Simple circuit simulations of classical and quantum Turing machines

TL;DR

This paper presents simple reversible Boolean circuits that efficiently simulate classical and quantum Turing machines, providing straightforward constructions and proofs for both cases.

Contribution

It introduces simple reversible circuit constructions for classical and quantum Turing machines along with clear simulation proofs.

Findings

Reversible Boolean circuits can efficiently simulate classical Turing machines.

The authors extend the circuit constructions to the quantum case.

The simulation proofs are straightforward and accessible.

Abstract

We construct reversible Boolean circuits efficiently simulating reversible Turing machines. Both the circuits and the simulation proof are rather simple. Then we give a fairly straightforward generalization of the circuits and the simulation proof to the quantum case.