Fundamental gravitational limitations to quantum computing

TL;DR

This paper explores how quantum gravity imposes fundamental limits on the computational speed of hypothetical ultimate quantum computers, reducing previously estimated bounds based on quantum mechanics alone.

Contribution

It introduces gravitational constraints into the analysis of quantum computing limits, refining the maximum operations per second for an idealized computer.

Findings

Quantum gravity further constrains computational speed to 10^{47} ops/sec.

Relational notion of time impacts quantum computational limits.

Gravitational effects are significant at small scales for quantum computing.

Abstract

Lloyd has considered the ultimate limitations physics places on quantum computers. He concludes in particular that for an ``ultimate laptop'' (a computer of one liter of volume and one kilogram of mass) the maximum number of operations per second is bounded by $10^{51}$. The limit is derived considering ordinary quantum mechanics. Here we consider additional limits that are placed by quantum gravity ideas, namely the use of a relational notion of time and fundamental gravitational limits that exist on time measurements. We then particularize for the case of an ultimate laptop and show that the maximum number of operations is further constrained to $10^{47}$ per second.