Termwise versus globally stoquastic local Hamiltonians: questions of complexity and sign-curing

• URL: http://arxiv.org/abs/2007.11964v2
• Date: Wed, 27 Apr 2022 12:10:16 GMT
• Title: Termwise versus globally stoquastic local Hamiltonians: questions of complexity and sign-curing
• Authors: Marios Ioannou, Stephen Piddock, Milad Marvian, Joel Klassen and Barbara M. Terhal
• Abstract summary: We show that the stoquastic local Hamiltonian problem is $textbfStoqMA$-complete even for globally stoquastic Hamiltonians. We expand the class of sign-curing transformations by showing how Clifford transformations can sign-cure a class of disordered 1D $XYZ$ Hamiltonians.
• Score: 3.762360672951513
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We elucidate the distinction between global and termwise stoquasticity for local Hamiltonians and prove several complexity results. We show that the stoquastic local Hamiltonian problem is $\textbf{StoqMA}$-complete even for globally stoquastic Hamiltonians. We study the complexity of deciding whether a local Hamiltonian is globally stoquastic or not. In particular, we prove $\textbf{coNP}$-hardness of deciding global stoquasticity in a fixed basis and $\Sigma_2^p$-hardness of deciding global stoquasticity under single-qubit transformations. As a last result, we expand the class of sign-curing transformations by showing how Clifford transformations can sign-cure a class of disordered 1D $XYZ$ Hamiltonians.

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