Solving MaxCut with quantum imaginary time evolution

Alam, Rizwanul; Siopsis, George; Herrman, Rebekah; Ostrowski, James; Lotshaw, Phillip C.; Humble, Travis S.

doi:10.1007/s11128-023-04045-7

Solving MaxCut with quantum imaginary time evolution

Journal Article · Wed Jul 12 04:00:00 EDT 2023 · Quantum Information Processing (Online)

DOI:https://doi.org/10.1007/s11128-023-04045-7· OSTI ID:1993702

Alam, Rizwanul ^[1]; ^[1]; Herrman, Rebekah ^[1]; Ostrowski, James ^[1]; ^[2]; ^[2]

Univ. of Tennessee, Knoxville, TN (United States)
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Quantum Computing Inst.

We introduce a method to solve the MaxCut problem efficiently based on quantum imaginary time evolution (QITE). We employ a linear Ansatz for unitary updates and an initial state involving no entanglement, as well as an imaginary-time-dependent Hamiltonian interpolating between a given graph and a subgraph with two edges excised. We apply the method to thousands of randomly selected graphs with up to fifty vertices. We show that our algorithm exhibits a 93% and above performance converging to the maximum solution of the MaxCut problem for all considered graphs. Our results compare favorably with the performance of classical algorithms, such as the greedy and Goemans–Williamson algorithms. We also discuss the overlap of the final state of the QITE algorithm with the ground state as a performance metric, which is a quantum feature not shared by other classical algorithms.

View Accepted Manuscript (DOE)

Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1993702

Journal Information:: Quantum Information Processing (Online), Journal Name: Quantum Information Processing (Online) Journal Issue: 7 Vol. 22; ISSN 1573-1332

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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