Quantum最新文献

{"title":"On the connection between least squares, regularization, and classical shadows","authors":"Zhihui Zhu, Joseph M. Lukens, Brian T. Kirby","doi":"10.22331/q-2024-08-29-1455","DOIUrl":"https://doi.org/10.22331/q-2024-08-29-1455","url":null,"abstract":"Classical shadows (CS) offer a resource-efficient means to estimate quantum observables, circumventing the need for exhaustive state tomography. Here, we clarify and explore the connection between CS techniques and least squares (LS) and regularized least squares (RLS) methods commonly used in machine learning and data analysis. By formal identification of LS and RLS \"shadows\" completely analogous to those in CS – namely, point estimators calculated from the empirical frequencies of single measurements – we show that both RLS and CS can be viewed as regularizers for the underdetermined regime, replacing the pseudoinverse with invertible alternatives. Through numerical simulations, we evaluate RLS and CS from three distinct angles: the tradeoff in bias and variance, mismatch between the expected and actual measurement distributions, and the interplay between the number of measurements and number of shots per measurement. Compared to CS, RLS attains lower variance at the expense of bias, is robust to distribution mismatch, and is more sensitive to the number of shots for a fixed number of state copies – differences that can be understood from the distinct approaches taken to regularization. Conceptually, our integration of LS, RLS, and CS under a unifying \"shadow\" umbrella aids in advancing the overall picture of CS techniques, while practically our results highlight the tradeoffs intrinsic to these measurement approaches, illuminating the circumstances under which either RLS or CS would be preferred, such as unverified randomness for the former or unbiased estimation for the latter.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"58 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142090079","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}

{"title":"GraphiQ: Quantum circuit design for photonic graph states","authors":"Jie Lin, Benjamin MacLellan, Sobhan Ghanbari, Julie Belleville, Khuong Tran, Luc Robichaud, Roger G. Melko, Hoi-Kwong Lo, Piotr Roztocki","doi":"10.22331/q-2024-08-28-1453","DOIUrl":"https://doi.org/10.22331/q-2024-08-28-1453","url":null,"abstract":"$tt{GraphiQ}$ is a versatile open-source framework for designing photonic graph state generation schemes, with a particular emphasis on photon-emitter hybrid circuits. Built in Python, GraphiQ consists of a suite of design tools, including multiple simulation backends and optimization methods. The library supports scheme optimization in the presence of circuit imperfections, as well as user-defined optimization goals. Our framework thus represents a valuable tool for the development of practical schemes adhering to experimentally-relevant constraints. As graph states are a key resource for measurement-based quantum computing, all-photonic quantum repeaters, and robust quantum metrology, among others, we envision GraphiQ's broad impact for advancing quantum technologies.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"21 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142084817","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}

{"title":"Expanding the reach of quantum optimization with fermionic embeddings","authors":"Andrew Zhao, Nicholas C. Rubin","doi":"10.22331/q-2024-08-28-1451","DOIUrl":"https://doi.org/10.22331/q-2024-08-28-1451","url":null,"abstract":"Quadratic programming over orthogonal matrices encompasses a broad class of hard optimization problems that do not have an efficient quantum representation. Such problems are instances of the little noncommutative Grothendieck problem (LNCG), a generalization of binary quadratic programs to continuous, noncommutative variables. In this work, we establish a natural embedding for this class of LNCG problems onto a fermionic Hamiltonian, thereby enabling the study of this classical problem with the tools of quantum information. This embedding is accomplished by a new representation of orthogonal matrices as fermionic quantum states, which we achieve through the well-known double covering of the orthogonal group. Correspondingly, the embedded LNCG Hamiltonian is a two-body fermion model. Determining extremal states of this Hamiltonian provides an outer approximation to the original problem, a quantum analogue to classical semidefinite relaxations. In particular, when optimizing over the $special$ orthogonal group our quantum relaxation obeys additional, powerful constraints based on the convex hull of rotation matrices. The classical size of this convex-hull representation is exponential in matrix dimension, whereas our quantum representation requires only a linear number of qubits. Finally, to project the relaxed solution back into the feasible space, we propose rounding procedures which return orthogonal matrices from appropriate measurements of the quantum state. Through numerical experiments we provide evidence that this rounded quantum relaxation can produce high-quality approximations.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"2 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142084818","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}

{"title":"Quantum multi-anomaly detection","authors":"Santiago Llorens, Gael Sentís, Ramon Muñoz-Tapia","doi":"10.22331/q-2024-08-28-1452","DOIUrl":"https://doi.org/10.22331/q-2024-08-28-1452","url":null,"abstract":"A source assumed to prepare a specified reference state sometimes prepares an anomalous one. We address the task of identifying these anomalous states in a series of $n$ preparations with $k$ anomalies. We analyze the minimum-error protocol and the zero-error (unambiguous) protocol and obtain closed expressions for the success probability when both reference and anomalous states are known to the observer and anomalies can appear equally likely in any position of the preparation series. We find the solution using results from association schemes theory, thus establishing a connection between graph theory and quantum hypothesis testing. In particular, we use the Johnson association scheme which arises naturally from the Gram matrix of this problem. We also study the regime of large $n$ and obtain the expression of the success probability that is non-vanishing. Finally, we address the case in which the observer is blind to the reference and the anomalous states. This scenario requires a universal protocol for which we prove that in the asymptotic limit, the success probability corresponds to the average of the known state scenario.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"48 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142084876","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}

{"title":"Device-independent lower bounds on the conditional von Neumann entropy","authors":"Peter Brown, Hamza Fawzi, Omar Fawzi","doi":"10.22331/q-2024-08-27-1445","DOIUrl":"https://doi.org/10.22331/q-2024-08-27-1445","url":null,"abstract":"The rates of several device-independent (DI) protocols, including quantum key-distribution (QKD) and randomness expansion (RE), can be computed via an optimization of the conditional von Neumann entropy over a particular class of quantum states. In this work we introduce a numerical method to compute lower bounds on such rates. We derive a sequence of optimization problems that converge to the conditional von Neumann entropy of systems defined on general separable Hilbert spaces. Using the Navascués-Pironio-Acín hierarchy we can then relax these problems to semidefinite programs, giving a computationally tractable method to compute lower bounds on the rates of DI protocols. Applying our method to compute the rates of DI-RE and DI-QKD protocols we find substantial improvements over all previous numerical techniques, demonstrating significantly higher rates for both DI-RE and DI-QKD. In particular, for DI-QKD we show a minimal detection efficiency threshold which is within the realm of current capabilities. Moreover, we demonstrate that our method is capable of converging rapidly by recovering all known tight analytical bounds up to several decimal places. Finally, we note that our method is compatible with the entropy accumulation theorem and can thus be used to compute rates of finite round protocols and subsequently prove their security.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"5 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142084874","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}

{"title":"Fast erasure decoder for hypergraph product codes","authors":"Nicholas Connolly, Vivien Londe, Anthony Leverrier, Nicolas Delfosse","doi":"10.22331/q-2024-08-27-1450","DOIUrl":"https://doi.org/10.22331/q-2024-08-27-1450","url":null,"abstract":"We propose a decoder for the correction of erasures with hypergraph product codes, which form one of the most popular families of quantum LDPC codes. Our numerical simulations show that this decoder provides a close approximation of the maximum likelihood decoder that can be implemented in $O(N^2)$ bit operations where $N$ is the length of the quantum code. A probabilistic version of this decoder can be implemented in $O(N^{1.5})$ bit operations.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"6 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142084816","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}

{"title":"Double or nothing: a Kolmogorov extension theorem for multitime (bi)probabilities in quantum mechanics","authors":"Davide Lonigro, Fattah Sakuldee, Łukasz Cywiński, Dariusz Chruściński, Piotr Szańkowski","doi":"10.22331/q-2024-08-27-1447","DOIUrl":"https://doi.org/10.22331/q-2024-08-27-1447","url":null,"abstract":"The multitime probability distributions obtained by repeatedly probing a quantum system via the measurement of an observable generally violate Kolmogorov's consistency property. Therefore, one cannot interpret such distributions as the result of the sampling of a single trajectory. We show that, nonetheless, they do result from the sampling of one $pair$ of trajectories. In this sense, rather than give up on trajectories, quantum mechanics requires to double down on them. To this purpose, we prove a generalization of the Kolmogorov extension theorem that applies to families of complex-valued bi-probability distributions (that is, defined on pairs of elements of the original sample spaces), and we employ this result in the quantum mechanical scenario. We also discuss the relation of our results with the quantum comb formalism.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"12 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142084875","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}

{"title":"Hamiltonian simulation for low-energy states with optimal time dependence","authors":"Alexander Zlokapa, Rolando D. Somma","doi":"10.22331/q-2024-08-27-1449","DOIUrl":"https://doi.org/10.22331/q-2024-08-27-1449","url":null,"abstract":"We consider the task of simulating time evolution under a Hamiltonian $H$ within its low-energy subspace. Assuming access to a block-encoding of $H':=(H-E)/lambda$, for some $lambda gt 0$ and $E in mathbb R$, the goal is to implement an $epsilon$-approximation to the evolution operator $e^{-itH}$ when the initial state is confined to the subspace corresponding to eigenvalues $[-1, -1+Delta/lambda]$ of $H'$, for $Delta leq lambda$. We present a quantum algorithm that requires $mathcal{O}(tsqrt{lambdaGamma} + sqrt{lambda/Gamma}log(1/epsilon))$ queries to the block-encoding for any choice of $Gamma$ such that $Delta leq Gamma leq lambda$. When the parameters satisfy $log(1/epsilon) = o(tlambda)$ and $Delta/lambda = o(1)$, this result improves over generic methods with query complexity $Omega(tlambda)$. Our quantum algorithm leverages spectral gap amplification and the quantum singular value transform.<br/>\u0000<br/> For a given $H$, the block-encoding of its $H'$ must be prepared efficiently to achieve an asymptotic speedup in simulating the low-energy subspace; we refer to these Hamiltonians as $gap-amplifiable$. We show necessary and sufficient conditions for gap amplifiability in terms of an operationally useful decomposition of $H$ into a sum of squares. Gap-amplifiable Hamiltonians include physically relevant examples such as frustration-free systems, and it encompasses all previously considered settings of low energy simulation algorithms. Any Hamiltonian can be expressed as a gap-amplifiable Hamiltonian after simple transformations, and our algorithm retains the asymptotic improvement over generic methods as long as the conditions on the parameters are met.<br/>\u0000<br/> We also provide lower bounds for simulating dynamics of low-energy states. In the worst case, we show that the low-energy condition cannot be used to improve the runtime of Hamiltonian simulation methods. For gap-amplifiable Hamiltonians, we prove that our algorithm is tight in the query model with respect to $t$, $Delta$, and $lambda$. In the practically relevant regime where $log (1/epsilon) = o(tDelta)$ and $Delta/lambda = o(1)$, we also prove a matching lower bound in gate complexity (up to logarithmic factors). To establish the query lower bounds, we consider oracular problems including search and $mathrm{PARITY}circmathrm{OR}$, and also bounds on the degrees of trigonometric polynomials. To establish the lower bound on gate complexity, we use a circuit-to-Hamiltonian reduction, where a “clock Hamiltonian'' acting on a low-energy state can simulate any quantum circuit.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"29 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142084815","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}

{"title":"Quantum computation from dynamic automorphism codes","authors":"Margarita Davydova, Nathanan Tantivasadakarn, Shankar Balasubramanian, David Aasen","doi":"10.22331/q-2024-08-27-1448","DOIUrl":"https://doi.org/10.22331/q-2024-08-27-1448","url":null,"abstract":"We propose a new model of quantum computation comprised of low-weight measurement sequences that simultaneously encode logical information, enable error correction, and apply logical gates. These measurement sequences constitute a new class of quantum error-correcting codes generalizing Floquet codes, which we call dynamic automorphism (DA) codes. We construct an explicit example, the DA color code, which is assembled from short measurement sequences that can realize all 72 automorphisms of the 2D color code. On a stack of $N$ triangular patches, the DA color code encodes $N$ logical qubits and can implement the full logical Clifford group by a sequence of two- and, more rarely, three-qubit Pauli measurements. We also make the first step towards universal quantum computation with DA codes by introducing a 3D DA color code and showing that a non-Clifford logical gate can be realized by adaptive two-qubit measurements.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"51 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142084813","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}

{"title":"Quantum Chaos and Coherence: Random Parametric Quantum Channels","authors":"Apollonas S. Matsoukas-Roubeas, Tomaž Prosen, Adolfo del Campo","doi":"10.22331/q-2024-08-27-1446","DOIUrl":"https://doi.org/10.22331/q-2024-08-27-1446","url":null,"abstract":"The survival probability of an initial Coherent Gibbs State (CGS) is a natural extension of the Spectral Form Factor (SFF) to open quantum systems. To quantify the interplay between quantum chaos and decoherence away from the semi-classical limit, we investigate the relation of this generalized SFF with the corresponding $l_1$-norm of coherence. As a working example, we introduce Parametric Quantum Channels (PQC), a discrete-time model of unitary evolution mixed with the effects of measurements or transient interactions with an environment. The Energy Dephasing (ED) dynamics arises as a specific case in the Markovian limit. We demonstrate our results in a series of random matrix models.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"71 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142084820","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}