Abstract

We examine the problem of determining whether a multiqubit two-local Hamiltonian can be made stoquastic by single-qubit unitary transformations. We prove that when such a Hamiltonian contains one-local terms, then this task can be NP-hard. This is shown by constructing a class of Hamiltonians for which performing this task is equivalent to deciding 3-SAT. In contrast, we show that when such a Hamiltonian contains no one-local terms then this task is easy; namely, we present an algorithm which decides, in a number of arithmetic operations over which is polynomial in the number of qubits, whether the sign problem of the Hamiltonian can be cured by single-qubit rotations.

Date

2020

Authors

Joel Klassen, Milad Marvian, Stephen Piddock, Marios Ioannou, Itay Hen, Barbara M Terhal

Journal

SIAM Journal on Computing

Volume

49

Issue

6

Pages

1332-1362

Publisher

Society for Industrial and Applied Mathematics