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Physical Review A 2022年第4期106卷 042443-042443页

作者： Andrew Jena Scott N. Genin Michele Mosca Department of Combinatorics and Optimization University of Waterloo Waterloo N2L 3G1 ON Canada Institute for Quantum Computing University of Waterloo Waterloo N2L 3G1 ON Canada OTI Lumionics Inc. 3415 American Drive Unit 1 Mississauga L4V 1T4 ON Canada Perimeter Institute for Theoretical Physics Waterloo N2L 2Y5 ON Canada

Measuring the expectation value of Pauli operators on prepared quantum states is a fundamental task in a multitude of quantum algorithms. Simultaneously measuring sets of Pauli operators allows for fewer measurements and an overall speedup of the measurement process. Using results from coloring random graphs, we give evidence for an upper bound on the expected minimum number of simultaneously measurable parts necessary to partition a set of Pauli operators. By expanding our gate set to allow multiqubit Clifford gates before measurement, we were able to cut down the number of measurements considerably compared to previous approaches. We conjecture that this improvement is, in general, linear with respect to the lengths of the Pauli operators. We conclude by demonstrating the feasibility of this approach by implementing the variational quantum eigensolver on the Aspen-4-4Q-A quantum processor unit. In doing so, we calculate the ground-state energies of H2 using fewer measurements than is possible with single-qubit gates with no statistically significant difference in accuracy.

关键词： Electronic structure Electronic structure of atoms & molecules quantum algorithms quantum computation

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

ALKPU: an active learning method for the DeePMD model with Kalman filter

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arXiv 2024年

作者： Li, Haibo Wu, Xingxing Liu, Liping Wang, Lin-Wang Wang, Long Tan, Guangming Jia, Weile School of Mathematics and Statistics The University of Melbourne MelbourneVIC3010 Australia Technology Department Longxun Quantum Inc. Beijing100192 China Institute of Semiconductors Chinese Academy of Sciences Beijing100083 China Computing System Optimization Lab Huawei Technologies Co. Ltd. Beijing100094 China State Key Lab of Processors Institute of Computing Technology Chinese Academy of Sciences Beijing100190 China University of Chinese Academy of Sciences Beijing101408 China

Neural network force field models such as DeePMD have enabled highly efficient large-scale molecular dynamics simulations with ab initio accuracy. However, building such models heavily depends on the training data obtained by costly electronic structure calculations, thereby it is crucial to carefully select and label the most representative configurations during model training to improve both extrapolation capability and training efficiency. To address this challenge, based on the Kalman filter theory we propose the Kalman Prediction Uncertainty (KPU) to quantify uncertainty of the model’s prediction. With KPU we design the Active Learning by KPU (ALKPU) method, which can efficiently select representative configurations that should be labelled during model training. We prove that ALKPU locally leads to the fastest reduction of model’s uncertainty, which reveals its rationality as a general active learning method. We test the ALKPU method using various physical system simulations and demonstrate that it can efficiently coverage the system’s configuration space. Our work demonstrates the benefits of ALKPU as a novel active learning method, enhancing training efficiency and reducing computational resource demands. © 2024, CC BY.

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Capacity approaching coding for low noise interactive quantum communication part I: Large alphabets

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arXiv 2020年

作者： Leung, Debbie Nayak, Ashwin Shayeghi, Ala Touchette, Dave Yao, Penghui Yu, Nengkun Department of Combinatorics and Optimization Institute for Quantum Computing University of Waterloo and Perimeter Institute Department of Combinatorics and Optimization Institute for Quantum Computing University of Waterloo Department of Computer Science Institut Quantique Université de Sherbrooke Institute for Quantum Computing University of Waterloo Perimeter Institute State Key Laboratory for Novel Software Technology Nanjing University Centre for Quantum Software and Information Faculty of Engineering and Information Technology University of Technology Sydney

We consider the problem of implementing two-party interactive quantum communication over noisy channels, a necessary endeavor if we wish to fully reap quantum advantages for communication. For an arbitrary protocol with n messages, designed for a noiseless qudit channel over a poly (n) size alphabet, our main result is a simulation method that fails with probability less than 2-θ(n∈) and uses a qudit channel over the same alphabet n(1 + θ(√∈)) times, of which an ∈ fraction can be corrupted adversarially. The simulation is thus capacity achieving to leading order, and we conjecture that it is optimal up to a constant factor in the √ ∈ term. Furthermore, the simulation is in a model that does not require pre-shared resources such as randomness or entanglement between the communicating parties. Our work improves over the best previously known quantum result where the overhead is a non-explicit large constant [Brassard et al., FOCS'14] for low ∈. Copyright © 2020, The Authors. All rights reserved.

关键词： quantum communication

A polynomial time and space heuristic algorithm for T-count

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arXiv 2020年

作者： Mosca, Michele Mukhopadhyay, Priyanka Institute for Quantum Computing University of Waterloo Canada Department of Combinatorics and Optimization University of Waterloo Canada Perimeter Institute for Theoretical Physics Waterloo Canada

An important part of reaping computational advantage from a quantum computer is to reduce the quantum resources needed to implement a desired quantum algorithm. quantum algorithms that are too large to be practical on noisy intermediate scale quantum (NISQ) devices will require fault-tolerant error correction. This work focuses on reducing the physical cost of implementing quantum algorithms when using the state-of-the-art fault-tolerant quantum error correcting codes, in particular, those for which implementing the T gate consumes vastly more resources than the other gates in the gate set. More specifically, in this paper we consider the group of unitaries that can be exactly implemented by a quantum circuit consisting of the Clifford+T gate set. The Clifford+T gate set is a universal gate set and in this group, using state-of-the-art surface codes, the T gate is by far the most expensive component to implement fault-tolerantly. So it is important to minimize the number of T gates necessary for a fault-tolerant implementation. Our primary interest is to compute a circuit for a given n-qubit unitary U, using the minimum possible number of T gates (called the T-count of unitary U). We consider the problem COUNT-T, the optimization version of which aims to find the T-count of U. In its decision version the goal is to decide if the T-count is at most some positive integer m. Given an oracle for COUNT-T, we can compute a T-count-optimal circuit in time polynomial in the T-count and dimension of U. We give a provable classical algorithm that solves COUNT-T (decision) in time O (Equation presented), where N = 2n and c ≥ 2. This gives a space-time trade-off for solving this problem with variants of meet-in-the-middle techniques. We also introduce an asymptotically faster multiplication method that shaves a factor of N0.7457 off of the overall complexity. Lastly, beyond our improvements to the rigorous algorithm, we give a heuristic algorithm that outputs a T-count-optimal

关键词： Heuristic algorithms

Entanglement cost for infinite-dimensional physical systems

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arXiv 2024年

作者： Yamasaki, Hayata Kuroiwa, Kohdai Hayden, Patrick Lami, Ludovico Department of Physics Graduate School of Science The Univerisity of Tokyo 7–3–1 Hongo Bunkyo-ku Tokyo113–0033 Japan Institute for Quantum Computing Department of Combinatorics and Optimization University of Waterloo ONN2L 3G1 Canada Perimeter Institute for Theoretical Physics ONN2L 2Y5 Canada Stanford Institute for Theoretical Physics Stanford University StanfordCA94305 United States QuSoft Science Park 123 Amsterdam1098 XG Netherlands Korteweg–de Vries Institute for Mathematics University of Amsterdam Science Park 105–107 Amsterdam1098 XG Netherlands Institute for Theoretical Physics University of Amsterdam Science Park 904 Amsterdam1098 XH Netherlands

We prove that the entanglement cost equals the regularized entanglement of formation for any infinite-dimensional quantum state pAB with finite quantum entropy on at least one of the subsystems A or B. This generalizes a foundational result in quantum information theory that was previously formulated only for operations and states on finite-dimensional systems. The extension to infinite dimensions is nontrivial because the conventional tools for establishing both the direct and converse bounds, i.e., strong typically, monotonicity, and asymptotic continuity, are no longer directly applicable. To address this problem, we construct a new entanglement dilution protocol for infinite-dimensional states implementable by local operations and a finite amount of one-way classical communication (one-way LOCC), using weak and strong typicality multiple times. We also prove the optimality of this protocol among all protocols even under infinite-dimensional separable operations by developing an argument based on alternative forms of monotonicity and asymptotic continuity of the entanglement of formation for infinite-dimensional states. Along the way, we derive a new integral representation for the quantum entropy of infinite-dimensional states, which we believe to be of independent interest. Our results allow us to fully characterize an important operational entanglement measure — the entanglement cost — for all infinite-dimensional physical systems. Copyright © 2024, The Authors. All rights reserved.

关键词： quantum optics

Solving an Industrially Relevant quantum Chemistry Problem on quantum Hardware

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arXiv 2024年

作者： Nützel, Ludwig Gresch, Alexander Hehn, Lukas Marti, Lucas Freund, Robert Steiner, Alex Marciniak, Christian D. Eckstein, Timo Stockinger, Nina Wolf, Stefan Monz, Thomas Kühn, Michael Hartmann, Michael J. Department of Physics Friedrich-Alexander Universität Erlangen-Nürnberg Erlangen Germany Heinrich Heine University Düsseldorf Faculty of Mathematics and Natural Sciences Germany Institute for Quantum Inspired and Quantum Optimization Hamburg University of Technology Germany BASF SE Next Generation Computing Pfalzgrafenstr. 1 Ludwigshafen67061 Germany Universität Innsbruck Institut für Experimentalphysik Innsbruck Austria Max Planck Institute for the Science of Light Staudtstraße 2 Erlangen91058 Germany Department of Chemistry Technical University of Munich Garching Germany Alpine Quantum Technologies GmbH Innsbruck Austria

quantum chemical calculations are among the most promising applications for quantum computing. Implementations of dedicated quantum algorithms on available quantum hardware were so far, however, mostly limited to comparatively simple systems without strong correlations. As such, they can also be addressed by classically efficient single-reference methods. In this work, we calculate the lowest energy eigenvalue of active space Hamiltonians of industrially relevant and strongly correlated metal chelates on trapped ion quantum hardware, and integrate the results into a typical industrial quantum chemical workflow to arrive at chemically meaningful properties. We are able to achieve chemical accuracy by training a variational quantum algorithm on quantum hardware, followed by a classical diagonalization in the subspace of states measured as outputs of the quantum circuit. This approach is particularly measurement-efficient, requiring 600 single-shot measurements per cost function evaluation on a ten qubit system, and allows for efficient post-processing to handle erroneous runs. © 2024, CC BY-NC-ND.

关键词： Cost functions

Improved Approximation Algorithms for Bounded-Degree Local Hamiltonians

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Physical Review Letters 2021年第25期127卷 250502-250502页

作者： Anurag Anshu David Gosset Karen J. Morenz Korol Mehdi Soleimanifar Department of EECS & Challenge Institute for Quantum Computation University of California Berkeley California 94720 USA and Simons Institute for the Theory of Computing Berkeley California 94720 USA Department of Combinatorics and Optimization and Institute for Quantum Computing University of Waterloo Waterloo N2L 3G1 Canada Perimeter Institute for Theoretical Physics Waterloo N2L 2Y5 Canada Department of Chemistry University of Toronto Toronto M5S 3H6 Canada Center for Theoretical Physics Massachusetts Institute of Technology Cambridge 02139 USA

The low-temperature properties of interacting quantum systems are believed to require exponential resources to compute in the general case. Quantifying the extent to which such properties can be approximated using efficient algorithms remains a significant open challenge. Here, we consider the task of approximating the ground state energy of two-local quantum Hamiltonians with bounded-degree interaction graphs. Most existing algorithms optimize the energy over the set of product states. We propose and analyze a family of shallow quantum circuits that can be used to improve the approximation ratio achieved by a given product state. The algorithm takes as input an n-qubit product state with variance Var and improves its energy by an amount proportional to Var2/n. In a typical case, this results in an extensive improvement in the estimated energy. We extend our results to k-local Hamiltonians and entangled initial states.

关键词： quantum algorithms quantum simulation

Exploring the unexpected: Disharmonized harmonic pulsation modes in high-amplitude δ Scuti stars

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arXiv 2024年

作者： Xue, Hui-Fang Niu, Jia-Shu 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 Institute of Theoretical Physics Shanxi University Taiyuan030006 China State Key Laboratory of Quantum Optics and Quantum Optics Devices Shanxi University Taiyuan030006 China Collaborative Innovation Center of Extreme Optics Shanxi University Taiyuan Shanxi030006 China

Harmonics are a ubiquitous feature across various pulsating stars. They are traditionally viewed as mere replicas of the independent primary pulsation modes and have thus been excluded from asteroseismological models. Recent research, however, has uncovered a significant discrepancy: in high-amplitude δ Scuti (HADS) stars, harmonics exhibit uncorrelated variations in amplitude and frequency relative to their independent primary pulsation modes. The nature of these disharmonized harmonics is a question of critical importance. In our study we analysed five triple-mode HADS stars observed by the Transiting Exoplanet Survey Satellite (TESS) and discovered some pervasive patterns of disharmonized harmonics in both the fundamental ( f0) and first overtone ( f1) pulsation modes. Intriguingly, through an in-depth frequency interaction analysis of V1393 Cen, we identified 2 f1as an independent pulsation mode, distinct from f1, and identified it as the progenitor of the frequency variations observed in 3 f1, 4 f1, 5 f1, and 6 f1. Similar behaviour can be found in DO CMi and GSC 06047-00749, in which 2 f1and 3 f1are the independent pulsation modes, respectively. Notably, we found an interesting pattern when decomposing the harmonics that might suggest a generation process of harmonics. These findings serve as a new window on the research of harmonics, which remains a hidden corner of contemporary asteroseismology. © 2024, CC BY.

关键词： Stars

Optimality of the pretty good measurement for port-based teleportation

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arXiv 2020年

作者： Leditzky, Felix Department of Mathematics IQUIST University of Illinois Urbana-Champaign Institute for Quantum Computing Department of Combinatorics and Optimization University of Waterloo Perimeter Institute for Theoretical Physics Canada

Port-based teleportation (PBT) is a protocol in which Alice teleports an unknown quantum state to Bob using measurements on a shared entangled multipartite state called the port state and forward classical communication. In this paper, we give an explicit proof that the so-called pretty good measurement, or square-root measurement, is optimal for the PBT protocol with independent copies of maximally entangled states as the port state. We then show that the very same measurement remains optimal even when the port state is optimized to yield the best possible PBT protocol. Hence, there is one particular pretty good measurement achieving the optimal performance in both cases. The following well-known facts are key ingredients in the proofs of these results: (i) the natural symmetries of PBT, leading to a description in terms of representation-theoretic data;(ii) the operational equivalence of PBT with certain state discrimination problems, which allows us to employ duality of the associated semidefinite programs. Along the way, we rederive the representation-theoretic formulas for the performance of PBT protocols proved in [Studzinski et al., 2017] and [Mozrzymas et al., 2018] using only standard techniques from the representation theory of the unitary and symmetric groups. Providing a simplified derivation of these beautiful formulas is one of the main goals of this paper. Copyright © 2020, The Authors. All rights reserved.

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