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Quantum Simulation of Electronic Structure with Linear Depth and Connectivity

Kivlichan, Ian D. and McClean, Jarrod and Wiebe, Nathan and Gidney, Craig and Aspuru-Guzik, Alán and Chan, Garnet Kin-Lic and Babbush, Ryan (2018) Quantum Simulation of Electronic Structure with Linear Depth and Connectivity. Physical Review Letters, 120 (11). Art. No. 110501. ISSN 0031-9007.

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As physical implementations of quantum architectures emerge, it is increasingly important to consider the cost of algorithms for practical connectivities between qubits. We show that by using an arrangement of gates that we term the fermionic swap network, we can simulate a Trotter step of the electronic structure Hamiltonian in exactly N depth and with N^2/2 two-qubit entangling gates, and prepare arbitrary Slater determinants in at most N/2 depth, all assuming only a minimal, linearly connected architecture. We conjecture that no explicit Trotter step of the electronic structure Hamiltonian is possible with fewer entangling gates, even with arbitrary connectivities. These results represent significant practical improvements on the cost of most Trotter-based algorithms for both variational and phase-estimation-based simulation of quantum chemistry.

Item Type:Article
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URLURL TypeDescription Paper
Chan, Garnet Kin-Lic0000-0001-8009-6038
Additional Information:© 2018 American Physical Society. Received 16 November 2017; revised manuscript received 20 January 2018; published 13 March 2018. We thank Zhang Jiang, Sergio Boixo, Eddie Farhi, James McClain, Kevin Sung, and Guang Hao Low for helpful discussions. I. D. K. acknowledges partial support from the National Sciences and Engineering Research Council of Canada. A. A.-G. acknowledges the Army Research Office under Grant No. W911NF-15-1-0256. We thank contributors to the open source library OpenFermion [51] which was used to verify some equations of this work.
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Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Army Research Office (ARO)W911NF-15-1-0256
Issue or Number:11
Record Number:CaltechAUTHORS:20171120-105229610
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83340
Deposited By: Donna Wrublewski
Deposited On:20 Nov 2017 19:10
Last Modified:03 Oct 2019 19:05

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