• Open Access

Low-Depth Quantum Simulation of Materials

Ryan Babbush, Nathan Wiebe, Jarrod McClean, James McClain, Hartmut Neven, and Garnet Kin-Lic Chan
Phys. Rev. X 8, 011044 – Published 21 March 2018

Abstract

Quantum simulation of the electronic structure problem is one of the most researched applications of quantum computing. The majority of quantum algorithms for this problem encode the wavefunction using N Gaussian orbitals, leading to Hamiltonians with O(N4) second-quantized terms. We avoid this overhead and extend methods to condensed phase materials by utilizing a dual form of the plane wave basis which diagonalizes the potential operator, leading to a Hamiltonian representation with O(N2) second-quantized terms. Using this representation, we can implement single Trotter steps of the Hamiltonians with linear gate depth on a planar lattice. Properties of the basis allow us to deploy Trotter- and Taylor-series-based simulations with respective circuit depths of O(N7/2) and O˜(N8/3) for fixed charge densities. Variational algorithms also require significantly fewer measurements in this basis, ameliorating a primary challenge of that approach. While our approach applies to the simulation of arbitrary electronic structure problems, the basis sets explored in this work will be most practical for treating periodic systems, such as crystalline materials, in the near term. We conclude with a proposal to simulate the uniform electron gas (jellium) using a low-depth variational ansatz realizable on near-term quantum devices. From these results, we identify simulations of low-density jellium as a promising first setting to explore quantum supremacy in electronic structure.

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  • Received 2 June 2017
  • Revised 5 February 2018

DOI:https://doi.org/10.1103/PhysRevX.8.011044

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 & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Ryan Babbush1,*, Nathan Wiebe2, Jarrod McClean1, James McClain3, Hartmut Neven1, and Garnet Kin-Lic Chan3,†

  • 1Google Inc., Venice, California 90291, USA
  • 2Microsoft Research, Redmond, Washington 98052, USA
  • 3Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA

  • *Corresponding author. ryanbabbush@gmail.com
  • Corresponding author. gkc1000@gmail.com

Popular Summary

The ability to simulate on a computer the many ways that electrons can interact with one another and their parent atoms could allow researchers to understand and predict the properties of materials and chemicals without ever having to enter a laboratory. This would impact all areas of chemistry, condensed-matter physics, and materials science, and is of industrial relevance in the design and engineering of new pharmaceuticals, catalysts, and materials. Recently, quantum computers have emerged as promising tools for tackling this challenge in ways that traditional computers cannot. However, as efforts to demonstrate “quantum supremacy” increase, so has the need for practical quantum algorithms that require only a few circuit elements. We introduce a new quantum algorithm for simulating electronic structure that represents the problem in a way that is especially suited to quantum computation.

Our work extends the scope of earlier algorithms, which focused on molecules, to materials simulation. The computational cost of the algorithm is competitive with earlier techniques for small problems, and it improves on the cost of all prior algorithms for medium-scale systems of real interest and into the asymptotic regime. We conclude with a concrete proposal for studying the physics of the uniform electron gas on a quantum computer in a classically challenging regime—as a first test of the power of quantum algorithms.

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Vol. 8, Iss. 1 — January - March 2018

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