• Open Access

Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator

Cornelius Hempel, Christine Maier, Jonathan Romero, Jarrod McClean, Thomas Monz, Heng Shen, Petar Jurcevic, Ben P. Lanyon, Peter Love, Ryan Babbush, Alán Aspuru-Guzik, Rainer Blatt, and Christian F. Roos
Phys. Rev. X 8, 031022 – Published 24 July 2018

Abstract

Quantum-classical hybrid algorithms are emerging as promising candidates for near-term practical applications of quantum information processors in a wide variety of fields ranging from chemistry to physics and materials science. We report on the experimental implementation of such an algorithm to solve a quantum chemistry problem, using a digital quantum simulator based on trapped ions. Specifically, we implement the variational quantum eigensolver algorithm to calculate the molecular ground-state energies of two simple molecules and experimentally demonstrate and compare different encoding methods using up to four qubits. Furthermore, we discuss the impact of measurement noise as well as mitigation strategies and indicate the potential for adaptive implementations focused on reaching chemical accuracy, which may serve as a cross-platform benchmark for multiqubit quantum simulators.

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  • Received 27 March 2018
  • Revised 10 May 2018

DOI:https://doi.org/10.1103/PhysRevX.8.031022

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Cornelius Hempel1,3,*, Christine Maier1,2, Jonathan Romero4, Jarrod McClean5, Thomas Monz2, Heng Shen1,2, Petar Jurcevic1,2, Ben P. Lanyon1,2, Peter Love6, Ryan Babbush5, Alán Aspuru-Guzik4, Rainer Blatt1,2, and Christian F. Roos1,2

  • 1Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Technikerstraße 21A, 6020 Innsbruck, Austria
  • 2Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25, 6020 Innsbruck, Austria
  • 3ARC Centre of Excellence for Engineered Quantum Systems, School of Physics, University of Sydney, New South Wales 2006, Australia
  • 4Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, Massachusetts 02138, USA
  • 5Google Inc., 340 Main Street, Venice, California 90291, USA
  • 6Department of Physics and Astronomy, Tufts University, 574 Boston Avenue, Medford, Massachusetts 02155, USA

  • *Corresponding author. cornelius.hempel@gmail.com

Popular Summary

Quantum computers are rapidly approaching the point at which they will become useful for practical calculations of challenging problems in chemistry, physics, and materials science. As work progresses on realizing ever more complex quantum computers, it is important to also develop algorithms that make use of these improving devices. This is where quantum-classical hybrid algorithms can help. These algorithms leverage the unique capabilities of quantum devices by incorporating them into classical calculations. Here, we implement the first scalable trapped-ion demonstration of one such algorithm known as the variational quantum eigensolver (VQE).

We use up to four qubits encoded in trapped calcium ions to calculate the ground-state energy of molecular hydrogen and lithium hydride, and we directly compare two commonly used strategies to translate the fermionic electronic structure problem to a form that can be implemented on a gate-based quantum simulator. We particularly focus on the challenges brought about by errors on both the quantum and classical sides of the VQE algorithm, and we demonstrate ways around these obstacles.

With future algorithmic and experimental improvements, the VQE approach may be the first to unlock a quantum advantage over existing classical techniques in this highly sought-after near-term quantum computing application.

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Vol. 8, Iss. 3 — July - September 2018

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