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Linear Combination of Hamiltonian Simulation for Nonunitary Dynamics with Optimal State Preparation Cost

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Physical Review Letters 2023年第15期131卷 150603-150603页

作者： Dong An Jin-Peng Liu Lin Lin Joint Center for Quantum Information and Computer Science University of Maryland College Park Maryland 20742 USA Department of Mathematics University of California Berkeley California 94720 USA Simons Institute for the Theory of Computing University of California Berkeley California 94720 USA Center for Theoretical Physics Massachusetts Institute of Technology Cambridge Massachusetts 02139 USA Lawrence Berkeley National Laboratory Applied Mathematics and Computational Research Division Berkeley California 94720 USA Challenge Institute for Quantum Computation University of California Berkeley California 94720 USA

We propose a simple method for simulating a general class of nonunitary dynamics as a linear combination of Hamiltonian simulation (LCHS) problems. LCHS does not rely on converting the problem into a dilated linear system problem or on the spectral mapping theorem. The latter is the mathematical foundation of many quantum algorithms for solving a wide variety of tasks involving nonunitary processes, such as the quantum singular value transformation. The LCHS method can achieve optimal cost in terms of state preparation. We also demonstrate an application for open quantum dynamics simulation using the complex absorbing potential method with near-optimal dependence on all parameters.

关键词： Open quantum systems quantum algorithms quantum algorithms & computation quantum simulation Differential equations

Differentiable quantum computing for Large-scale Linear Control

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arXiv 2024年

作者： Clayton, Connor Leng, Jiaqi Yang, Gengzhi Qiao, Yi-Ling Lin, Ming C. Wu, Xiaodi Joint Center for Quantum Information and Computer Science University of Maryland United States Department of Computer Science University of Maryland United States Department of Mathematics University of Maryland United States Center for Machine Learning University of Maryland United States Department of Mathematics Simons Institute The Theory of Computing UC Berkeley United States

As industrial models and designs grow increasingly complex, the demand for optimal control of large-scale dynamical systems has significantly increased. However, traditional methods for optimal control incur significant overhead as problem dimensions grow. In this paper, we introduce an end-to-end quantum algorithm for linear-quadratic control with provable speedups. Our algorithm, based on a policy gradient method, incorporates a novel quantum subroutine for solving the matrix Lyapunov equation. Specifically, we build a quantum-assisted differentiable simulator for efficient gradient estimation that is more accurate and robust than classical methods relying on stochastic approximation. Compared to the classical approaches, our method achieves a super-quadratic speedup. To the best of our knowledge, this is the first end-to-end quantum application to linear control problems with provable quantum advantage. Copyright © 2024, The Authors. All rights reserved.

关键词： Stochastic systems

Efficient quantum algorithm for nonlinear reaction-diffusion equations and energy estimation

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arXiv 2022年

作者： Liu, Jin-Peng An, Dong Fang, Di Wang, Jiasu Low, Guang Hao Jordan, Stephen Joint Center for Quantum Information and Computer Science University of Maryland MD United States Simons Institute for the Theory of Computing BerkeleyCA United States Department of Mathematics University of California BerkeleyCA United States Center for Theoretical Physics Massachusetts Institute of Technology CambridgeMA United States Department of Mathematics and Duke Quantum Center Duke University DurhamNC United States Microsoft Quantum RedmondWA United States Google Quantum AI Santa BarbaraCA United States

Nonlinear differential equations exhibit rich phenomena in many fields but are notoriously challenging to solve. Recently, Liu et al. [1] demonstrated the first efficient quantum algorithm for dissipative quadratic differential equations under the condition R 2 norm. Here we develop an efficient quantum algorithm based on [1] for reaction-diffusion equations, a class of nonlinear partial differential equations (PDEs). To achieve this, we improve upon the Carleman linearization approach introduced in [1] to obtain a faster convergence rate under the condition RD D measures the ratio of nonlinearity to dissipation using the ∞ norm. Since RD is independent of the number of spatial grid points n while R increases with n, the criterion RD © 2022, CC BY.

关键词： Kinetic energy

Small correlation is sufficient for optimal noisy quantum metrology

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arXiv 2024年

作者： Yin, Chao Albert, Victor V. Zhou, Sisi Department of Physics Center for Theory of Quantum Matter University of Colorado BoulderCO80309 United States Joint Center for Quantum Information and Computer Science NIST University of Maryland College ParkMD United States Perimeter Institute for Theoretical Physics WaterlooONN2L 2Y5 Canada Department of Physics and Astronomy Institute for Quantum Computing University of Waterloo ONN2L 2Y5 Canada

We propose a class of metrological resource states whose quantum Fisher information scales optimally in both system size and noise rate. In these states, qubits are partitioned into sensing groups with relatively large correlations within a group but small correlations between groups. The states are obtainable from local Hamiltonian evolution, and we design a metrologically optimal and efficient measurement protocol utilizing time-reversed dynamics and single-qubit local measurements. Using quantum domino dynamics, we also present a protocol free of the time-reversal step that has an estimation error roughly twice the best possible value. Copyright © 2024, The Authors. All rights reserved.

关键词： Qubits

quantum Gravity in the Lab. I. Teleportation by Size and Traversable Wormholes

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PRX quantum 2023年第1期4卷 010320-010320页

作者： Adam R. Brown Hrant Gharibyan Stefan Leichenauer Henry W. Lin Sepehr Nezami Grant Salton Leonard Susskind Brian Swingle Michael Walter Google Mountain View California 94043 USA Department of Physics Stanford University Stanford California 94305 USA Institute for Quantum Information and Matter Caltech Pasadena California 91125 USA Physics Department Princeton University Princeton New Jersey 08540 USA Amazon Quantum Solutions Lab Seattle Washington 98170 USA Amazon Web Services (AWS) Center for Quantum Computing Pasadena California 91125 USA Condensed Matter Theory Center Joint Center for Quantum Information and Computer Science Maryland Center for Fundamental Physics and Department of Physics University of Maryland College Park Maryland 20742 USA Faculty of Computer Science Ruhr University Bochum D-44801 Bochum Germany Korteweg–de Vries Institute for Mathematics Institute for Theoretical Physics Institute for Logic Language and Computation & QuSoft University of Amsterdam 1090 GE Amsterdam Kingdom of the Netherlands

With the long-term goal of studying models of quantum gravity in the lab, we propose holographic teleportation protocols that can be readily executed in table-top experiments. These protocols exhibit similar behavior to that seen in the recent traversable-wormhole constructions of Gao et al. [J. High Energy Phys., 2017, 151 (2017)] and Maldacena et al. [Fortschr. Phys., 65, 1700034 (2017)]: information that is scrambled into one half of an entangled system will, following a weak coupling between the two halves, unscramble into the other half. We introduce the concept of teleportation by size to capture how the physics of operator-size growth naturally leads to information transmission. The transmission of a signal through a semiclassical holographic wormhole corresponds to a rather special property of the operator-size distribution that we call size winding. For more general systems (which may not have a clean emergent geometry), we argue that imperfect size winding is a generalization of the traversable-wormhole phenomenon. In addition, a form of signaling continues to function at high temperature and at large times for generic chaotic systems, even though it does not correspond to a signal going through a geometrical wormhole but, rather, to an interference effect involving macroscopically different emergent geometries. Finally, we outline implementations that are feasible with current technology in two experimental platforms: Rydberg-atom arrays and trapped ions.

关键词： quantum algorithms quantum entanglement quantum gravity quantum teleportation

A quantum central path algorithm for linear optimization

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arXiv 2023年

作者： Augustino, Brandon Leng, Jiaqi Nannicini, Giacomo Terlaky, Tamás Wu, Xiaodi Sloan School of Management Massachusetts Institute of Technology United States Simons Institute for the Theory of Computing Department of Mathematics University of California Berkeley United States Department of Industrial and Systems Engineering University of Southern California United States Department of Industrial and Systems Engineering Lehigh University United States Quantum Computing and Optimization Lab Lehigh University United States Department of Mathematics University of Maryland College Park United States Department of Computer Science University of Maryland College Park United States Joint Center for Quantum Information and Computer Science University of Maryland United States

We propose a novel quantum algorithm for solving linear optimization problems by quantum-mechanical simulation of the central path. While interior point methods follow the central path with an iterative algorithm that works with successive linearizations of the perturbed KKT conditions, we perform a single simulation working directly with the nonlinear complementarity equations. This approach yields an algorithm for solving linear optimization problems involving m constraints and n variables to Ε-optimality using O (√m + n · RΕ1) queries to an oracle that evaluates a potential function, where R1 is an 1-norm upper bound on the size of the optimal solution. In the standard gate model (i.e., without access to quantum RAM) our algorithm can obtain highly-precise solutions to LO problems using at most O (√m + n · nnz(A)RΕ1) elementary gates, where nnz(A) is the total number of non-zero elements found in the constraint matrix. © 2023, CC BY.

关键词： Optimization algorithms

QHDOPT: A Software for Nonlinear Optimization with quantum Hamiltonian Descent

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arXiv 2024年

作者： Kushnir, Samuel Leng, Jiaqi Peng, Yuxiang Fan, Lei Wu, Xiaodi Department of Computer Science University of Maryland United States Department of Mathematics University of Maryland United States Joint Center for Quantum Information and Computer Science University of Maryland United States Department of Mathematics Simons Institute for the Theory of Computing University of California Berkeley United States Department of Engineering Technology University of Houston United States Department of Electrical and Computer Engineering University of Houston United States

We develop an open-source, end-to-end software (named QHDOPT), which can solve nonlinear optimization problems using the quantum Hamiltonian descent (QHD) algorithm. QHDOPT offers an accessible interface and automatically maps tasks to various supported quantum backends (i.e., quantum hardware machines). These features enable users, even those without prior knowledge or experience in quantum computing, to utilize the power of existing quantum devices for nonlinear and nonconvex optimization tasks. In its intermediate compilation layer, QHDOPT employs SimuQ, an efficient interface for Hamiltonian-oriented programming, to facilitate multiple algorithmic specifications and ensure compatible cross-hardware deployment. The detailed documentation of QHDOPT is available at https://***/jiaqileng/QHDOPT. Copyright © 2024, The Authors. All rights reserved.

关键词： quantum computers

Distributed exact quantum algorithms for Deutsch-Jozsa problem

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arXiv 2023年

作者： Li, Hao Qiu, Daowen Luo, Le Institute of Quantum Computing and Computer Theory School of Computer Science and Engineering Sun Yat-sen University Guangzhou510006 China The Guangdong Key Laboratory of Information Security Technology Sun Yat-sen University 510006 China School of Physics and Astronomy Sun Yat-sen University Zhuhai519082 China QUDOOR Technologies Inc. Guangzhou China

Deutsch-Jozsa (DJ) problem is one of the most important problems demonstrating the power of quantum algorithm. DJ problem can be described as a Boolean function f: {0, 1}n → {0, 1} with promising it is either constant or balanced, and the purpose is to determine which type it is. DJ algorithm can solve it exactly with one query. In this paper, we first discover the inherent structure of DJ problem in distributed scenario by giving a number of equivalence characterizations between f being constant (balanced) and some properties of f’s subfunctions, and then we propose three distributed exact quantum algorithms for solving DJ problem. Our algorithms have essential acceleration over distributed classical deterministic algorithm, and can be extended to the case of multiple computing nodes. Compared with DJ algorithm, our algorithms can reduce the number of qubits and the depth of circuit implementing a single query operator. Therefore, we find that the structure of problem should be clarified for designing distributed quantum algorithm to solve it. Copyright © 2023, The Authors. All rights reserved.

关键词： Boolean functions

quantum Phase Estimation by Compressed Sensing

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arXiv 2023年

作者： Yi, Changhao Zhou, Cunlu Takahashi, Jun State Key Laboratory of Surface Physics Department of Physics Center for Field Theory and Particle Physics Fudan University Shanghai China Institute for Nanoelectronic Devices and Quantum Computing Fudan University Shanghai China Shanghai Research Center for Quantum Sciences Shanghai China Department of Computer Science & Institut Quantique Université de Sherbrooke QC Canada Center for Quantum Information and Control Department of Physics and Astronomy University of New Mexico NM United States Institute of Solid State Physics University of Tokyo Chiba Japan

As a signal recovery algorithm, compressed sensing is particularly effective when the data has low complexity and samples are scarce, which aligns natually with the task of quantum phase estimation (QPE) on early fault-tolerant quantum computers. In this work, we present a new Heisenberg-limited, robust QPE algorithm based on compressed sensing, which requires only sparse and discrete sampling of times. Specifically, given multiple copies of a suitable initial state and queries to a specific unitary matrix, our algorithm can recover the phase with a total runtime of O(ϵ−1poly log(ϵ−1)), where ϵ is the desired accuracy. Additionally, the maximum runtime satisfies Tmaxϵ π, making it comparable to state-of-the-art algorithms. Furthermore, our result resolves the basis mismatch problem in certain cases by introducing an additional parameter to the traditional compressed sensing framework. © 2023, CC BY.

关键词： Fault tolerant computer systems