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

TLDR

Quantum information processors promise fast algorithms, but qubits are noisy and require fault‑tolerant error correction, which protects against general noise only if each operation’s error is below a threshold quantified by the diamond norm; until now, assessments relied on randomized benchmarking, which is not sensitive to all errors and cannot be compared to diamond norm thresholds. The study uses gate set tomography to fully characterize trapped‑Yb⁺ ion qubit operations and aims to demonstrate, with >95 % confidence, that they meet a rigorous fault‑tolerant threshold (diamond norm ≤ 6.7 × 10⁻⁴). Gate set tomography was employed to fully characterize the operations of a trapped‑Yb⁺ ion qubit. The results show, with >95 % confidence, that the characterized operations meet the rigorous fault‑tolerant threshold (diamond norm ≤ 6.7 × 10⁻⁴).

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 $\leq6.7\times10^{-4}$).