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Low rank representations for quantum simulation of electronic structure

Motta, Mario and Ye, Erika and McClean, Jarrod R. and Li, Zhendong and Minnich, Austin J. and Babbush, Ryan and Chan, Garnet Kin-Lic (2018) Low rank representations for quantum simulation of electronic structure. . (Submitted)

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The quantum simulation of quantum chemistry is a promising application of quantum computers. However, for N molecular orbitals, the O(N^4) gate complexity of performing Hamiltonian and unitary Coupled Cluster Trotter steps makes simulation based on such primitives challenging. We substantially reduce the gate complexity of such primitives through a two-step low-rank factorization of the Hamiltonian and cluster operator, accompanied by truncation of small terms. Using truncations that incur errors below chemical accuracy, we are able to perform Trotter steps of the arbitrary basis electronic structure Hamiltonian with O(N^3) gate complexity in small simulations, which reduces to O(N^2 logN) gate complexity in the asymptotic regime, while our unitary Coupled Cluster Trotter step has O(N^3) gate complexity as a function of increasing basis size for a given molecule. In the case of the Hamiltonian Trotter step, these circuits have O(N^2) depth on a linearly connected array, an improvement over the O(N^3) scaling assuming no truncation. As a practical example, we show that a chemically accurate Hamiltonian Trotter step for a 50 qubit molecular simulation can be carried out in the molecular orbital basis with as few as 4,000 layers of parallel nearest-neighbor two-qubit gates, consisting of fewer than 100,000 non-Clifford rotations. We also apply our algorithm to iron-sulfur clusters relevant for elucidating the mode of action of metalloenzymes.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper
Motta, Mario0000-0003-1647-9864
Li, Zhendong0000-0002-0683-6293
Minnich, Austin J.0000-0002-9671-9540
Chan, Garnet Kin-Lic0000-0001-8009-6038
Additional Information:RB, GKC and MM contributed to the conception of the project; MM, JRM, ZL, RB and GKC contributed to the theoretical analysis; MM, ZL, EY and GKC contributed to the electronic structure calculations; MM, JRM, EY, RB and GKC contributed to the gate counts analysis. All authors contributed to the drafting of the paper. MM, ZL, and GKC (theoretical analysis, electronic structure calculations, drafting of the paper) were supported by NSF grant number 1839204. EY (gate counts, electronic structure calculations) was supported by a Google graduate fellowship and a Google award to GKC. AM (drafting of the paper) was supported by NSF grant CBET CAREER number 1254213. MM gratefully acknowledges Shiwei Zhang and James Shee for valuable interaction.
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Record Number:CaltechAUTHORS:20181029-100728436
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90459
Deposited By: Tony Diaz
Deposited On:29 Oct 2018 17:41
Last Modified:03 Oct 2019 20:25

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