Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography

TL;DR

This paper demonstrates that qubit operations in a trapped-ion system meet the rigorous fault-tolerance threshold using gate set tomography, providing a more complete error characterization than traditional methods.

Contribution

It applies gate set tomography to accurately assess qubit errors and confirms they are below the fault-tolerance threshold with high confidence.

Findings

Qubit operations satisfy the fault-tolerance threshold with >95% confidence.

GST provides a comprehensive error characterization surpassing randomized benchmarking.

Physical qubit errors are below the diamond norm threshold for fault-tolerant quantum computing.

Abstract

Quantum information processors promise fast algorithms for problems inaccessible to classical computers. But since qubits are noisy and error-prone, they will depend on fault-tolerant quantum error correction (FTQEC) to compute reliably. Quantum error correction can protect against general noise if -- and only if -- the error in each physical qubit operation is smaller than a certain threshold. The threshold for general errors is quantified by their diamond norm. Until now, qubits have been assessed primarily by randomized benchmarking, which reports a different "error rate" that is not sensitive to all errors, and cannot be compared directly to diamond norm thresholds. Here we use gate set tomography (GST) to completely characterize operations on a trapped-Yb$^+$-ion qubit and demonstrate with very high ($>95\%$) confidence that they satisfy a rigorous threshold for FTQEC (diamond norm $\leq6.7\times10^{-4}$).