Fault-Tolerant Operation of a Quantum Error-Correction Code

TL;DR

This paper demonstrates fault-tolerant quantum operations on a Bacon-Shor logical qubit using trapped ions, significantly reducing error rates and achieving key components for universal fault-tolerant quantum computing.

Contribution

First experimental demonstration of fault-tolerant protocols on a physical quantum system with native noise characteristics, using 13 trapped ion qubits.

Findings

Significant reduction in logical primitive error rates with fault-tolerant protocols.

Achieved state preparation and measurement errors of 0.6% and Clifford gate errors of 0.3%.

Prepared magic states exceeding distillation thresholds.

Abstract

Quantum error correction protects fragile quantum information by encoding it into a larger quantum system. These extra degrees of freedom enable the detection and correction of errors, but also increase the operational complexity of the encoded logical qubit. Fault-tolerant circuits contain the spread of errors while operating the logical qubit, and are essential for realizing error suppression in practice. While fault-tolerant design works in principle, it has not previously been demonstrated in an error-corrected physical system with native noise characteristics. In this work, we experimentally demonstrate fault-tolerant preparation, measurement, rotation, and stabilizer measurement of a Bacon-Shor logical qubit using 13 trapped ion qubits. When we compare these fault-tolerant protocols to non-fault tolerant protocols, we see significant reductions in the error rates of the logical primitives in the presence of noise. The result of fault-tolerant design is an average state preparation and measurement error of 0.6% and a Clifford gate error of 0.3% after error correction. Additionally, we prepare magic states with fidelities exceeding the distillation threshold, demonstrating all of the key single-qubit ingredients required for universal fault-tolerant operation. These results demonstrate that fault-tolerant circuits enable highly accurate logical primitives in current quantum systems. With improved two-qubit gates and the use of intermediate measurements, a stabilized logical qubit can be achieved.