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  A Single-shot Measurement of the Energy of Product States in a Translation Invariant Spin Chain Can Replace Any Quantum Computation

Janzing, D., Wocjan, P., & Zhang, S. (2008). A Single-shot Measurement of the Energy of Product States in a Translation Invariant Spin Chain Can Replace Any Quantum Computation. New Journal of Physics, 10(8): 093004, pp. 1-18. doi:10.1088/1367-2630/10/9/093004.

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 Creators:
Janzing, D1, 2, Author              
Wocjan, P, Author
Zhang, S, Author
Affiliations:
1Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              

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 Abstract: In measurement-based quantum computation, quantum algorithms are implemented via sequences of measurements. We describe a translationally invariant finite-range interaction on a one-dimensional qudit chain and prove that a single-shot measurement of the energy of an appropriate computational basis state with respect to this Hamiltonian provides the output of any quantum circuit. The required measurement accuracy scales inverse polynomially with the size of the simulated quantum circuit. This shows that the implementation of energy measurements on generic qudit chains is as hard as the realization of quantum computation. Here, a ‘measurement‘ is any procedure that samples from the spectral measurement induced by the observable and the state under consideration. As opposed to measurement-based quantum computation, the post-measurement state is irrelevant.

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 Dates: 2008-09
 Publication Status: Published in print
 Pages: -
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 Table of Contents: -
 Rev. Type: -
 Identifiers: DOI: 10.1088/1367-2630/10/9/093004
BibTex Citekey: 5395
 Degree: -

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Title: New Journal of Physics
  Abbreviation : New J. Phys.
Source Genre: Journal
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Publ. Info: Bristol : IOP Publishing
Pages: - Volume / Issue: 10 (8) Sequence Number: 093004 Start / End Page: 1 - 18 Identifier: ISSN: 1367-2630
CoNE: https://pure.mpg.de/cone/journals/resource/954926913666