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Low Depth Quantum Simulation of Electronic Structure

Babbush, Ryan and Wiebe, Nathan and McClean, Jarrod and McClain, James and Neven, Hartmut and Chan, Garnet Kin-Lic (2017) Low Depth Quantum Simulation of Electronic Structure. , Pasadena, CA. (Submitted)

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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 the condensed phase 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 Õ(N^(8/3)) for fixed charge densities - both are large asymptotic improvements over all prior results. Variational algorithms also require significantly fewer measurements to find the mean energy in this basis, ameliorating a primary challenge of that approach. 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:Report or Paper (Discussion Paper)
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Chan, Garnet Kin-Lic0000-0001-8009-6038
Additional Information:The authors thank Eddie Farhi, Sergio Boixo, John Martinis, Ian Kivlichan, Craig Gidney, Dominic Berry, PierreLuc Dallaire-Demers, Peter Love and Matthias Troyer for helpful comments about an early draft. We thank Alireza Shabani for helping to initiate the collaboration between Google and Caltech. The authors thank Wei Sun for contributing code to the open source package FermiLib which was used to verify some equations of this paper.
Record Number:CaltechAUTHORS:20170615-082208152
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78237
Deposited By: Donna Wrublewski
Deposited On:15 Jun 2017 16:37
Last Modified:03 Oct 2019 18:06

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