Scalable Postselection of Quantum Resources

TL;DR

This paper proposes a scalable postselection method that reduces quantum computing overhead by probabilistically selecting sub-circuits with improved logical error rates, enhancing fault-tolerance.

Contribution

It introduces a new scalable postselection approach using decoder soft information and a partial gap metric to lower quantum error correction overhead.

Findings

Achieves a 4x reduction in overhead per logical gate

Demonstrates scalable improvements in logical error rates

Validates approach in the context of teleportation-based logical gates

Abstract

The large overhead imposed by quantum error correction is a critical challenge to the realization of quantum computers, and motivates searching for alternative error correcting codes and fault-tolerant circuit constructions. Postselection is a powerful tool that builds large programs out of probabilistically generated sub-circuits, and has been shown to increase the threshold of quantum error correction based on fusing fixed-size resource states or concatenated codes. In this work, we present an approach to lower the overhead of quantum computing using scalable postselection, based on directly postselecting sub-circuits with a size extensive in the code distance using decoder soft information. We introduce a metric, the partial gap, that estimates what the logical gap of a resource state will be after it is consumed, and show that postselection based on the partial gap leads to scalable improvements in the logical error rate. In the specific context of implementing logical gates via teleportation through a cluster state, we demonstrate that scalable postselection provides a $4\times$ reduction in the overhead per logical gate, at the same logical error probability.