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Klassen, Joel; Marvian, Milad; Piddock, Stephen; Ioannou, Marios; Hen, Itay and Terhal, Barbara M. (2020): HARDNESS AND EASE OF CURING THE SIGN PROBLEM FOR TWO-LOCAL QUBIT HAMILTONIANS. In: Siam Journal on Computing, Vol. 49, No. 6: pp. 1332-1362

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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 R which is polynomial in the number of qubits, whether the sign problem of the Hamiltonian can be cured by single-qubit rotations.

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