A fault-tolerant pairwise measurement-based code on eight qubits

TL;DR

This paper introduces a new eight-qubit pairwise measurement-based quantum error-correcting code with fault tolerance, capable of correcting circuit noise and supporting fault-tolerant logical operations, with estimated pseudo-thresholds around 10^-5 to 10^-4.

Contribution

The paper presents a novel eight-qubit code with fault-tolerance, efficient syndrome extraction, and logical operations generating the full Clifford group, advancing quantum error correction methods.

Findings

Fault-tolerant code with distance 3 on 8 qubits.

Estimated pseudo-threshold between 10^-5 and 2×10^-4.

Post-selection can enhance error thresholds significantly.

Abstract

We construct a pairwise measurement-based code on eight qubits that is error correcting for circuit noise, with fault distance 3. The code can be implemented on a subset of a rectangular array of qubits with nearest neighbor connectivity of pairwise Pauli measurements, with a syndrome extraction circuit of depth 28. We describe fault-tolerant logical operations on patches of this eight-qubit code that generate the full Clifford group. We estimate the performance under circuit noise both during logical idle and during a logical two-qubit measurement. We estimate the pseudo-threshold to be between $10^{-5}$ and $2\times 10^{-4}$, depending on the amount of noise on idle physical qubits. The use of post-selection in addition to error correction (correcting all degree one faults and rejecting a subset of the higher degree faults) can improve the pseudo-threshold by up to an order of magnitude.