Parallelism of quantum computations from prequantum classical statistical field theory (PCSFT)

TL;DR

This paper offers a realistic interpretation of quantum parallelism through prequantum classical statistical field theory, explaining how quantum computers process information using classical random fields instead of purely quantum states.

Contribution

It introduces a novel interpretation of quantum parallelism based on PCSFT, linking quantum states to classical field ensembles and explaining quantum computation as transformations of these fields.

Findings

Quantum states are represented as ensembles of classical fields.

Quantum computer operations correspond to transformations of classical random fields.

Provides a realistic interpretation of quantum parallelism.

Abstract

This paper is devoted to such a fundamental problem of quantum computing as quantum parallelism. It is well known that quantum parallelism is the basis of the ability of quantum computer to perform in polynomial time computations performed by classical computers for exponential time. Therefore better understanding of quantum parallelism is important both for theoretical and applied research, cf. e.g. David Deutsch \cite{DD}. We present a realistic interpretation based on recently developed prequantum classical statistical field theory (PCSFT). In the PCSFT-approach to QM quantum states (mixed as well as pure) are labels of special ensembles of classical fields. Thus e.g. a single (!) ``electron in the pure state'' $\psi$ can be identified with a special `` electron random field,'' say $\Phi_\psi(\phi).$ Quantum computer operates with such random fields. By one computational step for e.g. a Boolean function $f(x_1,...,x_n)$ the initial random field $\Phi_{\psi_0}(\phi)$ is transformed into the final random field $\Phi_{\psi_f}(\phi)$ ``containing all values'' of $f.$ This is the objective of quantum computer's ability to operate quickly with huge amounts of information -- in fact, with classical random fields.