Forced Gap Post-Selection for Quantum LDPC Codes and their Operations

TL;DR

This paper introduces a simple post-selection method for quantum LDPC codes that improves logical error rates by over four times using FPGA-friendly belief propagation, applicable across different decoders.

Contribution

The authors present a general, lightweight post-selection strategy for high-rate quantum codes that enhances error correction performance without high latency decoding.

Findings

Achieved over 4x reduction in logical error rate compared to previous methods.

Applicable to 72-qubit and 144-qubit bivariate bicycle codes and surgery gadgets.

Strategy is FPGA-friendly and requires only belief propagation.

Abstract

We develop a simple and general post-selection strategy for high-rate quantum codes that is transferrable across decoders. After an initial baseline run, the decoder is re-run once per logical observable, and forced in these latter runs to provide a solution where the given observable has the complementary outcome. Shots are rejected that find logically complementary solutions with similar likelihoods compared to the baseline. Using the Relay-BP decoder, we benchmark the strategy on the $72$-qubit and $144$-qubit bivariate bicycle codes, as well as surgery gadgets for the latter. In comparison to previous post-selection strategies, our results offer an improved logical error rate by over a factor of $4$ on the same circuit and physical error rate, and at the same rate of post-selection. Our strategies are also lightweight, relying only on FPGA-friendly belief propagation, whereas the previous best used repeated rounds of a high-latency BP-OSD decoder.