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Misiewicz J, Evangelista FA. Implementation of the Projective Quantum Eigensolver on a Quantum Computer. J Phys Chem A 2024; 128:2220-2235. [PMID: 38452262 PMCID: PMC10961848 DOI: 10.1021/acs.jpca.3c07429] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2023] [Revised: 01/29/2024] [Accepted: 02/20/2024] [Indexed: 03/09/2024]
Abstract
We study the performance of our previously proposed projective quantum eigensolver (PQE) on IBM's quantum hardware in conjunction with error mitigation techniques. For a single qubit model of H2, we find that we are able to obtain energies within 4 millihartree (2.5 kcal/mol) of the exact energy along the entire potential energy curve, with the accuracy limited by both the stochastic error and the inconsistent performance of the IBM devices. We find that an optimization algorithm using direct inversion of the iterative subspace can converge swiftly, even to excited states, but stochastic noise can prompt large parameter updates. For the 4-site transverse-field Ising model at its critical point, PQE with an appropriate application of qubit tapering can recover 99% of the correlation energy, even after discarding several parameters. The large number of CNOT gates needed for the additional parameters introduces a concomitant error that, on the IBM devices, results in a loss of accuracy despite the increased expressivity of the trial state. Error extrapolation techniques and tapering or postselection are recommended to mitigate errors in PQE hardware experiments.
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Affiliation(s)
| | - Francesco A. Evangelista
- Department of Chemistry and
Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
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Fauseweh B. Quantum many-body simulations on digital quantum computers: State-of-the-art and future challenges. Nat Commun 2024; 15:2123. [PMID: 38459040 PMCID: PMC10923891 DOI: 10.1038/s41467-024-46402-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2023] [Accepted: 02/14/2024] [Indexed: 03/10/2024] Open
Abstract
Simulating quantum many-body systems is a key application for emerging quantum processors. While analog quantum simulation has already demonstrated quantum advantage, its digital counterpart has recently become the focus of intense research interest due to the availability of devices that aim to realize general-purpose quantum computers. In this perspective, we give a selective overview of the currently pursued approaches, review the advances in digital quantum simulation by comparing non-variational with variational approaches and identify hardware and algorithmic challenges. Based on this review, the question arises: What are the most promising problems that can be tackled with digital quantum simulation? We argue that problems of a qualitative nature are much more suitable for near-term devices then approaches aiming purely for a quantitative accuracy improvement.
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Affiliation(s)
- Benedikt Fauseweh
- Institute for Software Technology, German Aerospace Center (DLR), Linder Höhe, 51147, Cologne, Germany.
- Department of Physics, TU Dortmund University, Otto-Hahn-Str. 4, 44227, Dortmund, Germany.
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Mazzola G. Quantum computing for chemistry and physics applications from a Monte Carlo perspective. J Chem Phys 2024; 160:010901. [PMID: 38165101 DOI: 10.1063/5.0173591] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2023] [Accepted: 10/18/2023] [Indexed: 01/03/2024] Open
Abstract
This Perspective focuses on the several overlaps between quantum algorithms and Monte Carlo methods in the domains of physics and chemistry. We will analyze the challenges and possibilities of integrating established quantum Monte Carlo solutions into quantum algorithms. These include refined energy estimators, parameter optimization, real and imaginary-time dynamics, and variational circuits. Conversely, we will review new ideas for utilizing quantum hardware to accelerate the sampling in statistical classical models, with applications in physics, chemistry, optimization, and machine learning. This review aims to be accessible to both communities and intends to foster further algorithmic developments at the intersection of quantum computing and Monte Carlo methods. Most of the works discussed in this Perspective have emerged within the last two years, indicating a rapidly growing interest in this promising area of research.
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Affiliation(s)
- Guglielmo Mazzola
- Institute for Computational Science, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
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Kovyrshin A, Skogh M, Tornberg L, Broo A, Mensa S, Sahin E, Symons BCB, Crain J, Tavernelli I. Nonadiabatic Nuclear-Electron Dynamics: A Quantum Computing Approach. J Phys Chem Lett 2023; 14:7065-7072. [PMID: 37527463 DOI: 10.1021/acs.jpclett.3c01589] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/03/2023]
Abstract
Coupled quantum electron-nuclear dynamics is often associated with the Born-Huang expansion of the molecular wave function and the appearance of nonadiabatic effects as a perturbation. On the other hand, native multicomponent representations of electrons and nuclei also exist, which do not rely on any a priori approximation. However, their implementation is hampered by prohibitive scaling. Consequently, quantum computers offer a unique opportunity for extending their use to larger systems. Here, we propose a quantum algorithm for simulating the time-evolution of molecular systems and apply it to proton transfer dynamics in malonaldehyde, described as a rigid scaffold. The proposed quantum algorithm can be easily generalized to include the explicit dynamics of the classically described molecular scaffold. We show how entanglement between electronic and nuclear degrees of freedom can persist over long times if electrons do not follow the nuclear displacement adiabatically. The proposed quantum algorithm may become a valid candidate for the study of such phenomena when sufficiently powerful quantum computers become available.
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Affiliation(s)
- Arseny Kovyrshin
- Data Science and Modelling, Pharmaceutical Sciences, R&D, AstraZeneca Gothenburg, Pepparedsleden 1, Molndal SE-431 83, Sweden
| | - Mårten Skogh
- Data Science and Modelling, Pharmaceutical Sciences, R&D, AstraZeneca Gothenburg, Pepparedsleden 1, Molndal SE-431 83, Sweden
- Department of Chemistry and Chemical Engineering, Chalmers University of Technology, 412 96 Gothenburg, Sweden
| | - Lars Tornberg
- Data Science and Modelling, Pharmaceutical Sciences, R&D, AstraZeneca Gothenburg, Pepparedsleden 1, Molndal SE-431 83, Sweden
| | - Anders Broo
- Data Science and Modelling, Pharmaceutical Sciences, R&D, AstraZeneca Gothenburg, Pepparedsleden 1, Molndal SE-431 83, Sweden
| | - Stefano Mensa
- The Hartree Centre, STFC, Sci-Tech Daresbury, Warrington WA4 4AD, United Kingdom
| | - Emre Sahin
- The Hartree Centre, STFC, Sci-Tech Daresbury, Warrington WA4 4AD, United Kingdom
| | - Benjamin C B Symons
- The Hartree Centre, STFC, Sci-Tech Daresbury, Warrington WA4 4AD, United Kingdom
| | - Jason Crain
- IBM Research Europe, Hartree Centre STFC Laboratory, Sci-Tech Daresbury, Warrington WA4 4AD, United Kingdom
- Department of Biochemistry, University of Oxford, Oxford OX1 3QU, U.K
| | - Ivano Tavernelli
- IBM Quantum, IBM Research Europe-Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
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