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Quantum localization bounds Trotter errors in digital quantum simulation
A fundamental challenge in digital quantum simulation (DQS) is the control of an inherent error, which appears when discretizing the time evolution of a quantum many-body system as a sequence of quantum gates, called Trotterization. Here, we show that quantum localization-by constraining the time ev...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
American Association for the Advancement of Science
2019
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6461450/ https://www.ncbi.nlm.nih.gov/pubmed/30993199 http://dx.doi.org/10.1126/sciadv.aau8342 |
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author | Heyl, Markus Hauke, Philipp Zoller, Peter |
author_facet | Heyl, Markus Hauke, Philipp Zoller, Peter |
author_sort | Heyl, Markus |
collection | PubMed |
description | A fundamental challenge in digital quantum simulation (DQS) is the control of an inherent error, which appears when discretizing the time evolution of a quantum many-body system as a sequence of quantum gates, called Trotterization. Here, we show that quantum localization-by constraining the time evolution through quantum interference-strongly bounds these errors for local observables, leading to an error independent of system size and simulation time. DQS is thus intrinsically much more robust than suggested by known error bounds on the global many-body wave function. This robustness is characterized by a sharp threshold as a function of the Trotter step size, which separates a localized region with controllable Trotter errors from a quantum chaotic regime. Our findings show that DQS with comparatively large Trotter steps can retain controlled errors for local observables. It is thus possible to reduce the number of gate operations required to represent the desired time evolution faithfully. |
format | Online Article Text |
id | pubmed-6461450 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2019 |
publisher | American Association for the Advancement of Science |
record_format | MEDLINE/PubMed |
spelling | pubmed-64614502019-04-16 Quantum localization bounds Trotter errors in digital quantum simulation Heyl, Markus Hauke, Philipp Zoller, Peter Sci Adv Research Articles A fundamental challenge in digital quantum simulation (DQS) is the control of an inherent error, which appears when discretizing the time evolution of a quantum many-body system as a sequence of quantum gates, called Trotterization. Here, we show that quantum localization-by constraining the time evolution through quantum interference-strongly bounds these errors for local observables, leading to an error independent of system size and simulation time. DQS is thus intrinsically much more robust than suggested by known error bounds on the global many-body wave function. This robustness is characterized by a sharp threshold as a function of the Trotter step size, which separates a localized region with controllable Trotter errors from a quantum chaotic regime. Our findings show that DQS with comparatively large Trotter steps can retain controlled errors for local observables. It is thus possible to reduce the number of gate operations required to represent the desired time evolution faithfully. American Association for the Advancement of Science 2019-04-12 /pmc/articles/PMC6461450/ /pubmed/30993199 http://dx.doi.org/10.1126/sciadv.aau8342 Text en Copyright © 2019 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC). http://creativecommons.org/licenses/by-nc/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license (http://creativecommons.org/licenses/by-nc/4.0/) , which permits use, distribution, and reproduction in any medium, so long as the resultant use is not for commercial advantage and provided the original work is properly cited. |
spellingShingle | Research Articles Heyl, Markus Hauke, Philipp Zoller, Peter Quantum localization bounds Trotter errors in digital quantum simulation |
title | Quantum localization bounds Trotter errors in digital quantum simulation |
title_full | Quantum localization bounds Trotter errors in digital quantum simulation |
title_fullStr | Quantum localization bounds Trotter errors in digital quantum simulation |
title_full_unstemmed | Quantum localization bounds Trotter errors in digital quantum simulation |
title_short | Quantum localization bounds Trotter errors in digital quantum simulation |
title_sort | quantum localization bounds trotter errors in digital quantum simulation |
topic | Research Articles |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6461450/ https://www.ncbi.nlm.nih.gov/pubmed/30993199 http://dx.doi.org/10.1126/sciadv.aau8342 |
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