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arXiv · 2007.11964

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

Marios Ioannou·Stephen Piddock·Milad Marvian·Joel Klassen·Barbara M. Terhal
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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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Marios Ioannou, Stephen Piddock, Milad Marvian, Joel Klassen, Barbara M. Terhal. 2020-07-23. Termwise versus globally stoquastic local Hamiltonians: questions of complexity and sign-curing. https://arxiv.org/abs/2007.11964

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