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quantum algorithms for Estimating quantum Entropies

Physical Review Applied 2023年第4期19卷 044041-044041页

作者： Youle Wang Benchi Zhao Xin Wang Institute for Quantum Computing Baidu Research 100193 Beijing China Center for Quantum Software and Information University of Technology Sydney New South Wales 2007 Australia

The von Neumann and quantum Rényi entropies characterize fundamental properties of quantum systems and lead to many theoretical and practical applications. quantum algorithms using a purified quantum query model can speed up quantum entropy estimation, while little is known about the complexity of using identical copies of the quantum state. This paper presents quantum entropy estimation algorithms with a cost of copies scaling polynomially in the rank of the state. In contrast to current methods that depend on the dimension of the system, our methods could provide exponential resource savings in the scenario of low-rank states. Furthermore, we show how to construct quantum circuits using primitive single-qubit or two-qubit gates efficiently and thus provide practical methods for estimating quantum entropies of quantum systems. We also conduct simulation experiments to show the effectiveness and noise robustness of our algorithms.

关键词： Entanglement entropy quantum algorithms quantum computation

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Dual-Frequency quantum Phase Estimation Mitigates the Spectral Leakage of quantum algorithms

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IEEE SIGNAL PROCESSING LETTERS 2022年 29卷 1222-1226页

作者： Xiong, Yifeng Ng, Soon Xin Long, Gui-Lu Hanzo, Lajos Univ Southampton Sch Elect & Comp Sci Southampton SO17 1BJ Hants England Tsinghua Univ Beijing 100084 Peoples R China

quantum phase estimation is an important component in diverse quantum algorithms. However, it suffers from spectral leakage, when the reciprocal of the record length is not an integer multiple of the unknown phase, which incurs an accuracy degradation. For the existing single-sample estimation scheme, window-based methods have been proposed for spectral leakage mitigation. As a further advance, we propose a dual-frequency estimator, which asymptotically approaches the Cramer-Rao bound, when multiple samples are available. Numerical results show that the proposed estimator outperforms the existing window-based methods, when the number of samples is sufficiently high.

关键词： Phase estimation Maximum likelihood estimation Signal processing algorithms Registers Probability distribution Frequency control Computers Algorithmic error mitigation dual-frequency estimator quantum algorithms quantum phase estimation

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quantum algorithms for optimal effective theory of many-body systems

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Physical Review A 2023年第3期108卷 032403-032403页

作者： Yongdan Yang Zongkang Zhang Xiaosi Xu Bing-Nan Lu Ying Li Graduate School of China Academy of Engineering Physics Beijing 100193 China

A common situation in quantum many-body physics is that the underlying theories are known but too complicated to solve efficiently. In such cases one usually builds simpler effective theories as low-energy or large-scale alternatives to the original theories. Here the central tasks are finding the optimal effective theories and proving their equivalence to the original theories. Recently quantum computing has shown the potential of solving quantum many-body systems by exploiting its inherent parallelism. It is thus an interesting topic to discuss the emergence of effective theories and design efficient tools for finding them based on the results from quantum computing. As the first step towards this direction, in this paper, we propose two approaches that apply quantum computing to find the optimal effective theory of a quantum many-body system given its full Hamiltonian. The first algorithm searches the space of effective Hamiltonians by quantum phase estimation and amplitude amplification. The second algorithm is based on a variational approach that is promising for near-future applications.

关键词： quantum algorithms quantum computation

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Contextuality and Sparsity in quantum algorithms

Contextuality and Sparsity in Quantum Algorithms

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作者： Kirby, William M. Tufts University

学位级别：Ph.D., Doctor of Philosophy

In this thesis we study quantum algorithms motivated by two unifying concepts: contextuality and sparsity. Contextuality is a characteristic feature of quantum mechanics, and identifying contextuality in quantum algorithms provides a means for distinguishing them from their classical counterparts. We first describe how contextuality may be identified in variational quantum eigensolvers (VQEs), which are a leading algorithm for noisy intermediate-scale quantum computers. We then show how to construct a classical phase-space model for any noncontextual Hamiltonian, which provides a classical simulation algorithm for noncontextual VQE and allows us to prove that the \textsc{noncontextual Hamiltonian problem} is only NP-complete, rather than QMA-complete. Finally, we describe an approximation method called contextual subspace VQE that permits us to partition a general Hamiltonian into a noncontextual part and a contextual part, and estimate its ground state energy using a technique that combines classical simulation of the noncontextual part with quantum simulation of the contextual part. By using more quantum resources (in qubits and simulated terms of the Hamiltonian), we can increase the accuracy of the approximation. We present results of simulating contextual subspace VQE on electronic structure Hamiltonians, and find that to reach chemical accuracy in most cases it requires fewer qubits and simulated terms than standard VQE. A Hamiltonian is sparse in some particular basis when it contains only polynomially-many nonzero entries in each row and column, meaning that each basis state only propagates into polynomially-many others at first order. Time evolution under sparse Hamiltonians is generally efficiently simulable by quantum algorithms provided efficient unitaries (oracles) exist that identify the locations and values of the nonzero matrix elements. We present two new results on sparse Hamiltonian simulation. The first is an extension of VQE to the sparse Hamilt

关键词： quantum algorithms quantum computing quantum contextuality quantum simulation Sparse matrices

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Controller-Based Energy-Aware Wireless Sensor Network Routing Using quantum algorithms

IEEE TRANSACTIONS ON QUANTUM ENGINEERING

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IEEE TRANSACTIONS ON quantum ENGINEERING 2022年第1期3卷 1页

作者： Chen, Jie Date, Prasanna Chancellor, Nicholas Atiquzzaman, Mohammed Sreenan, Cormac Univ Durham Phys Dept Durham DH1 3LE England Oak Ridge Natl Lab Oak Ridge TN 37830 USA Oklahoma Univ Comp Sci Dept Norman OK 73019 USA Univ Coll Cork Dept Comp Sci Cork T12 K8AF Ireland

Energy-efficient routing in wireless sensor networks has attracted attention from researchers in both academia and industry, most recently motivated by the opportunity to use software-defined network-inspired approaches. These problems are NP-hard, with algorithms needing computation time that scales faster than polynomials in the problem size. Consequently, heuristic algorithms are used in practice, which are unable to guarantee optimally. In this article, we show proof-of-principle for the use of a quantum annealing processor instead of a classical processor, to find optimal or nearly optimal solutions very quickly. Our preliminary results for small networks show that this approach using quantum computing has great promise and may open the door for other significant improvements in the efficacy of network algorithms.

关键词： Next generation networking routing protocols wireless sensor network quantum algorithms

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quantum algorithms for approximate function loading

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Physical Review Research 2023年第3期5卷 033114-033114页

作者： Gabriel Marin-Sanchez Javier Gonzalez-Conde Mikel Sanz Department of Physical Chemistry University of the Basque Country UPV/EHU Apartado 644 48080 Bilbao Spain EHU Quantum Center University of the Basque Country UPV/EHU Apartado 644 48080 Bilbao Spain IKERBASQUE Basque Foundation for Science Plaza Euskadi 5 48009 Bilbao Spain Basque Center for Applied Mathematics (BCAM) Alameda de Mazarredo 14 48009 Bilbao Spain

Loading classical data into quantum computers represents an essential stage in many relevant quantum algorithms, especially in the field of quantum machine learning. Therefore, the inefficiency of this loading process means a major bottleneck for the application of these algorithms. Here, we introduce two approximate quantum-state preparation methods for the noisy intermediate-scale quantum era inspired by the Grover-Rudolph algorithm, which partially solve the problem of loading real functions. Indeed, by allowing for an infidelity ε and under certain smoothness conditions, we prove that the complexity of the implementation of the Grover-Rudolph algorithm without ancillary qubits, first introduced by Möttönen et al., results into O(2k0(ε)), with n the number of qubits and k0(ε) asymptotically independent of n. This leads to a dramatic reduction in the number of required two-qubit gates. Aroused by this result, we also propose a variational algorithm capable of loading functions beyond the aforementioned smoothness conditions. Our variational Ansatz is explicitly tailored to the landscape of the function, leading to a quasioptimized number of hyperparameters. This allows us to achieve high fidelity in the loaded state with high speed convergence for the studied examples.

关键词： quantum algorithms quantum computation

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Benchmarking adaptative variational quantum algorithms on QUBO instances

Benchmarking adaptative variational quantum algorithms on QU...

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2023 International Workshop on AI for quantum and quantum for AI, AIQxQIA 2023

作者： Turati, Gloria Dacrema, Maurizio Ferrari Cremonesi, Paolo Politecnico di Milano Italy

Adaptative Variational quantum algorithms (adapt-VQAs) are innovative algorithms that can dynamically adjust their circuit by adding and removing gates. While various adaptative methods have been proposed, a comprehensive comparison among them is still missing in the literature. This paper aims to fill this gap by benchmarking three adaptative algorithms against the fixed-structure QAOA. Our findings reveal that the adaptative methods generate circuits leading to solutions with approximation ratios comparable with QAOA, but use fewer gates. This leads to a decrease in computational time and an increased resilience to noise. © 2022 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).

关键词： Adaptative VQAs Benchmark NISQ quantum algorithms QUBO

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Time- and Query-optimal quantum algorithms Based on Decision Trees

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ACM TRANSACTIONS ON quantum COMPUTING 2022年第4期3卷 1–31页

作者： Beigi, Salman Taghavi, Leila Tajdini, Artin Phanous Res & Innovat Ctr QuOne Lab Tehran Iran

It has recently been shown that starting with a classical query algorithm (decision tree) and a guessing algorithm that tries to predict the query answers, we can design a quantum algorithm with query complexity O( root GT) where T is the query complexity of the classical algorithm (depth of the decision tree) and G is the maximum number of wrong answers by the guessing algorithm [3, 14]. In this article, we show that, given some constraints on the classical algorithms, this quantum algorithm can be implemented in time O-similar to (root GT). Our algorithm is based on non-binary span programs and their efficient implementation. We conclude that various graph-theoretic problems including bipartiteness, cycle detection, and topological sort can be solved in time O(n(3/2) log(2) n) and with O(n(3/2) ) quantum queries. Moreover, finding a maximal matching can be solved with O(n(3/2)) quantum queries in time O(n(3/2) log(2) n), and maximum bipartite matching can be solved in time O(n(2) log(2) n).

关键词： quantum query complexity quantum algorithms span programs quantum time complexity

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Simulating Strongly Coupled Many-Body Systems With quantum algorithms

Simulating Strongly Coupled Many-Body Systems With Quantum A...

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作者： Hlatshwayo, Manqoba Q. Western Michigan University

学位级别：Ph.D., Doctor of Philosophy

The complexity of the nuclear many-body problem is a severe obstacle to finding a general and accurate numerical approach needed to simulate medium-mass and heavy nuclei. Even with the advent of exascale classical computing, the impediment of exponential growth of the Hilbert space renders the problem intractable for most classical calculations. In the last few years, quantum algorithms have become an attractive alternative for practitioners because quantum computers are more efficient in simulating quantum physics than classical computers. While a fully fault-tolerant universal quantum computer will not be realized soon, this dissertation explores quantum algorithms for simulating nuclear physics suitable for noisy intermediate-scale quantum (NISQ) devices. To achieve high simulation accuracy on the currently available NISQ hardware, one must design noise-resilient algorithms and utilize techniques that suppress noise errors while maximizing quantum gate fidelity. This work satisfies this desideratum by employing variational quantum algorithms, error-mitigation techniques, and numerically engineered high-fidelity custom gates. First, an efficient encoding scheme for the Lipkin model is proposed, and the quantum equation of motion algorithm is shown to have a special quantum benefit for simulating strongly coupled many-body systems. Second, microwave pulses to perform custom two-qubit gates on a superconducting quantum computer are engineered. This results in significantly higher gate fidelity and lower execution duration than the default quantum hardware gates. Lastly, simulations are done for model nuclear Hamiltonians, and the results from using IBM superconducting quantum computers are in close agreement with classical calculations. Therefore, this study contributes toward transformative nuclear physics simulations on near-term quantum computers.

关键词： Nuclear theory quantum algorithms quantum equation of motion Optimal control Classical computers

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quantum algorithms for Testing Hamiltonian Symmetry

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Physical Review Letters 2022年第16期129卷 160503-160503页

作者： Margarite L. LaBorde Mark M. Wilde Hearne Institute for Theoretical Physics Department of Physics and Astronomy and Center for Computation and Technology Louisiana State University Baton Rouge Louisiana 70803 USA

Symmetries in a Hamiltonian play an important role in quantum physics because they correspond directly with conserved quantities of the related system. In this Letter, we propose quantum algorithms capable of testing whether a Hamiltonian exhibits symmetry with respect to a group. We demonstrate that familiar expressions of Hamiltonian symmetry in quantum mechanics correspond directly with the acceptance probabilities of our algorithms. We execute one of our symmetry-testing algorithms on existing quantum computers for simple examples of both symmetric and asymmetric cases.

关键词： quantum computation quantum information processing Group theory quantum algorithms

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