Computational complexity of exterior products and multiparticle amplitudes of noninteracting fermions in entangled states

Computational complexity of exterior products and multiparticle amplitudes of noninteracting... Noninteracting bosons were proposed to be used for a demonstration of quantum-computing supremacy in a boson-sampling setup. A similar demonstration with fermions would require that the fermions are initially prepared in an entangled state. I suggest that pairwise entanglement of fermions would be sufficient for this purpose. Namely, it is shown that computing multiparticle scattering amplitudes for fermions entangled pairwise in groups of four single-particle states is #P-hard. In linear algebra, such amplitudes are expressed as exterior products of two-forms of rank 2. In particular, a permanent of a N×N matrix may be expressed as an exterior product of N2 two forms of rank 2 in dimension 2N2, which establishes the #P-hardness of the latter. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review A American Physical Society (APS)

Computational complexity of exterior products and multiparticle amplitudes of noninteracting fermions in entangled states

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Computational complexity of exterior products and multiparticle amplitudes of noninteracting fermions in entangled states

Abstract

Noninteracting bosons were proposed to be used for a demonstration of quantum-computing supremacy in a boson-sampling setup. A similar demonstration with fermions would require that the fermions are initially prepared in an entangled state. I suggest that pairwise entanglement of fermions would be sufficient for this purpose. Namely, it is shown that computing multiparticle scattering amplitudes for fermions entangled pairwise in groups of four single-particle states is #P-hard. In linear algebra, such amplitudes are expressed as exterior products of two-forms of rank 2. In particular, a permanent of a N×N matrix may be expressed as an exterior product of N2 two forms of rank 2 in dimension 2N2, which establishes the #P-hardness of the latter.
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Publisher
The American Physical Society
Copyright
Copyright © ©2017 American Physical Society
ISSN
1050-2947
eISSN
1094-1622
D.O.I.
10.1103/PhysRevA.96.012322
Publisher site
See Article on Publisher Site

Abstract

Noninteracting bosons were proposed to be used for a demonstration of quantum-computing supremacy in a boson-sampling setup. A similar demonstration with fermions would require that the fermions are initially prepared in an entangled state. I suggest that pairwise entanglement of fermions would be sufficient for this purpose. Namely, it is shown that computing multiparticle scattering amplitudes for fermions entangled pairwise in groups of four single-particle states is #P-hard. In linear algebra, such amplitudes are expressed as exterior products of two-forms of rank 2. In particular, a permanent of a N×N matrix may be expressed as an exterior product of N2 two forms of rank 2 in dimension 2N2, which establishes the #P-hardness of the latter.

Journal

Physical Review AAmerican Physical Society (APS)

Published: Jul 17, 2017

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