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Low-Depth Quantum Simulation of Materials

Babbush, Ryan and Wiebe, Nathan and McClean, Jarrod and McClain, James and Neven, Hartmut and Chan, Garnet Kin-Lic (2018) Low-Depth Quantum Simulation of Materials. Physical Review X, 8 (1). Art. No. 011044. ISSN 2160-3308.

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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(N^4) 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(N^2) 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(N^(7/2)) and O(N^(8/3)) 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.

Item Type:Article
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Chan, Garnet Kin-Lic0000-0001-8009-6038
Alternate Title:Low Depth Quantum Simulation of Electronic Structure
Additional Information:© 2018 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. Received 2 June 2017; revised manuscript received 5 February 2018; published 21 March 2018. The authors thank Eddie Farhi, Sergio Boixo, John Martinis, Ian Kivlichan, Craig Gidney, Dominic Berry, Murphy Yuezhen Niu, Pierre-Luc Dallaire-Demers, Peter Love, and Matthias Troyer for helpful comments about an early draft. We thank Alireza Shabani for helping initiate the collaboration between Google and Caltech. The authors thank Wei Sun for contributing code to the open source quantum simulation library OpenFermion [112,113], which was used to verify some equations of this paper. G. K. C. was supported by the Simons Foundation via the Simons collaboration on the many electron problem and the Simons investigator program in theoretical physics.
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Simons FoundationUNSPECIFIED
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Record Number:CaltechAUTHORS:20180327-103500774
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:85452
Deposited By: Tony Diaz
Deposited On:27 Mar 2018 18:31
Last Modified:03 Oct 2019 19:31

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