On the Universality of Memcomputing Machines

TL;DR

This paper demonstrates that universal memcomputing machines (UMMs) can simulate both liquid-state and quantum computing models, establishing their broad computational universality through set theory and cardinality arguments.

Contribution

The paper introduces a theoretical framework showing UMMs' ability to simulate liquid-state and quantum machines, expanding understanding of their computational capabilities.

Findings

UMMs can simulate liquid-state machines.

UMMs can simulate quantum machines.

UMMs are both 'liquid-' and 'quantum-complete'.

Abstract

Universal memcomputing machines (UMMs) [IEEE Trans. Neural Netw. Learn. Syst. 26, 2702 (2015)] represent a novel computational model in which memory (time non-locality) accomplishes both tasks of storing and processing of information. UMMs have been shown to be Turing-complete, namely they can simulate any Turing machine. In this paper, using set theory and cardinality arguments, we compare them with liquid-state machines (or "reservoir computing") and quantum machines ("quantum computing"). We show that UMMs can simulate both types of machines, hence they are both "liquid-" or "reservoir-complete" and "quantum-complete". Of course, these statements pertain only to the type of problems these machines can solve, and not to the amount of resources required for such simulations. Nonetheless, the method presented here provides a general framework in which to describe the relation between UMMs and any other type of computational model.