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

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Khrennikov, Andrei

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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.

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Quantum Physics