Dynamical Purification Phase Transition Induced by Quantum Measurements

Continuously monitoring the environment of a quantum many-body system reduces the entropy of (purifies) the reduced density matrix of the system, conditional on the outcomes of the measurements. We show that, for mixed initial states, a balanced competition between measurements and entangling intera...

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Autores principales:	Michael J. Gullans, David A. Huse
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2020
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/b29489d04a944b3cbcf1bf2d2561ee07
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spelling	oai:doaj.org-article:b29489d04a944b3cbcf1bf2d2561ee072021-12-02T11:39:28ZDynamical Purification Phase Transition Induced by Quantum Measurements10.1103/PhysRevX.10.0410202160-3308https://doaj.org/article/b29489d04a944b3cbcf1bf2d2561ee072020-10-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.10.041020http://doi.org/10.1103/PhysRevX.10.041020https://doaj.org/toc/2160-3308Continuously monitoring the environment of a quantum many-body system reduces the entropy of (purifies) the reduced density matrix of the system, conditional on the outcomes of the measurements. We show that, for mixed initial states, a balanced competition between measurements and entangling interactions within the system can result in a dynamical purification phase transition between (i) a phase that locally purifies at a constant system-size-independent rate and (ii) a “mixed” phase where the purification time diverges exponentially in the system size. The residual entropy density in the mixed phase implies the existence of a quantum error-protected subspace, where quantum information is reliably encoded against the future nonunitary evolution of the system. We show that these codes are of potential relevance to fault-tolerant quantum computation as they are often highly degenerate and satisfy optimal trade-offs between encoded information densities and error thresholds. In spatially local models in 1+1 dimensions, this phase transition for mixed initial states occurs concurrently with a recently identified class of entanglement phase transitions for pure initial states. The purification transition studied here also generalizes to systems with long-range interactions, where conventional notions of entanglement transitions have to be reformulated. We numerically explore this transition for monitored random quantum circuits in 1+1 dimensions and all-to-all models. Unlike in pure initial states, the mutual information of an initially completely mixed state in 1+1 dimensions grows sublinearly in time due to the formation of the error-protected subspace. Purification dynamics is likely a more robust probe of the transition in experiments, where imperfections generically reduce entanglement and drive the system towards mixed states. We describe the motivations for studying this novel class of nonequilibrium quantum dynamics in the context of advanced quantum computing platforms and fault-tolerant quantum computation.Michael J. GullansDavid A. HuseAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 10, Iss 4, p 041020 (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Michael J. Gullans David A. Huse Dynamical Purification Phase Transition Induced by Quantum Measurements
description	Continuously monitoring the environment of a quantum many-body system reduces the entropy of (purifies) the reduced density matrix of the system, conditional on the outcomes of the measurements. We show that, for mixed initial states, a balanced competition between measurements and entangling interactions within the system can result in a dynamical purification phase transition between (i) a phase that locally purifies at a constant system-size-independent rate and (ii) a “mixed” phase where the purification time diverges exponentially in the system size. The residual entropy density in the mixed phase implies the existence of a quantum error-protected subspace, where quantum information is reliably encoded against the future nonunitary evolution of the system. We show that these codes are of potential relevance to fault-tolerant quantum computation as they are often highly degenerate and satisfy optimal trade-offs between encoded information densities and error thresholds. In spatially local models in 1+1 dimensions, this phase transition for mixed initial states occurs concurrently with a recently identified class of entanglement phase transitions for pure initial states. The purification transition studied here also generalizes to systems with long-range interactions, where conventional notions of entanglement transitions have to be reformulated. We numerically explore this transition for monitored random quantum circuits in 1+1 dimensions and all-to-all models. Unlike in pure initial states, the mutual information of an initially completely mixed state in 1+1 dimensions grows sublinearly in time due to the formation of the error-protected subspace. Purification dynamics is likely a more robust probe of the transition in experiments, where imperfections generically reduce entanglement and drive the system towards mixed states. We describe the motivations for studying this novel class of nonequilibrium quantum dynamics in the context of advanced quantum computing platforms and fault-tolerant quantum computation.
format	article
author	Michael J. Gullans David A. Huse
author_facet	Michael J. Gullans David A. Huse
author_sort	Michael J. Gullans
title	Dynamical Purification Phase Transition Induced by Quantum Measurements
title_short	Dynamical Purification Phase Transition Induced by Quantum Measurements
title_full	Dynamical Purification Phase Transition Induced by Quantum Measurements
title_fullStr	Dynamical Purification Phase Transition Induced by Quantum Measurements
title_full_unstemmed	Dynamical Purification Phase Transition Induced by Quantum Measurements
title_sort	dynamical purification phase transition induced by quantum measurements
publisher	American Physical Society
publishDate	2020
url	https://doaj.org/article/b29489d04a944b3cbcf1bf2d2561ee07
work_keys_str_mv	AT michaeljgullans dynamicalpurificationphasetransitioninducedbyquantummeasurements AT davidahuse dynamicalpurificationphasetransitioninducedbyquantummeasurements
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Dynamical Purification Phase Transition Induced by Quantum Measurements

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