Limits to Computational Acceleration Imposed by Quantum Field Theory and Quantum Gravity

TL;DR

This paper investigates the fundamental physical limits imposed by quantum field theory and quantum gravity on computational acceleration, showing that physical effects prevent surpassing certain bounds even with relativistic effects.

Contribution

The authors demonstrate that quantum gravity and quantum field effects impose strict limits on acceleration and memory capacity, constraining computational speedups.

Findings

Acceleration rate is limited to at most olds per unit time by physical effects.

Energy and memory bounds are related through isher bound and Bekenstein bound.

Physical effects prevent exploiting spacetime curvature for unbounded computational acceleration.

Abstract

A computer, in order to perform a given computation, requires a certain amount of space (memory) and a certain amount of time (runtime). This leaves certain computations beyond reach due to technological limits on processing speed and memory density. Some computations, such as the halting problem, are not possible even in principle. However, curved spacetimes and exotic fields appear to provide avenues to accelerate computation, for instance by exploiting time dilation. Impossible computations seemingly become tractable, butting up against intuition. However, we show that such schemes are consistently thwarted by physical effects from quantum gravity (including swampland conjectures) and quantum field theory in curved space. More precisely, we show that an observer and a computer able to withstand energy scales up to order $E$ can, by using relativistic effects, accelerate computation at a rate of at most $\mathcal O(1)E$ e-folds per unit time in natural units: $(\ln\alpha)/\tau\lesssim E$. The Bekenstein bound for entropy can then be understood as the space (memory) analogue to (run)time: if a computer of length scale $D$, operating at energies up to order $E$, has access to $N$ different memory states, then $(\ln N)/D\lesssim E$.