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Entanglement Theory Quantum Correlations Open Quantum Systems Decoherence Quantum State Preparation Representation Quantum Simulation

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

arXiv
Authors: Marios Ioannou, Stephen Piddock, Milad Marvian, Joel Klassen, Barbara M. Terhal

Year

2020

Paper ID

22012

Status

Preprint

Abstract Read

~2 min

Abstract Words

99

Citations

N/A

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 Σ2p-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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  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
  • It adds a 2020 reference point for readers tracking recent quantum research.
  • We elucidate the distinction between global and termwise stoquasticity for local Hamiltonians and prove several complexity results.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2007.11964 [2] arXiv https://arxiv.org/abs/2007.11964 [3] Publisher https://arxiv.org/abs/2007.11964

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