An Algebraic Quantum Circuit Compression Algorithm for Hamiltonian Simulation

Camps, Daan; Kökcü, Efekan; Bassman Oftelie, Lindsay; de Jong, Wibe A.; Kemper, Alexander F.; Van Beeumen, Roel

doi:10.1137/21m1439298

An Algebraic Quantum Circuit Compression Algorithm for Hamiltonian Simulation

Journal Article · Mon Jul 11 00:00:00 EDT 2022 · SIAM Journal on Matrix Analysis and Applications

DOI:https://doi.org/10.1137/21m1439298· OSTI ID:1884777

^[1]; Kökcü, Efekan ^[2]; Bassman Oftelie, Lindsay ^[1]; de Jong, Wibe A. ^[1]; Kemper, Alexander F. ^[2]; ^[1]

Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
North Carolina State Univ., Raleigh, NC (United States)

Quantum computing is a promising technology that harnesses the peculiarities of quantum mechanics to deliver computational speedups for some problems that are intractable to solve on a classical computer. Current generation noisy intermediate-scale quantum (NISQ) computers are severely limited in terms of chip size and error rates. Shallow quantum circuits with uncomplicated topologies are essential for successful applications in the NISQ era. In this work, based on matrix analysis, we derive localized circuit transformations to efficiently compress quantum circuits for simulation of certain spin Hamiltonians known as free fermions. The depth of the compressed circuits is independent of simulation time and grows linearly with the number of spins. The proposed numerical circuit compression algorithm behaves backward stable and scales cubically in the number of spins enabling circuit synthesis beyond O(10³) spins. The resulting quantum circuits have a simple nearest-neighbor topology, which makes them ideally suited for NISQ devices.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division

Grant/Contract Number:: AC02-05CH11231; SC0019469

OSTI ID:: 1884777

Journal Information:: SIAM Journal on Matrix Analysis and Applications, Journal Name: SIAM Journal on Matrix Analysis and Applications Journal Issue: 3 Vol. 43; ISSN 0895-4798

Publisher:: Society for Industrial and Applied Mathematics (SIAM)Copyright Statement

Country of Publication:: United States

Language:: English

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Hamiltonian simulation
97 MATHEMATICS AND COMPUTING
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algebraic circuit compression
free fermions
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