Exponential suppression of bit or phase flip errors with repetitive error correction

TL;DR

This paper demonstrates exponential suppression of logical errors in superconducting qubits using 1D repetition codes embedded in a 2D grid, achieving over 100-fold error reduction and stable performance over 50 rounds, advancing fault-tolerant quantum computing.

Contribution

It introduces a scalable method for error suppression in superconducting qubits and analyzes error correlations and locality, supporting the viability of fault-tolerant quantum computing.

Findings

Logical error per round reduced by over 100x with more qubits

Error suppression remains stable over 50 rounds

Error correlations characterized and match simple models

Abstract

Realizing the potential of quantum computing will require achieving sufficiently low logical error rates. Many applications call for error rates in the $10^{-15}$ regime, but state-of-the-art quantum platforms typically have physical error rates near $10^{-3}$. Quantum error correction (QEC) promises to bridge this divide by distributing quantum logical information across many physical qubits so that errors can be detected and corrected. Logical errors are then exponentially suppressed as the number of physical qubits grows, provided that the physical error rates are below a certain threshold. QEC also requires that the errors are local and that performance is maintained over many rounds of error correction, two major outstanding experimental challenges. Here, we implement 1D repetition codes embedded in a 2D grid of superconducting qubits which demonstrate exponential suppression of bit or phase-flip errors, reducing logical error per round by more than $100\times$ when increasing the number of qubits from 5 to 21. Crucially, this error suppression is stable over 50 rounds of error correction. We also introduce a method for analyzing error correlations with high precision, and characterize the locality of errors in a device performing QEC for the first time. Finally, we perform error detection using a small 2D surface code logical qubit on the same device, and show that the results from both 1D and 2D codes agree with numerical simulations using a simple depolarizing error model. These findings demonstrate that superconducting qubits are on a viable path towards fault tolerant quantum computing.