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We examine the problem of determining whether a multi-qubit two-localHamiltonian can be made stoquastic by single-qubit unitary transformations. Weprove that when such a Hamiltonian contains one-local terms, then this task canbe NP-hard. This is shown by constructing a class of Hamiltonians for whichperforming this task is equivalent to deciding $3$-SAT. In contrast, we showthat when such a Hamiltonian contains no one-local terms then this task iseasy, namely we present an algorithm which decides, in a number of arithmeticoperations over $\mathbb{R}$ which is polynomial in the number of qubits,whether the sign problem of the Hamiltonian can be cured by single-qubitrotations.

Hardness and Ease of Curing the Sign Problem for Two-Local Qubit Hamiltonians