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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, Domink and Wocjan, Pawel and Zhang, Shengyu (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 (9). 093004. ISSN 1367-2630. doi:10.1088/1367-2630/10/9/093004.

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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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Additional Information:© 2008 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. Received 26 June 2008. Published 5 September 2008. PW acknowledges the support by NSF grant CCF-0726771. SZ was supported by NSF grant PHY-0456720 and ARO grant W911NF-05-1-0294. We thank Daniel Nagaj for his helpful discussions about the transition rules of the quantum cellular automaton.
Funding AgencyGrant Number
National Science FoundationCCF-0726771
National Science FoundationPHY-0456720
Army Research OfficeW911NF-05-1-0294
Issue or Number:9
Record Number:CaltechAUTHORS:JANnjp08
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:11601
Deposited By: Archive Administrator
Deposited On:09 Sep 2008 17:53
Last Modified:08 Nov 2021 22:01

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