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.

Correlation measure equivalence in dynamic causal structures of quantum gravity

“…The theory of quantum gravity (QG) fuses the dynamic (nonfixed) causal structure of general relativity and the quantum uncertainty of quantum mechanics . quantum gravity information processing (QGIP) proposes a framework to perform quantum information processing and quantum computations in a causally unbiased space‐time structure. The theory of QGIP allows us to build QG computers that are not only just equipped with the power of quantum computers but also operating on a dynamic causal structure …”

Theory of quantum gravity information processing

“…This work also defines a quantum computation model that can be used to simulate an indefinite causal structure. For the structural attributes of an indefinite causal structure, see also the work of Milz et al A special computational framework has been defined by Bang et al This work also studies the problem of quantifiable simulation of quantum computation beyond stochastic ensemble computation. Mahmud et al studied the emulation of quantum algorithms at high precision and high throughput and evaluated a computational model.…”