A Universal Constraint on Computational Rates in Physical Systems

TL;DR

This paper proves that in open quantum systems, thermally coupled computers inevitably dissipate entropy proportional to their computational rate, establishing a fundamental physical limit on dissipation.

Contribution

It provides a general proof that dissipationless reversible computing is impossible in thermally coupled quantum systems, establishing a universal lower bound on entropy dissipation.

Findings

Entropy dissipation is proportional to computational rate.

Dissipationless computation cannot be achieved in thermally coupled quantum systems.

A fundamental physical limit on computational rates is established.

Abstract

Conventional computing has many sources of heat dissipation, but one of these--the Landauer limit--poses a fundamental lower bound of 1 bit of entropy per bit erased. 'Reversible Computing' avoids this source of dissipation, but is dissipationless computation possible? In this paper, a general proof is given for open quantum systems showing that a computer thermally coupled to its environment will necessarily dissipate entropy (and hence heat). Specifically, a lower bound is obtained that corresponds to the adiabatic regime, in which the amount of entropy dissipated per computational operation is proportional to the rate of computation.