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• W4293081753 abstract "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. 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." @default.
• W4293081753 created "2022-08-26" @default.
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• W4293081753 creator A5071548191 @default.
• W4293081753 date "2022-06-09" @default.
• W4293081753 modified "2023-10-17" @default.
• W4293081753 title "Simultaneous stoquasticity" @default.
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• W4293081753 doi "https://doi.org/10.1103/physreva.105.062601" @default.
• W4293081753 hasPublicationYear "2022" @default.
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