A dynamic circuit for the honeycomb Floquet code

TL;DR

This paper introduces a dynamic circuit for the honeycomb Floquet code that enhances error correction by increasing the code's distance, removing leakage, and significantly improving thresholds and logical error rates without using ancilla qubits.

Contribution

The paper presents a novel dynamic circuit approach for the honeycomb Floquet code that improves performance metrics and reduces qubit requirements compared to traditional ancilla-based methods.

Findings

Increases the timelike distance of the code.

Automatically removes leakage errors.

Reduces qubit requirements by nearly 3 times at a physical error rate of 10^-3.

Abstract

In the typical implementation of a quantum error-correcting code, each stabilizer is measured by entangling one or more ancilla qubits with the data qubits and measuring the ancilla qubits to deduce the value of the stabilizer. Recently, the dynamic circuit approach has been introduced, in which stabilizers are measured without ancilla qubits. Here, we demonstrate that dynamic circuits are particularly useful for the Floquet code. Our dynamic circuit increases the timelike distance of the code, automatically removes leakage, and both significantly increases the threshold and lowers the logical error rate compared to the standard ancilla-based circuit. At a physical error rate of $10^{-3}$, we estimate a nearly $3\times$ reduction in the number of qubits required to reach a $10^{-12}$ logical error rate.