检索结果-内蒙古大学图书馆

quantum optimization via four-body Rydberg gates

学校读者我要写书评

暂无评论

arXiv 2021年

作者： Dlaska, Clemens Ender, Kilian Mbeng, Glen Bigan Kruckenhauser, Andreas Lechner, Wolfgang van Bijnen, Rick Institute for Theoretical Physics University of Innsbruck InnsbruckA-6020 Austria Institute for Quantum Optics and Quantum Information Austrian Academy of Sciences InnsbruckA-6020 Austria Parity Quantum Computing GmbH InnsbruckA-6020 Austria Center for Quantum Physics Faculty of Mathematics Computer Science and Physics University of Innsbruck Innsbruck6020 Austria

There is a large ongoing research effort towards obtaining a quantum advantage in the solution of combinatorial optimization problems on near-term quantum devices. A particularly promising platform for testing and developing quantum optimization algorithms are arrays of trapped neutral atoms, laser-coupled to highly excited Rydberg states. However, encoding combinatorial optimization problems in atomic arrays is challenging due to the limited inter-qubit connectivity given by their native finite-range interactions. Here we propose and analyze a fast, high fidelity four-body Rydberg parity gate, enabling a direct and straightforward implementation of the Lechner-Hauke-Zoller (LHZ) scheme and its recent generalization, the parity architecture, a scalable architecture for encoding arbitrarily connected interaction graphs. Our gate relies on onetime-optimized adiabatic laser pulses and is fully programmable by adjusting two hold-times during operation. We numerically demonstrate an implementation of the quantum approximate optimization algorithm (QAOA) for a small scale test problem. Our approach allows for efficient execution of variational optimization steps with a constant number of system manipulations, independent of the system size, thus paving the way for experimental investigations of QAOA beyond the reach of numerical simulations. Copyright © 2021, The Authors. All rights reserved.

关键词： quantum theory

quantum Dense Coding Network using Multimode Squeezed States of Light

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Patra, Ayan Gupta, Rivu Roy, Saptarshi Das, Tamoghna Sen, Aditi Harish-Chandra Research Institute A CI of Homi Bhabha National Institute Chhatnag Road Jhunsi Prayagraj211019 India Quantum Information and Computation Initiative Department of Computer Science The University of Hong Kong Pokfulam Road Hong Kong HKU-Oxford Joint Laboratory for Quantum Information and Computation University of Gdańsk Gdańsk80-952 Poland International Centre for Theory of Quantum Technologies University of Gdańsk Gdańsk80-952 Poland

We present a framework of a multimode dense coding network with multiple senders and a single receiver using continuous variable systems. The protocol is scalable to arbitrary numbers of modes with the encoding being displacements while the decoding involves homodyne measurements of the modes after they are combined in a pairwise manner by a sequence of beam splitters, thereby exhibiting its potentiality to implement in laboratories with currently available resources. We compute the closed-form expression of the dense coding capacity for the cases of two and three senders that involve sharing of three- and four-mode states respectively. The dense coding capacity is computed with the constraint of fixed average energy transmission when the modes of the sender are transferred to the receiver after the encoding operation. In both cases, we demonstrate the quantum advantage of the protocol using paradigmatic classes of three- and four-mode states. The quantum advantage increases with the increase in the amount of energy that is allowed to be transmitted from the senders to the receiver. Copyright © 2022, The Authors. All rights reserved.

关键词： Network coding

A Complexity-Reduced Block-Selective Algebraic Multigrid Method for Implicitly Coupled Velocity-Pressure System on High Performance computers

学校读者我要写书评

暂无评论

SSRN

SSRN 2023年

作者： Liang, Yuechao Guo, Xiao-Wei Li, Chao Yuan, Fan Song, Min Zhang, Qingyang Chen, Xinhai Liu, Jie Science and Technology on Parallel and Distributed Processing Laboratory National University of Defense Technology Changsha410073 China Laboratory of Digitizing Software for Frontier Equipment National University of Defense Technology Changsha410073 China Institute for Quantum Information State Key Laboratory of High Performance Computing College of Computer Science and Technology National University of Defense Technology Changsha410073 China School of Mathematics and Computational Sciences Xiangtan University Xiangtan411105 China College of Computer Science and Technology National University of Defense Technology Changsha410073 China

The implicitly coupled pressure-based algorithm is widely acknowledged for its superior convergence and robustness in solving incompressible flow problems. However, the increased expansion scale of equations and difficulty in solving the resulting equation system has limited the widespread use of the coupling algorithm. This paper presents an optimized block-SAMG method, referred to as Red-SAMG, to significantly reduce computational complexity and memory consumption. Our approach employs a parallel modified independent set algorithm, allowing each process to perform matrix coarsening individually. An aggressive coarsening strategy further reduces complexity to address larger-scale problems. We conducted numerical experiments on a serial two-dimensional backward-facing step case and a parallel three-dimensional tunnel between rod bundles in the reactor core problem. The results demonstrate that the Red-SAMG method with aggressive coarsening reduces solution time by 12\% on the backward-facing step case. For large-scale three-dimensional problems under the same parallel conditions, the Red-SAMG method shortens the solution time by 14\% compared to the existing SAMG method. The Red-SAMG method with aggressive coarsening further reduces solution time by 49\%. Our optimized Red-SAMG method effectively reduces the complexity of the linear system arising from the implicitly coupled algorithm. The aggressive coarsening strategy also represents a significant advancement in improving the computational efficiency of the SAMG method. © 2023, The Authors. All rights reserved.

关键词： Coarsening

Robust Qubit Mapping Algorithm via Double-Source Optimal Routing on Large quantum Circuits

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Cheng, Chin-Yi Yang, Chien-Yi Kuo, Yi-Hsiang Wang, Ren-Chu Cheng, Hao-Chung Huang, Chung-Yang Department of Electrical Engineering National Taiwan University Taiwan Department of Computer Science and Engineering University of California San Diego United States Graduate Institute of Electronics Engineering National Taiwan University Taiwan College of Computing The Georgia Institute of Technology United States Department of Electrical Engineering Graduate Institute of Communication Engineering National Taiwan University Taiwan Center for Quantum Science and Engineering National Taiwan University Taiwan Physics Division and Mathematics Division National Center for Theoretical Sciences Taiwan Quantum Computing Center Taiwan Department of Electrical Engineering National Taiwan University Taiwan

Qubit Mapping is a critical aspect of implementing quantum circuits on real hardware devices. Currently, the existing algorithms for qubit mapping encounter difficulties when dealing with larger circuit sizes involving hundreds of qubits. In this paper, we introduce an innovative qubit mapping algorithm, Duostra, tailored to address the challenge of implementing large-scale quantum circuits on real hardware devices with limited connectivity. Duostra operates by efficiently determining optimal paths for double-qubit gates and inserting SWAP gates accordingly to implement the double-qubit operations on real devices. Together with two heuristic scheduling algorithms, the Limitedly-Exhausitive (LE) Search and the Shortest-Path (SP) Estimation, it yields results of good quality within a reasonable runtime, thereby striving toward achieving quantum advantage. Experimental results showcase our algorithm's superiority, especially for large circuits beyond the NISQ era. For example, on large circuits with more than 50 qubits, we can reduce the mapping cost on an average 21.75% over the virtual best results among QMAP, t|ket〉, Qiskit and SABRE. Besides, for mid-size circuits such as the SABRE-large benchmark, we improve the mapping costs by 4.5%, 5.2%, 16.3%, 20.7%, and 25.7%, when compared to QMAP, TOQM, t|ket〉, Qiskit, and SABRE, respectively. Copyright © 2022, The Authors. All rights reserved.

关键词： Qubits

Online Self-Concordant and Relatively Smooth Minimization, With Applications to Online Portfolio Selection and Learning quantum States

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Tsai, Chung-En Cheng, Hao-Chung Li, Yen-Huan Department of Computer Science and Information Engineering National Taiwan University Taiwan Department of Electrical Engineering Graduate Institute of Communication Engineering National Taiwan University Taiwan Department of Mathematics National Taiwan University Taiwan Quantum Computing Centre United Kingdom Center for Quantum Science and Engineering National Taiwan University Taiwan Physics Division National Center for Theoretical Sciences Taipei10617 Taiwan

Consider an online convex optimization problem where the loss functions are self-concordant barriers, smooth relative to a convex function h, and possibly non-Lipschitz. We analyze the regret of online mirror descent with h. Then, based on the result, we prove the following in a unified manner. Denote by T the time horizon and d the parameter dimension. 1. For online portfolio selection, the regret of (Equation), a variant of exponentiated gradient due to Helmbold et al. [1], is (Equation) when T > 4d/logd. This improves on the original Õ(T3/4d1/2) regret bound for (Equation). 2. For online portfolio selection, the regret of online mirror descent with the logarithmic barrier is (Equation). The regret bound is the same as that of Soft-Bayes due to Orseau et al. [2] up to logarithmic terms. 3. For online learning quantum states with the logarithmic loss, the regret of online mirror descent with the log-determinant function is also (Equation). Its per-iteration time is shorter than all existing algorithms we know. Copyright © 2022, The Authors. All rights reserved.

关键词： Mirrors

Fast quantum algorithm for differential equations

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Bagherimehrab, Mohsen Nakaji, Kouhei Wiebe, Nathan Aspuru-Guzik, Alán Chemical Physics Theory Group Department of Chemistry University of Toronto TorontoON Canada Department of Computer Science University of Toronto TorontoON Canada 1-1-1 Umezono Ibaraki Tsukuba305-8568 Japan Quantum Computing Center Keio University 3-14-1 Hiyoshi Kohoku-ku Kanagawa Yokohama223-8522 Japan Pacific Northwest National Laboratory RichlandWA United States Canadian Institute for Advanced Research TorontoON Canada Vector Institute for Artificial Intelligence TorontoON Canada Department of Chemical Engineering & Applied Chemistry University of Toronto TorontoON Canada Department of Materials Science & Engineering University of Toronto TorontoON Canada

Partial differential equations (PDEs) are ubiquitous in science and engineering. Prior quantum algorithms for solving the system of linear algebraic equations obtained from discretizing a PDE have a computational complexity that scales at least linearly with the condition number κ of the matrices involved in the computation. For many practical applications, κ scales polynomially with the size N of the matrices, rendering a polynomial-in-N complexity for these algorithms. Here we present a quantum algorithm with a complexity that is polylogarithmic in N but is independent of κ for a large class of PDEs. Our algorithm generates a quantum state that enables extracting features of the solution. Central to our methodology is using a wavelet basis as an auxiliary system of coordinates in which the condition number of associated matrices is independent of N by a simple diagonal preconditioner. We present numerical simulations showing the effect of the wavelet preconditioner for several differential equations. Our work could provide a practical way to boost the performance of quantum-simulation algorithms where standard methods are used for discretization. © 2023, CC BY.

关键词： Matrix algebra

Provably efficient machine learning for quantum many-body problems

学校读者我要写书评

暂无评论

arXiv 2021年

作者： Huang, Hsin-Yuan Kueng, Richard Torlai, Giacomo Albert, Victor V. Preskill, John Institute for Quantum Information and Matter Department of Computing and Mathematical Sciences Caltech PasadenaCA United States Institute for Integrated Circuits Johannes Kepler University Linz Austria AWS Center for Quantum Computing PasadenaCA United States Joint Center for Quantum Information and Computer Science National Institute of Standards and Technology University of Maryland College ParkMD United States

Classical machine learning (ML) provides a potentially powerful approach to solving challenging quantum many-body problems in physics and chemistry. However, the advantages of ML over more traditional methods have not been firmly established. In this work, we prove that classical ML algorithms can efficiently predict ground state properties of gapped Hamiltonians in finite spatial dimensions, after learning from data obtained by measuring other Hamiltonians in the same quantum phase of matter. In contrast, under widely accepted complexity theory assumptions, classical algorithms that do not learn from data cannot achieve the same guarantee. We also prove that classical ML algorithms can efficiently classify a wide range of quantum phases of matter. Our arguments are based on the concept of a classical shadow, a succinct classical description of a many-body quantum state that can be constructed in feasible quantum experiments and be used to predict many properties of the state. Extensive numerical experiments corroborate our theoretical results in a variety of scenarios, including Rydberg atom systems, 2D random Heisenberg models, symmetry-protected topological phases, and topologically ordered phases. © 2021, CC BY.

关键词： Machine learning

Fundamental Limits of Prompt Tuning Transformers: Universality, Capacity and Efficiency

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Hu, Jerry Yao-Chieh Wang, Wei-Po Gilani, Ammar Li, Chenyang Song, Zhao Liu, Han Center for Foundation Models and Generative AI Northwestern University EvanstonIL60208 United States Department of Computer Science Northwestern University EvanstonIL60208 United States Department of Physics National Taiwan University Taipei10617 Taiwan Maynooth International School of Engineering Fuzhou University Fuzhou350108 China Simons Institute for the Theory of Computing UC Berkeley BerkeleyCA94720 United States Department of Statistics and Data Science Northwestern University EvanstonIL60208 United States

We investigate the statistical and computational limits of prompt tuning for transformer-based foundation models. Our key contributions are prompt tuning on single-head transformers with only a single self-attention layer: (i) is universal, and (ii) supports efficient (even nearlylinear time) algorithms under the Strong Exponential Time Hypothesis (SETH). Statistically, we prove that prompt tuning on such simplest possible transformers are universal approximators for sequence-to-sequence Lipschitz functions. In addition, we provide an exponential-in-dL and -in- (1/ϵ) lower bound on the required soft-prompt tokens for prompt tuning to memorize any dataset with 1-layer, 1-head transformers. Computationally, we identify a phase transition in the efficiency of prompt tuning, determined by the norm of the soft-prompt-induced keys and queries, and provide an upper bound criterion. Beyond this criterion, no sub-quadratic (efficient) algorithm for prompt tuning exists under SETH. Within this criterion, we showcase our theory by proving the existence of almost-linear time prompt tuning inference algorithms. These fundamental limits provide important necessary conditions for designing expressive and efficient prompt tuning methods for practitioners. © 2024, CC BY-NC-SA.

关键词： Distribution transformers

Designing quantum Annealing Schedules using Bayesian Optimization

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Finžgar, Jernej Rudi Schuetz, Martin J.A. Brubaker, J. Kyle Nishimori, Hidetoshi Katzgraber, Helmut G. BMW AG Munich Germany Technical University Munich School of CIT Department of Computer Science Garching Germany Amazon Quantum Solutions Lab SeattleWA United States AWS Center for Quantum Computing PasadenaCA United States International Research Frontiers Initiative Tokyo Institute of Technology Shibaura Minato-ku Tokyo108-0023 Japan Graduate School of Information Sciences Tohoku University Sendai980-8579 Japan Saitama Wako351-0198 Japan

We propose and analyze the use of Bayesian optimization techniques to design quantum annealing schedules with minimal user and resource requirements. We showcase our scheme with results for two paradigmatic spin models. We find that Bayesian optimization is able to identify schedules resulting in fidelities several orders of magnitude better than standard protocols for both quantum and reverse annealing, as applied to the p-spin model. We also show that our scheme can help improve the design of hybrid quantum algorithms for hard combinatorial optimization problems, such as the maximum independent set problem, and illustrate these results via experiments on a neutral atom quantum processor available on Amazon Braket. Copyright © 2023, The Authors. All rights reserved.

关键词： quantum theory