Quantum最新文献_第10页

Taming Quantum Time Complexity 驯服量子时间复杂性

IF 6.4 2区物理与天体物理

Quantum Pub Date : 2024-08-23 DOI: 10.22331/q-2024-08-23-1444

Aleksandrs Belovs, Stacey Jeffery, Duyal Yolcu

{"title":"Taming Quantum Time Complexity","authors":"Aleksandrs Belovs, Stacey Jeffery, Duyal Yolcu","doi":"10.22331/q-2024-08-23-1444","DOIUrl":"https://doi.org/10.22331/q-2024-08-23-1444","url":null,"abstract":"Quantum query complexity has several nice properties with respect to composition. First, bounded-error quantum query algorithms can be composed without incurring log factors through error reduction $exactness$. Second, through careful accounting $thriftiness$, the total query complexity is smaller if subroutines are mostly run on cheaper inputs -- a property that is much less obvious in quantum algorithms than in their classical counterparts. While these properties were previously seen through the model of span programs (alternatively, the dual adversary bound), a recent work by two of the authors (Belovs, Yolcu 2023) showed how to achieve these benefits without converting to span programs, by defining $textit{quantum Las Vegas query complexity}$. Independently, recent works, including by one of the authors (Jeffery 2022), have worked towards bringing thriftiness to the more practically significant setting of quantum $time$ complexity.<br/>\u0000<br/> In this work, we show how to achieve both exactness and thriftiness in the setting of time complexity. We generalize the quantum subroutine composition results of Jeffery 2022 so that, in particular, no error reduction is needed. We give a time complexity version of the well-known result in quantum query complexity, $Q(fcirc g)=mathcal{O}(Q(f)cdot Q(g))$, without log factors.<br/>\u0000<br/> We achieve this by employing a novel approach to the design of quantum algorithms based on what we call $transducers$, and which we think is of large independent interest. While a span program is a completely different computational model, a transducer is a direct generalisation of a quantum algorithm, which allows for much greater transparency and control. Transducers naturally characterize general state conversion, rather than only decision problems; provide a very simple treatment of other quantum primitives such as quantum walks; and lend themselves well to time complexity analysis.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"1 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142042634","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

Classical-to-quantum non-signalling boxes 经典-量子非信号箱

IF 6.4 2区物理与天体物理

Quantum Pub Date : 2024-08-22 DOI: 10.22331/q-2024-08-22-1443

Carolina Moreira Ferrera, Robin Simmons, James Purcell, Daniel Collins, Sandu Popescu

引用次数: 0

Certification of quantum state functions under partial information 部分信息下的量子态函数认证

IF 6.4 2区物理与天体物理

Quantum Pub Date : 2024-08-16 DOI: 10.22331/q-2024-08-16-1442

Leonardo Zambrano, Donato Farina, Egle Pagliaro, Marcio M. Taddei, Antonio Acin

引用次数: 0

Quantum Reference Frames for Lorentz Symmetry 洛伦兹对称的量子参考框架

IF 6.4 2区物理与天体物理

Quantum Pub Date : 2024-08-14 DOI: 10.22331/q-2024-08-14-1440

Luca Apadula, Esteban Castro-Ruiz, Časlav Brukner

引用次数: 0

Approximate Quantum Codes From Long Wormholes 来自长虫洞的近似量子密码

IF 6.4 2区物理与天体物理

Quantum Pub Date : 2024-08-14 DOI: 10.22331/q-2024-08-14-1439

Gregory Bentsen, Phuc Nguyen, Brian Swingle

{"title":"Approximate Quantum Codes From Long Wormholes","authors":"Gregory Bentsen, Phuc Nguyen, Brian Swingle","doi":"10.22331/q-2024-08-14-1439","DOIUrl":"https://doi.org/10.22331/q-2024-08-14-1439","url":null,"abstract":"We discuss families of approximate quantum error correcting codes which arise as the nearly-degenerate ground states of certain quantum many-body Hamiltonians composed of non-commuting terms. For exact codes, the conditions for error correction can be formulated in terms of the vanishing of a two-sided mutual information in a low-temperature thermofield double state. We consider a notion of distance for approximate codes obtained by demanding that this mutual information instead be small, and we evaluate this mutual information for the SYK model and for a family of low-rank SYK models. After an extrapolation to nearly zero temperature, we find that both kinds of models produce fermionic codes with constant rate as the number, $N$, of fermions goes to infinity. For SYK, the distance scales as $N^{1/2}$, and for low-rank SYK, the distance can be arbitrarily close to linear scaling, e.g. $N^{.99}$, while maintaining a constant rate. We also consider an analog of the no low-energy trivial states property which we dub the no low-energy adiabatically accessible states property and show that these models do have low-energy states that can be prepared adiabatically in a time that does not scale with system size $N$. We discuss a holographic model of these codes in which the large code distance is a consequence of the emergence of a long wormhole geometry in a simple model of quantum gravity.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"419 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141980853","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

Study of noise in virtual distillation circuits for quantum error mitigation 研究虚拟蒸馏电路中的噪声以减少量子错误

IF 6.4 2区物理与天体物理

Quantum Pub Date : 2024-08-14 DOI: 10.22331/q-2024-08-14-1441

Pontus Vikstål, Giulia Ferrini, Shruti Puri

{"title":"Study of noise in virtual distillation circuits for quantum error mitigation","authors":"Pontus Vikstål, Giulia Ferrini, Shruti Puri","doi":"10.22331/q-2024-08-14-1441","DOIUrl":"https://doi.org/10.22331/q-2024-08-14-1441","url":null,"abstract":"Virtual distillation has been proposed as an error mitigation protocol for estimating the expectation values of observables in quantum algorithms. It proceeds by creating a cyclic permutation of $M$ noisy copies of a quantum state using a sequence of controlled-swap gates. If the noise does not shift the dominant eigenvector of the density operator away from the ideal state, then the error in expectation-value estimation can be exponentially reduced with $M$. In practice, subsequent error mitigation techniques are required to suppress the effect of noise in the cyclic permutation circuit itself, leading to increased experimental complexity. Here, we perform a careful analysis of the effect of uncorrelated, identical noise in the cyclic permutation circuit and find that the estimation of expectation value of observables are robust against dephasing noise. We support the analytical result with numerical simulations and find that $67%$ of errors are reduced for $M=2$, with physical dephasing error probabilities as high as $10%$. Our results imply that a broad class of quantum algorithms can be implemented with higher accuracy in the near-term with qubit platforms where non-dephasing errors are suppressed, such as superconducting bosonic qubits and Rydberg atoms.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"78 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141980859","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

Measurement-efficient quantum Krylov subspace diagonalisation 测量效率高的量子克雷洛夫子空间对角化

IF 6.4 2区物理与天体物理

Quantum Pub Date : 2024-08-13 DOI: 10.22331/q-2024-08-13-1438

Zongkang Zhang, Anbang Wang, Xiaosi Xu, Ying Li

{"title":"Measurement-efficient quantum Krylov subspace diagonalisation","authors":"Zongkang Zhang, Anbang Wang, Xiaosi Xu, Ying Li","doi":"10.22331/q-2024-08-13-1438","DOIUrl":"https://doi.org/10.22331/q-2024-08-13-1438","url":null,"abstract":"The Krylov subspace methods, being one category of the most important classical numerical methods for linear algebra problems, can be much more powerful when generalised to quantum computing. However, quantum Krylov subspace algorithms are prone to errors due to inevitable statistical fluctuations in quantum measurements. To address this problem, we develop a general theoretical framework to analyse the statistical error and measurement cost. Based on the framework, we propose a quantum algorithm to construct the Hamiltonian-power Krylov subspace that can minimise the measurement cost. In our algorithm, the product of power and Gaussian functions of the Hamiltonian is expressed as an integral of the real-time evolution, such that it can be evaluated on a quantum computer. We compare our algorithm with other established quantum Krylov subspace algorithms in solving two prominent examples. To achieve an error comparable to that of the classical Lanczos algorithm at the same subspace dimension, our algorithm typically requires orders of magnitude fewer measurements than others. Such an improvement can be attributed to the reduced cost of composing projectors onto the ground state. These results show that our algorithm is exceptionally robust to statistical fluctuations and promising for practical applications.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"78 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141973808","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

Maximum expectation of observables with restricted purity states 受限纯度态观测值的最大期望值

IF 6.4 2区物理与天体物理

Quantum Pub Date : 2024-08-13 DOI: 10.22331/q-2024-08-13-1437

Vikesh Siddhu, John Aaron Smolin

{"title":"Maximum expectation of observables with restricted purity states","authors":"Vikesh Siddhu, John Aaron Smolin","doi":"10.22331/q-2024-08-13-1437","DOIUrl":"https://doi.org/10.22331/q-2024-08-13-1437","url":null,"abstract":"Assessment of practical quantum information processing (QIP) remains partial without understanding limits imposed by noise. Unfortunately, mere description of noise grows exponentially with system size, becoming cumbersome even for modest sized systems of imminent practical interest. We fulfill the need for estimates on performing noisy quantum state preparation, verification, and observation. To do the estimation we propose fast numerical algorithms to maximize the expectation value of any $d$-dimensional observable over states of bounded purity. This bound on purity factors in noise in a measurable way. Our fastest algorithm takes $O(d)$ steps if the eigendecomposition of the observable is known, otherwise takes $O(d^3)$ steps at worst. The algorithms also solve maximum likelihood estimation for quantum state tomography with convex and even non-convex purity constraints. Numerics show performance of our key sub-routine (it finds in linear time a probability vector with bounded norm that most overlaps with a fixed vector) can be several orders of magnitude faster than a common state-of-the-art convex optimization solver. Our work fosters a practical way forward to asses limitations on QIP imposed by quantum noise. Along the way, we also give a simple but fundamental insight, noisy systems (equivalently noisy Hamiltonians) always give higher ground-state energy than their noiseless counterparts.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"39 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141973810","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

Non-Markovianity in High-Dimensional Open Quantum Systems using Next-generation Multicore Optical Fibers 使用下一代多芯光纤的高维开放量子系统中的非马尔可夫性

IF 6.4 2区物理与天体物理

Quantum Pub Date : 2024-08-12 DOI: 10.22331/q-2024-08-12-1436

Santiago Rojas-Rojas, Daniel Martínez, Kei Sawada, Luciano Pereira, Stephen P. Walborn, Esteban S. Gómez, Nadja K. Bernardes, Gustavo Lima

引用次数: 0

Hayden-Preskill recovery in chaotic and integrable unitary circuit dynamics 混沌和可积分单元电路动力学中的海登-普雷斯基尔恢复

IF 6.4 2区物理与天体物理

Quantum Pub Date : 2024-08-08 DOI: 10.22331/q-2024-08-08-1434

Michael A. Rampp, Pieter W. Claeys

{"title":"Hayden-Preskill recovery in chaotic and integrable unitary circuit dynamics","authors":"Michael A. Rampp, Pieter W. Claeys","doi":"10.22331/q-2024-08-08-1434","DOIUrl":"https://doi.org/10.22331/q-2024-08-08-1434","url":null,"abstract":"The Hayden-Preskill protocol probes the capability of information recovery from local subsystems after unitary dynamics. As such it resolves the capability of quantum many-body systems to dynamically implement a quantum error-correcting code. The transition to coding behavior has been mostly discussed using effective approaches, such as entanglement membrane theory. Here, we present exact results on the use of Hayden-Preskill recovery as a dynamical probe of scrambling in local quantum many-body systems. We investigate certain classes of unitary circuit models, both structured Floquet (dual-unitary) and Haar-random circuits. We discuss different dynamical signatures corresponding to information transport or scrambling, respectively, that go beyond effective approaches. Surprisingly, certain chaotic circuits transport information with perfect fidelity. In integrable dual-unitary circuits, we relate the information transmission to the propagation and scattering of quasiparticles. Using numerical and analytical insights, we argue that the qualitative features of information recovery extend away from these solvable points. Our results suggest that information recovery protocols can serve to distinguish chaotic and integrable behavior, and that they are sensitive to characteristic dynamical features, such as long-lived quasiparticles or dual-unitarity.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"191 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141904310","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