Measurement-based classical computation.
Measurement-based quantum computation (MBQC) is a model of quantum computation, in which computation proceeds via adaptive single qubit measurements on a multiqubit quantum state. It is computationally equivalent to the circuit model. Unlike the circuit model, however, its classical analog is little studied. Here we present a classical analog of MBQC whose computational complexity presents a rich structure. To do so, we identify uniform families of quantum computations [refining the circuits introduced by Bremner Proc. R. Soc. A 467, 459 (2010)] whose output is likely hard to exactly simulate (sample) classically. We demonstrate that these circuit families can be efficiently implemented in the MBQC model without adaptive measurement and, thus, can be achieved in a classical analog of MBQC whose resource state is a probability distribution which has been created quantum mechanically. Such states (by definition) violate no Bell inequality, but, if widely held beliefs about computational complexity are true, they, nevertheless, exhibit nonclassicality when used as a computational resource—an imprint of their quantum origin.
ICFO-Institut de Ciències Fotòniques, Mediterranean Technology Park, E-08860 Castelldefels (Barcelona), Spain.
Matty J
MJ
Hoban
Centre for Engineered Quantum Systems, School of Physics, The University of Sydney, Sydney, NSW 2006, Australia.
Joel J
JJ
Wallman
Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom.
Hussain
H
Anwar
Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom.
Naïri
N
Usher
Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada.
Robert
R
Raussendorf
Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom.
Dan E
DE
Browne