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  Quantum localization bounds Trotter errors in digital quantum simulation

Heyl, M., Hauke, P., & Zoller, P. (2019). Quantum localization bounds Trotter errors in digital quantum simulation. Science Advances, 5(4): eaau8342. doi:10.1126/sciadv.aau8342.

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Heyl, Markus1, Author           
Hauke, Philipp2, Author
Zoller, Peter2, Author
Affiliations:
1Max Planck Institute for the Physics of Complex Systems, Max Planck Society, ou_2117288              
2external, ou_persistent22              

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 MPIPKS: Time dependent processes
 Abstract: 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.

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 Dates: 2019-04-122019-04-12
 Publication Status: Issued
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 Identifiers: ISI: 000466398400027
DOI: 10.1126/sciadv.aau8342
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Title: Science Advances
  Other : Sci. Adv.
Source Genre: Journal
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Publ. Info: Washington : AAAS
Pages: - Volume / Issue: 5 (4) Sequence Number: eaau8342 Start / End Page: - Identifier: ISSN: 2375-2548
CoNE: https://pure.mpg.de/cone/journals/resource/2375-2548