Quantifiable simulation of quantum computation beyond stochastic ensemble computation

TL;DR

This paper introduces an information-theoretic inequality to demonstrate that classical stochastic ensemble machines cannot fully simulate quantum computation, highlighting a fundamental difference between classical and quantum computational models.

Contribution

The study proposes a novel readout inequality and uses it to prove that classical probabilistic models cannot replicate the full power of quantum computation.

Findings

Classical stochastic ensemble machines cannot simulate general quantum circuits.

The readout inequality is violated by quantum models, indicating fundamental differences.

Quantum computation surpasses classical probabilistic models in computational capabilities.

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 $\subseteq$ QC.