Macromux: scalable postselection for high-threshold fault-tolerant quantum computation

TL;DR

This paper introduces Macromux, a scalable postselection scheme that significantly enhances fault-tolerance thresholds in quantum computing with minimal overhead, applicable across various architectures including photonic systems.

Contribution

The paper presents Macromux, a hierarchical postselection method that improves fault-tolerance thresholds and can be integrated into existing protocols with low additional resource costs.

Findings

Achieved up to a sixfold increase in Pauli error thresholds.

Demonstrated doubling of loss thresholds in photonic fusion protocols.

Developed protocols with the highest thresholds reported in the literature.

Abstract

We introduce a new resource-efficient scheme for fault-tolerant quantum computation known as `macroscale multiplexing' (or simply `Macromux'), that utilizes scalable postselection to significantly improve the threshold of a given fault-tolerant protocol against both Pauli and erasure errors. Macromux is a hierarchical method for postselecting on constant-size space-time windows of a fault tolerant protocol, requiring only constant additional overheads. The method can be straightforwardly implemented for any fault-tolerant protocol and in any architecture that has access to routing and memory, such as linear-optical fusion-based architectures. We construct fault-tolerant protocols that, to our knowledge, have the highest thresholds in the literature; we perform simulations of fusion-based schemes based on the surface code, showing a maximum possible increase in Pauli thresholds of up to a factor of $\sim6$ (from $1.0\%$ to $5.9\%$). Our schemes are highly-resource efficient, and can for example, double the loss thresholds of some photonic fusion-based protocols using as little as $3 \times$ overhead.