Quantifiable Simulation of Quantum Computation beyond Stochastic Ensemble Computation

Abstract

In this study, a distinctive feature of quantum computation (QC) is characterized. To this end, a seemingly-powerful classical computing model, called "stochastic ensemble machine (SEnM)," is considered. The SEnM runs with an ensemble consisting of finite copies of a single probabilistic machine, hence is as powerful as a probabilistic Turing machine (PTM). Then the hypothesis-that is, the SEnM can effectively simulate a general circuit model of QC-is tested by introducing an information-theoretic inequality, named readout inequality. The inequality is satisfied by the SEnM and imposes a critical condition: if the hypothesis holds, the inequality should be satisfied by the probing model of QC. However, it is shown that the above hypothesis is not generally accepted with the inequality violation; namely, such a simulation necessarily fails, implying that PTM. QC.