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Cited by 113Quantum many-body systemsQuantum Computing Algorithms and ArchitectureQuantum Information and Cryptography

The DOI matches its Crossref record; 39 of the 39 references it cites were found in a registry or an index.

On entropy growth and the hardness of simulating time evolution

Open access
Schuch, N, Wolf, M M, Vollbrecht, K G H, Cirac, J I·2008·New Journal of Physics
DOI 10.1088/1367-2630/10/3/033032
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Abstract

The simulation of quantum systems is a task for which quantum computers are believed to give an exponential speed up as compared with classical ones. While ground states of one-dimensional systems can be efficiently approximated using matrix product states (MPS), their time evolution can encode quantum computations, so that simulating the latter should be hard classically. However, one might believe that for systems with high enough symmetry, and thus insufficient parameters to encode a quantum computation, efficient classical simulation is possible. We discuss supporting evidence to the contrary: we provide a rigorous proof of the observation that a time-independent local Hamiltonian can yield a linear increase of the entropy when acting on a product state in a translational invariant framework. This criterion has to be met by any classical simulation method, which in particular implies that every global approximation of the evolution requires exponential resources for any MPS-based method.

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Research works printed but not linked: 1

  1. Hastings M, 2007, J. Stat. Mech., 2007, P08024

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Metadata

Authors
Schuch, N., Wolf, M. M., Vollbrecht, K. G. H., & Cirac, J. I.
Affiliations
Max Planck Society (DE)
ORCID
Venue
New Journal of Physics
Publisher
IOP Publishing
Published
2008-03-20
Volume
10
Issue
3
Pages
033032
ISSN
1367-2630 (ISSN-L)
DOI
10.1088/1367-2630/10/3/033032
OpenAlex
W1970054335
Cited by
113
References
36
Citations by year
2026: 5 · 2025: 11 · 2024: 6 · 2023: 8 · 2022: 4 · 2021: 11 · 2020: 13 · 2019: 10 · 2018: 9 · 2017: 2 · 2016: 2 · 2015: 4 · 2014: 4 · 2013: 2 · 2012: 2
FWCI
3.86
Type
journal article
Language
en
Open access
Licence
cc-by
Locations
  • New Journal of Physics (publishedVersion, cc-by)
  • arXiv (Cornell University) (publishedVersion)
  • Max Planck Institute for Plasma Physics (submittedVersion)
  • MPG.PuRe (Max Planck Society) (submittedVersion, cc-by)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
Keywords
entropy increase, classical simulation of quantum dynamics, quantum advantage, matrix product states, local Hamiltonians, translation invariance, product states, ground state, one-dimensional systems

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