Simultaneous stoquasticity

Bringewatt, Jacob; Brady, Lucas T.

doi:10.1103/physreva.105.062601

Simultaneous stoquasticity

Journal Article · Thu Jun 09 00:00:00 EDT 2022 · Physical Review A

DOI:https://doi.org/10.1103/physreva.105.062601· OSTI ID:1973593

^[1]; Brady, Lucas T. ^[2]

NIST/Univ. of Maryland, College Park, MD (United States)
NIST/Univ. of Maryland, College Park, MD (United States); NASA Ames Research Center, Moffett Field, CA (United States); KBR, Houston, TX (United States)

Stoquastic Hamiltonians play a role in the computational complexity of the local Hamiltonian problem as well as the study of classical simulability. In particular, stoquastic Hamiltonians can be straightforwardly simulated using Monte Carlo techniques. We address the question of whether two or more Hamiltonians may be made simultaneously stoquastic via a unitary transformation. This question has important implications for the complexity of simulating quantum annealing where quantum advantage is related to the stoquasticity of the Hamiltonians involved in the anneal. We find that for almost all problems no such unitary exists and show that the problem of determining the existence of such a unitary is equivalent to identifying if there is a solution to a system of polynomial (in)equalities in the matrix elements of the initial and transformed Hamiltonians. Furthermore, solving such a system of equations is NP-hard. We highlight a geometric understanding of this problem in terms of a collection of generalized Bloch vectors.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Maryland, College Park, MD (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0019323; SC0019449; SC0019040; SC0020312

OSTI ID:: 1973593

Journal Information:: Physical Review A, Vol. 105, Issue 6; ISSN 2469-9926

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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