Measurement-based classical computation

TL;DR

This paper introduces a classical analog of measurement-based quantum computation (MBQC), revealing complex computational structures and non-classical features in resource states derived from quantum processes.

Contribution

It develops a classical analog of MBQC using non-adaptive measurement on quantum-derived probability distributions, highlighting non-classicality without Bell inequality violation.

Findings

Classical analog of MBQC can implement complex quantum circuits efficiently.

Resource states exhibit non-classicality despite not violating Bell inequalities.

Certain quantum circuit families are hard to simulate classically, even in the classical MBQC model.

Abstract

Measurement-based quantum computation (MBQC) is a model of quantum computation, in which computation proceeds via adaptive single qubit measurements on a multi-qubit 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, Jozsa and Shepherd in Proc. R. Soc. A 467, 459 (2011)) 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 nevertheless exhibit non-classicality when used as a computational resource - an imprint of their quantum origin.