF 6.4 2区物理与天体物理

Quantum Pub Date : 2024-10-10 DOI: 10.22331/q-2024-10-10-1496

Shantanav Chakraborty

{"title":"Implementing any Linear Combination of Unitaries on Intermediate-term Quantum Computers","authors":"Shantanav Chakraborty","doi":"10.22331/q-2024-10-10-1496","DOIUrl":"https://doi.org/10.22331/q-2024-10-10-1496","url":null,"abstract":"We develop three new methods to implement any Linear Combination of Unitaries (LCU), a powerful quantum algorithmic tool with diverse applications. While the standard LCU procedure requires several ancilla qubits and sophisticated multi-qubit controlled operations, our methods consume significantly fewer quantum resources. The first method ($textit{Single-Ancilla LCU}$) estimates expectation values of observables with respect to any quantum state prepared by an LCU procedure while requiring only a single ancilla qubit, and no multi-qubit controlled operations. The second approach ($textit{Analog LCU}$) is a simple, physically motivated, continuous-time analogue of LCU, tailored to hybrid qubit-qumode systems. The third method ($textit{Ancilla-free LCU}$) requires no ancilla qubit at all and is useful when we are interested in the projection of a quantum state (prepared by the LCU procedure) in some subspace of interest. We apply the first two techniques to develop new quantum algorithms for a wide range of practical problems, ranging from Hamiltonian simulation, ground state preparation and property estimation, and quantum linear systems. Remarkably, despite consuming fewer quantum resources they retain a provable quantum advantage. The third technique allows us to connect discrete and continuous-time quantum walks with their classical counterparts. It also unifies the recently developed optimal quantum spatial search algorithms in both these frameworks, and leads to the development of new ones that require fewer ancilla qubits. Overall, our results are quite generic and can be readily applied to other problems, even beyond those considered here.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"12 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142398000","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}

引用次数: 0

Iteration Complexity of Variational Quantum Algorithms 变分量子算法的迭代复杂性

IF 6.4 2区物理与天体物理

Quantum Pub Date : 2024-10-10 DOI: 10.22331/q-2024-10-10-1495

Vyacheslav Kungurtsev, Georgios Korpas, Jakub Marecek, Elton Yechao Zhu

{"title":"Iteration Complexity of Variational Quantum Algorithms","authors":"Vyacheslav Kungurtsev, Georgios Korpas, Jakub Marecek, Elton Yechao Zhu","doi":"10.22331/q-2024-10-10-1495","DOIUrl":"https://doi.org/10.22331/q-2024-10-10-1495","url":null,"abstract":"There has been much recent interest in near-term applications of quantum computers, i.e., using quantum circuits that have short decoherence times due to hardware limitations. Variational quantum algorithms (VQA), wherein an optimization algorithm implemented on a classical computer evaluates a parametrized quantum circuit as an objective function, are a leading framework in this space. An enormous breadth of algorithms in this framework have been proposed for solving a range of problems in machine learning, forecasting, applied physics, and combinatorial optimization, among others.<br/>\u0000<br/> In this paper, we analyze the iteration complexity of VQA, that is, the number of steps that VQA requires until its iterates satisfy a surrogate measure of optimality. We argue that although VQA procedures incorporate algorithms that can, in the idealized case, be modeled as classic procedures in the optimization literature, the particular nature of noise in near-term devices invalidates the claim of applicability of off-the-shelf analyses of these algorithms. Specifically, noise makes the evaluations of the objective function via quantum circuits $biased$. Commonly used optimization procedures, such as SPSA and the parameter shift rule, can thus be seen as derivative-free optimization algorithms with biased function evaluations, for which there are currently no iteration complexity guarantees in the literature. We derive the missing guarantees and find that the rate of convergence is unaffected. However, the level of bias contributes unfavorably to both the constant therein, and the asymptotic distance to stationarity, i.e., the more bias, the farther one is guaranteed, at best, to reach a stationary point of the VQA objective.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"1 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142397999","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}

引用次数: 0

Decoding algorithms for surface codes 面码的解码算法

IF 6.4 2区物理与天体物理

Quantum Pub Date : 2024-10-10 DOI: 10.22331/q-2024-10-10-1498

Antonio deMarti iOlius, Patricio Fuentes, Román Orús, Pedro M. Crespo, Josu Etxezarreta Martinez

{"title":"Decoding algorithms for surface codes","authors":"Antonio deMarti iOlius, Patricio Fuentes, Román Orús, Pedro M. Crespo, Josu Etxezarreta Martinez","doi":"10.22331/q-2024-10-10-1498","DOIUrl":"https://doi.org/10.22331/q-2024-10-10-1498","url":null,"abstract":"Quantum technologies have the potential to solve certain computationally hard problems with polynomial or super-polynomial speedups when compared to classical methods. Unfortunately, the unstable nature of quantum information makes it prone to errors. For this reason, quantum error correction is an invaluable tool to make quantum information reliable and enable the ultimate goal of fault-tolerant quantum computing. Surface codes currently stand as the most promising candidates to build near term error corrected qubits given their two-dimensional architecture, the requirement of only local operations, and high tolerance to quantum noise. Decoding algorithms are an integral component of any error correction scheme, as they are tasked with producing accurate estimates of the errors that affect quantum information, so that they can subsequently be corrected. A critical aspect of decoding algorithms is their speed, since the quantum state will suffer additional errors with the passage of time. This poses a connundrum, where decoding performance is improved at the expense of complexity and viceversa. In this review, a thorough discussion of state-of-the-art decoding algorithms for surface codes is provided. The target audience of this work are both readers with an introductory understanding of the field as well as those seeking to further their knowledge of the decoding paradigm of surface codes. We describe the core principles of these decoding methods as well as existing variants that show promise for improved results. In addition, both the decoding performance, in terms of error correction capability, and decoding complexity, are compared. A review of the existing software tools regarding surface codes decoding is also provided.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"14 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142398003","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}

引用次数: 0