An Algebraic Quantum Circuit Compression Algorithm for Hamiltonian Simulation

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 te...

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Bibliographic Details
Published in:SIAM journal on matrix analysis and applications Vol. 43; no. 3; pp. 1084 - 1108
Main Authors: Camps, Daan, Kökcü, Efekan, Bassman Oftelie, Lindsay, de Jong, Wibe A., Kemper, Alexander F., Van Beeumen, Roel
Format: Journal Article
Language:English
Published: United States Society for Industrial and Applied Mathematics (SIAM) 01.01.2022
Subjects:
algebraic circuit compression
free fermions
Hamiltonian simulation
MATHEMATICS AND COMPUTING
NISQ
quantum circuit synthesis
quantum computing
ISSN:0895-4798, 1095-7162
Online Access:Get full text
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Summary: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.
Bibliography:USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
AC02-05CH11231; SC0019469
USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division
USDOE Laboratory Directed Research and Development (LDRD) Program
ISSN:0895-4798
1095-7162
DOI:10.1137/21M1439298