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arxiv: 2007.11964 · v2 · pith:L25F35PS · submitted 2020-07-23 · quant-ph · cs.CC

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

Marios Ioannou , Stephen Piddock , Milad Marvian , Joel Klassen , Barbara M. Terhal This is my paper

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classification quant-ph cs.CC
keywords hamiltonianslocalstoquasticcomplexitydecidingglobalgloballystoquasticity
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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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Cited by 5 Pith papers

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