Time-optimal quantum computation

TL;DR

This paper presents a method for performing fault-tolerant quantum computation in a time-optimal manner, executing complex circuits within the duration of a single measurement by leveraging fast classical processing and communication.

Contribution

It introduces a scheme to achieve time-optimal quantum computation using existing error-correcting codes and transversal measurements, significantly reducing execution time.

Findings

Quantum computation can be performed in the time of a single measurement.

Execution time is independent of error correction strength.

Enables faster fault-tolerant quantum algorithms.

Abstract

Given any quantum error correcting code permitting universal fault-tolerant quantum computation and transversal measurement of logical X and Z, we describe how to perform time-optimal quantum computation, meaning the execution of an arbitrary Clifford circuit followed by a layer of independent T gates and any necessary feedforward measurement determined corrective S gates all in the time of a single physical measurement. We assume fast classical processing and classical communication, and argue the reasonableness of this assumption. This enables fault-tolerant quantum computation to be performed orders of magnitude faster than previously thought possible, with the execution time independent of the error correction strength.