A Small Quantum Computer is Needed to Optimize Fault-Tolerant Protocols

TL;DR

A small quantum computer is essential for optimizing fault-tolerant protocols, as current methods relying on noise modeling and simulations are limited, and direct characterization on small hardware offers a promising alternative.

Contribution

The paper critically analyzes existing optimization methods for fault-tolerant protocols and advocates for using small quantum computers for direct characterization.

Findings

Current optimization methods are limited by noise model dependence.

Numerical simulations of fault-tolerant protocols are computationally difficult.

Direct characterization on small quantum computers can bypass these limitations.

Abstract

As far as we know, a useful quantum computer will require fault-tolerant gates, and existing schemes demand a prohibitively large space and time overhead. We argue that a first generation quantum computer will be very valuable to design, test, and optimize fault-tolerant protocols tailored to the noise processes of the hardware. Our argument is essentially a critical analysis of the current methods envisioned to optimize fault-tolerant schemes, which rely on hardware characterization, noise modelling, and numerical simulations. We show that, even within a very restricted set of noise models, error correction protocols depend strongly on the details of the noise model. Combined to the intrinsic difficulty of hardware characterization and of numerical simulations of fault-tolerant protocols, we arrive at the conclusion that the currently envisioned optimization cycle is of very limited scope. On the other hand, the direct characterization of a fault-tolerant scheme on a small quantum computer bypasses these difficulties, and could provide a bootstrapping path to full-scale fault-tolerant quantum computation.