Reversible logic and quantum computers

TLDR

The article focuses on constructing a quantum‑mechanical Hamiltonian that describes a computer, achievable by ensuring each logical step is locally reversible rather than relying on global reversibility. The Hamiltonian drives a dynamical evolution that mimics elementary logical steps, while noise‑induced errors are mitigated through redundancy. The study demonstrates that reversible error‑correcting codes can be embedded in the Hamiltonian and provides an estimate of the minimal entropy that must be dissipated for a specified noise level and error tolerance.

Abstract

This article is concerned with the construction of a quantum-mechanical Hamiltonian describing a computer. This Hamiltonian generates a dynamical evolution which mimics a sequence of elementary logical steps. This can be achieved if each logical step is locally reversible (global reversibility is insufficient). Computational errors due to noise can be corrected by means of redundancy. In particular, reversible error-correcting codes can be embedded in the Hamiltonian itself. An estimate is given for the minimum amount of entropy which must be dissipated at a given noise level and tolerated error rate.