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This paper is devoted to such a fundamental problem of quantum computing asquantum parallelism. It is well known that quantum parallelism is the basis ofthe ability of quantum computer to perform in polynomial time computationsperformed by classical computers for exponential time. Therefore betterunderstanding of quantum parallelism is important both for theoretical andapplied research, cf. e.g. David Deutsch \cite{DD}. We present a realisticinterpretation based on recently developed prequantum classical statisticalfield theory (PCSFT). In the PCSFT-approach to QM quantum states (mixed as wellas pure) are labels of special ensembles of classical fields. Thus e.g. asingle (!) ``electron in the pure state'' $\psi$ can be identified with aspecial `` electron random field,'' say $\Phi_\psi(\phi).$ Quantum computeroperates with such random fields. By one computational step for e.g. a Booleanfunction $f(x_1,...,x_n)$ the initial random field $\Phi_{\psi_0}(\phi)$ istransformed into the final random field $\Phi_{\psi_f}(\phi)$ ``containing allvalues'' of $f.$ This is the objective of quantum computer's ability to operatequickly with huge amounts of information -- in fact, with classical randomfields.

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