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 to completely characterize operations on a trapped-Yb+-ion qubit and demonstrate with greater than 95% confidence that they satisfy a rigorous threshold for FTQEC (diamond norm ≤6.7 × 10−4).
Highlights
Quantum information processors promise fast algorithms for problems inaccessible to classical computers
gate set tomography (GST) is a self-calibrating tomography protocol that solves both of these problems
Lower-randomized benchmarking (RB) error rates have been reported in trapped-ion qubits[15,16], our gates are the first to demonstrably surpass a rigorous Fault tolerance (FT) threshold against general noise
Summary
Quantum information processors promise fast algorithms for problems inaccessible to classical computers. Since qubits are noisy and error-prone, they will depend on fault-tolerant quantum error correction (FTQEC) to compute reliably. Qubits are intrinsically noisy and errorprone, and will require active, fault-tolerant quantum error correction (FTQEC18) to operate reliably. Fault tolerance (FT) thresholds for quantum computing have been proven against various noise models, and generally require per-gate failure rates between 10 À 6 and 10 À 2 (refs 19–22). Because RB is relatively insensitive to unitary errors[27] that dominate diamond norm error[28] and have unpredictable consequences for FTQEC20, it cannot efficiently measure diamond norm error to high precision This makes it nearly impossible to demonstrate suitability for FT using RB alone, unless errors are assumed to be strictly incoherent. There are variants of RB that characterize and report additional parameters, but none of them are well suited for diamond norm characterization or comparison to FT thresholds[29,30,31]
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