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arXiv 2022年

作者： Lowe, Angus Nayak, Ashwin Department of Combinatorics & Optimization Institute for Quantum Computing University of Waterloo 200 University Ave. W. WaterlooONN2L 3G1 Canada

We study the problems of quantum tomography and shadow tomography using measurements performed on individual, identical copies of an unknown d-dimensional state. We first revisit known lower bounds [HHJ+17] on quantum tomography with accuracy Ε in trace distance, when the measurement choices are independent of previously observed outcomes, i.e., they are nonadaptive. We give a succinct proof of these results through the χ2-divergence between suitable distributions. Unlike prior work, we do not require that the measurements be given by rank-one operators. This leads to stronger lower bounds when the learner uses measurements with a constant number of outcomes (e.g., two-outcome measurements). In particular, this rigorously establishes the optimality of the folklore "Pauli tomography" algorithm in terms of its sample complexity. We also derive novel bounds of Ω(r2d/Ε2) and Ω(r2d2/Ε2) for learning rank r states using arbitrary and constant-outcome measurements, respectively, in the nonadaptive case. In addition to the sample complexity, a resource of practical significance for learning quantum states is the number of unique measurement settings required (i.e., the number of different measurements used by an algorithm, each possibly with an arbitrary number of outcomes). Motivated by this consideration, we employ concentration of measure of χ2-divergence of suitable distributions to extend our lower bounds to the case where the learner performs possibly adaptive measurements from a fixed set of exp(O(d)) possible measurements. This implies in particular that adaptivity does not give us any advantage using single-copy measurements that are efficiently implementable. We also obtain a similar bound in the case where the goal is to predict the expectation values of a given sequence of observables, a task known as shadow tomography. Finally, in the case of adaptive, single-copy measurements implementable with polynomial-size circuits, we prove that a straightforward strategy

关键词： Tomography

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Period Variation Rates of Four Radial Single-Mode High-Amplitude Delta Scuti Stars

arXiv

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arXiv 2025年

作者： Ma, Tian-Fang Niu, Jia-Shu Xue, Hui-Fang Institute of Theoretical Physics Shanxi University Taiyuan030006 China State Key Laboratory of Quantum Optics Technologies and Devices Shanxi University Taiyuan030006 China Collaborative Innovation Center of Extreme Optics Shanxi University Taiyuan030006 China Department of Physics Taiyuan Normal University Jinzhong030619 China Institute of Computational and Applied Physics Taiyuan Normal University Jinzhong030619 China Shanxi Key Laboratory for Intelligent Optimization Computing and Blockchain Technology Jinzhong030619 China

In this work, we present a study on the long time-scale period variations of four single-mode high-amplitude delta Scuti stars (HADS) via the classical O − C analysis. The target HADS are (i) XX Cygni, (ii) YZ Bootis, (iii) GP Andromedae, and (iv) ZZ Microscopii. The newly determined times of maximum light came from the Transiting Exoplanet Survey Satellite (TESS), American Association of Variable Star Observers (AAVSO), and Bundesdeutsche Arbeitsgemeinschaft für Veränderliche Sterne (BAV) projects. Together with the times of maximum light obtained in the historical literature, the O − C analysis was performed on these HADS, in which we obtained the linear period variation rates P/P as (9.2 ± 0.2) × 10−9 yr−1, (3.2 ± 0.2) × 10−9 yr−1, (4.22 ± 0.03) × 10−8 yr−1, and (−2.06 ± 0.02) × 10−8 yr−1, respectively. Based on these results and some earlier research, we also discuss the evolutionary stages and the mechanisms of the period variation of these four HADS. © 2025, CC BY.

关键词： Pulsars

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Interacting Boson Problems Can Be QMA Hard

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Physical Review Letters 2010年第4期104卷 040501-040501页

作者： Tzu-Chieh Wei Michele Mosca Ashwin Nayak Institute for Quantum Computing University of Waterloo Waterloo Ontario Canada Department of Physics and Astronomy University of Waterloo Waterloo Ontario Canada Department of Physics and Astronomy University of British Columbia Vancouver British Columbia Canada Department of Combinatorics and Optimization University of Waterloo Waterloo Ontario Canada Perimeter Institute for Theoretical Physics Waterloo Ontario Canada

computing the ground-state energy of interacting electron problems has recently been shown to be hard for quantum Merlin Arthur (QMA), a quantum analogue of the complexity class NP. Fermionic problems are usually hard, a phenomenon widely attributed to the so-called sign problem. The corresponding bosonic problems are, according to conventional wisdom, tractable. Here, we demonstrate that the complexity of interacting boson problems is also QMA hard. Moreover, the bosonic version of N-representability problem is QMA complete. Consequently, these problems are unlikely to have efficient quantum algorithms.

关键词： Ground state

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On the Entanglement Cost of One-Shot Compression

arXiv

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arXiv 2019年

作者： Hadiashar, Shima Bab Nayak, Ashwin Department of Combinatorics and Optimization Institute for Quantum Computing University of Waterloo 200 University Ave. W. WaterlooONN2L 3G1 Canada

We revisit the task of compressing an ensemble of quantum states in the one-shot setting. The protocols achieving the best compression use shared entanglement that may be much larger than the original message, while others (with potentially larger communication cost) have entanglement cost bounded by the message length. This motivates the question as to whether entanglement is truly necessary for compression, and if so, how much of it is *** by questions in communication complexity, we lift certain restrictions imposed on compression protocols in tasks such as state-splitting and channel simulation. We show that an ensemble constructed by Jain, Radhakrishnan, and Sen (ICALP’03) saturates the known bounds on the sum of communication and entanglement costs, even with the relaxed compression protocols we *** ensemble and the associated one-way communication protocol have several remarkable properties. The ensemble is incompressible by more than a constant number of qubits without entanglement, even when constant error is allowed. Moreover, in the presence of entanglement, the communication cost of compression can be arbitrarily smaller than the entanglement cost. The quantum information cost of the protocol can thus be arbitrarily smaller than the cost of compression without entanglement. The ensemble can also be used to show the impossibility of reducing, via compression, the entanglement used in two-party protocols for computing Boolean functions. Copyright © 2019, The Authors. All rights reserved.

关键词： quantum entanglement

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quantum advantage from measurement-induced entanglement in random shallow circuits

arXiv

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arXiv 2024年

作者： Watts, Adam Bene Gosset, David Liu, Yinchen Soleimanifar, Mehdi Department of Pure Mathematics University of Waterloo Canada Institute for Quantum Computing University of Waterloo Canada Department of Combinatorics and Optimization University of Waterloo Canada Perimeter Institute for Theoretical Physics Waterloo Canada California Institute of Technology United States

We study random constant-depth quantum circuits in a two-dimensional architecture. While these circuits only produce entanglement between nearby qubits on the lattice, long-range entanglement can be generated by measuring a subset of the qubits of the output state. It is conjectured that this long-range measurement-induced entanglement (MIE) proliferates when the circuit depth is at least a constant critical value d∗. For circuits composed of Haar-random two-qubit gates, it is also believed that this coincides with a quantum advantage phase transition in the classical hardness of sampling from the output distribution. Here we provide evidence for a quantum advantage phase transition in the setting of random Clifford circuits. Our work extends the scope of recent separations between the computational power of constant-depth quantum and classical circuits, demonstrating that this kind of advantage is present in canonical random circuit sampling tasks. In particular, we show that in any architecture of random shallow Clifford circuits, the presence of long-range MIE gives rise to an unconditional quantum advantage. In contrast, any depth-d 2D quantum circuit that satisfies a short-range MIE property can be classically simulated efficiently and with depth O(d). Finally, we introduce a two-dimensional, depth-2, "coarse-grained" circuit architecture, composed of random Clifford gates acting on O(log(n)) qubits, for which we prove the existence of long-range MIE and establish an unconditional quantum advantage. © 2024, CC BY.

关键词： Qubits

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Fault-tolerant quantum error correction using error weight parities

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Physical Review A 2021年第4期104卷 042410-042410页

作者： Theerapat Tansuwannont Debbie Leung Institute for Quantum Computing and Department of Physics and Astronomy University of Waterloo Waterloo Ontario N2L 3G1 Canada Institute for Quantum Computing and Department of Combinatorics and Optimization University of Waterloo Waterloo Ontario N2L 3G1 Canada Perimeter Institute for Theoretical Physics Waterloo Ontario N2L 2Y5 Canada

In quantum error correction using imperfect primitives, errors of high weight arising from a few faults are major concerns since they might not be correctable by the quantum error correcting code. Fortunately, some errors of different weights are logically equivalent, and the same correction procedure is applicable to all equivalent errors; thus correcting high-weight errors is sometimes possible. In this work, we introduce a technique called weight parity error correction (WPEC) which can correct Pauli error of any weight in some stabilizer codes provided that the parity of the weight of the error is known. We show that the technique is applicable to concatenated codes constructed from the [[7,1,3]] Steane code or the [[23,1,7]] Golay code. We also provide a fault-tolerant error correction protocol using WPEC for the [[49,1,9]] concatenated Steane code which can correct up to three faults and requires only two ancillas.

关键词： quantum error correction

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quantum Algorithms for Hidden Nonlinear Structures

Quantum Algorithms for Hidden Nonlinear Structures

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Annual IEEE Symposium on Foundations of Computer Science

作者： Andrew M. Childs Leonard J. Schulman Umesh V. Vazirani Department of Combinatorics & Optimization and Institute for Quantum Computing University of Waterloo Waterloo ONT Canada Department of Computer Science California Institute of Technology Pasadena CA USA Computer Science Division University of California Berkeley CA USA

Attempts to find new quantum algorithms that outperform classical computation have focused primarily on the nonAbelian hidden subgroup problem, which generalizes the central problem solved by Shor's factoring algorithm. We suggest an alternative generalization, namely to problems of finding hidden nonlinear structures over finite fields. We give examples of two such problems that can be solved efficiently by a quantum computer, but not by a classical computer. We also give some positive results on the quantum query complexity of finding hidden nonlinear structures.

关键词： quantum computing Polynomials Interference Fourier transforms Computer science USA Councils Galois fields Vectors quantum mechanics Level set

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Classical algorithms for forrelation

arXiv

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arXiv 2021年

作者： Bravyi, Sergey Gosset, David Grier, Daniel Schaeffer, Luke IBM Quantum IBM T.J. Watson Research Center United States Institute for Quantum Computing University of Waterloo Canada Department of Combinatorics and Optimization University of Waterloo Canada Cheriton School of Computer Science University of Waterloo Canada

We study the forrelation problem: given a pair of n-bit Boolean functions f and g, estimate the correlation between f and the Fourier transform of g. This problem is known to provide the largest possible quantum speedup in terms of its query complexity and achieves the landmark oracle separation between the complexity class BQP and the Polynomial Hierarchy. Our first result is a classical algorithm for the forrelation problem which has runtime O(n2n/2). This is a nearly quadratic improvement over the best previously known algorithm. Secondly, we show that quantum query algorithm that makes t queries to an n-bit oracle can be simulated by classical query algorithm making only O(2n(1-1/2t)) queries. This fixes a gap in the literature arising from a recently discovered critical error in a previous proof;it matches recently established lower bounds (up to poly(n, t)) factors) and thus characterizes the maximal separation in query complexity between quantum and classical algorithms. Finally, we introduce a graph-based forrelation problem where n binary variables live at vertices of some fixed graph and the functions f, g are products of terms describing interactions between nearest-neighbor variables. We show that the graph-based forrelation problem can be solved on a classical computer in time O(n) for any bipartite graph, any planar graph, or, more generally, any graph which can be partitioned into two subgraphs of constant treewidth. The graph-based forrelation is simply related to the variational energy achieved by the quantum Approximate optimization Algorithm (QAOA) with two entangling layers and Ising-type cost functions. By exploiting the connection between QAOA and the graph-based forrelation we were able to simulate the recently proposed Recursive QAOA with two entangling layers and 225 qubits on a laptop computer. Copyright © 2021, The Authors. All rights reserved.

关键词： Graphic methods

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A rapidly mixing Markov chain from any gapped quantum many-body system

arXiv

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arXiv 2022年

作者： Bravyi, Sergey Carleo, Giuseppe Gosset, David Liu, Yinchen IBM Quantum IBM T.J. Watson Research Center Yorktown Heights United States Institute of Physics LausanneCH-1015 Switzerland Department of Combinatorics and Optimization Institute for Quantum Computing University of Waterloo Canada Perimeter Institute for Theoretical Physics Waterloo Canada

We consider the computational task of sampling a bit string x from a distribution π(x) = |〈x|ψ〉|2, where ψ is the unique ground state of a local Hamiltonian H. Our main result describes a direct link between the inverse spectral gap of H and the mixing time of an associated continuous-time Markov Chain with steady state π. The Markov Chain can be implemented efficiently whenever ratios of ground state amplitudes 〈y|ψ〉/〈x|ψ〉 are efficiently computable, the spectral gap of H is at least inverse polynomial in the system size, and the starting state of the chain satisfies a mild technical condition that can be efficiently checked. This extends a previously known relationship between sign-problem free Hamiltonians and Markov chains. The tool which enables this generalization is the so-called fixed-node Hamiltonian construction, previously used in quantum Monte Carlo simulations to address the fermionic sign problem. We implement the proposed sampling algorithm numerically and use it to sample from the ground state of Haldane-Shastry Hamiltonian with up to 56 qubits. We observe empirically that our Markov chain based on the fixed-node Hamiltonian mixes more rapidly than the standard Metropolis-Hastings Markov chain. © 2022, CC BY.

关键词： Hamiltonians

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Self-assembly of viral capsids via a Hamiltonian paths approach: The case of bacteriophage MS2

Self-assembly of viral capsids via a Hamiltonian paths appro...

引用

4th Conference on Foundations of Nanoscience: Self-Assembled Architectures and Devices, FNANO 2007

作者： Keef, T. Grayson, N. Severini, S. Twarock, R. Department of Mathematics University of York York YO10 5DD United Kingdom Department of Biology University of York York YO10 5DD United Kingdom Institute for Quantum Computing Department of Combinatorics and Optimisation University of Waterloo Waterloo ON Canada

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