Algebraic compression of quantum circuits for Hamiltonian evolution

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

doi:10.1103/physreva.105.032420

Algebraic compression of quantum circuits for Hamiltonian evolution

Journal Article · Thu Mar 10 00:00:00 EST 2022 · Physical Review A

DOI:https://doi.org/10.1103/physreva.105.032420· OSTI ID:1860355

^[1]; ^[2]; Bassman, Lindsay ^[2]; Freericks, J. K. ^[3]; de Jong, Wibe A. ^[2]; ^[2]; ^[1]

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

Here unitary evolution under a time-dependent Hamiltonian is a key component of simulation on quantum hardware. Synthesizing the corresponding quantum circuit is typically done by breaking the evolution into small time steps, also known as Trotterization, which leads to circuits the depth of which scales with the number of steps. When the circuit elements are limited to a subset of SU(4) - or equivalently, when the Hamiltonian may be mapped onto free fermionic models - several identities exist that combine and simplify the circuit. Based on this, we present an algorithm that compresses the Trotter steps into a single block of quantum gates using algebraic relations between adjacent circuit elements. This results in a fixed depth time evolution for certain classes of Hamiltonians. We explicitly show how this algorithm works for several spin models, and demonstrate its use for adiabatic state preparation of the transverse field Ising model.

View Accepted Manuscript (DOE)

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

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

Grant/Contract Number:: AC02-05CH11231; AC05-00OR22725; SC0019469

OSTI ID:: 1860355

Alternate ID(s):: OSTI ID: 1891373

Journal Information:: Physical Review A, Journal Name: Physical Review A Journal Issue: 3 Vol. 105; ISSN 2469-9926

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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