Probing the Planck scale with quantum computation

TL;DR

This paper explores how quantum computers operating beyond classical limits could test the incompatibility of general relativity and quantum mechanics at the Planck scale, suggesting that future quantum tech might challenge current physical theories.

Contribution

It quantifies the relationship between logical qubits and the ability to challenge classical physics, proposing that 500 logical qubits suffice to test quantum gravity theories.

Findings

500 logical qubits can challenge laboratory-confined theories

Current quantum computers may soon surpass the necessary operational limits

Operational costs are considered up to the scale of the observable universe

Abstract

General relativity and quantum mechanics are incompatible at the Planck scale. This contention can be examined if a quantum computer is set to operate at a rate that exceeds the classical limit of one operation per Planck volume-time, or equivalently $2^{491}$ m$^{-3}$ s$^{-1}$. Here we quantify the relation between the logical qubit count and the extent to which classicality is challenged. We argue that 500 logical qubits are sufficient to reject theories confined to a laboratory. We account for the operational cost of computation and communication at all scales up to and including the observable universe, ultimately constrained by a 1600-logical-qubit computer. Remarkably, current plans for commercial quantum computers are projected to surpass this limit, thereby putting the quantum-gravity standoff to the test.