Demonstration of logical qubits and repeated error correction with better-than-physical error rates

TL;DR

This paper demonstrates that fault-tolerant encoding and repeated error correction in a trapped-ion quantum processor can significantly reduce logical error rates below physical error rates, marking progress toward scalable, reliable quantum computing.

Contribution

The study presents experimental evidence of logical qubits with error rates much lower than physical qubits, and demonstrates repeated error correction with logical error rates approaching physical gate error rates.

Findings

Logical qubits with error rates 9.8 to 500 times lower than physical qubits.

Logical qubits with error rates 4.7 to 800 times lower using post-selection.

Repeated error correction cycles with logical error rates approaching physical CNOT error rates.

Abstract

The promise of quantum computers hinges on the ability to scale to large system sizes, e.g., to run quantum computations consisting of more than 100 million operations fault-tolerantly. This in turn requires suppressing errors to levels inversely proportional to the size of the computation. As a step towards this ambitious goal, we present experiments on a trapped-ion QCCD processor where, through the use of fault-tolerant encoding and error correction, we are able to suppress logical error rates to levels below the physical error rates. In particular, we entangled logical qubits encoded in the [[7,1,3]] code with error rates 9.8 times to 500 times lower than at the physical level, and entangled logical qubits encoded in a [[12,2,4]] code based on Knill's C4/C6 scheme with error rates 4.7 times to 800 times lower than at the physical level, depending on the judicious use of post-selection. Moreover, we demonstrate repeated error correction with the [[12,2,4]] code, with logical error rates below physical circuit baselines corresponding to repeated CNOTs, and show evidence that the error rate per error correction cycle, which consists of over 100 physical CNOTs, approaches the error rate of two physical CNOTs. These results signify a transition from noisy intermediate scale quantum computing to reliable quantum computing, and demonstrate advanced capabilities toward large-scale fault-tolerant quantum computing.