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Open Quantum Systems Decoherence Quantum Simulation

An Information-Theoretic Proof of the Constructive Commutative Quantum Lovász Local Lemma

arXiv
Authors: Martin Schwarz, Toby S. Cubitt, Frank Verstraete

Year

2013

Paper ID

31745

Status

Preprint

Abstract Read

~2 min

Abstract Words

103

Citations

N/A

Abstract

The Quantum Lovász Local Lemma (QLLL) [AKS12] establishes non-constructively that any quantum system constrained by a local Hamiltonian has a zero-energy ground state, if the local Hamiltonian terms overlap only in a certain restricted way. In this paper, we present an efficient quantum algorithm to prepare this ground state for the special case of commuting projector terms. The related classical problem has been open for more than 34 years. Our algorithm follows the breakthrough ideas of Moser's [Moser09] classical algorithm and lifts his information theoretic argument to the quantum setting. A similar result has been independently published by Arad and Sattath [AS13] recently.

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  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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  • The Quantum Lovász Local Lemma (QLLL) [AKS12] establishes non-constructively that any quantum system constrained by a local Hamiltonian has a zero-energy ground state, if the...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1311.6474 [2] arXiv https://arxiv.org/abs/1311.6474 [3] Publisher https://arxiv.org/abs/1311.6474

Local Citation Graph (Related-Paper Links)

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