To increase this ratio, one prevalent way is to increase the coherence times of the quantum devices, including the energy relaxation time and the dephasing time. One of the essential requirements for the reliable implementation of circuit-based quantum computation is a sufficiently large ratio between the coherence time and the gate length. To further improve the single-qubit gate fidelity, identifying the nature of the dominant errors is particularly important for improving performance and the fidelity of single-qubit can be seen as the upper boundary of two-qubit gate. The single- and two-qubit gate errors in transmon qubit are below 10 −3 and 10 −2 3, 4, 5, 6, 7, 8, 9, 10 respectively, and the single-qubit gate error in fluxonium qubit is below 10 −4 owing to a millisecond coherence time 10. As to the superconducting quantum computation, great progress has been made over the past two decades, including the realization of accurate and precise quantum gates. As a result, considerable efforts have been invested in realizing high-fidelity single qubit gates in leading platforms for quantum information processing, such as the trapped-ion and neutral atoms systems 1, 2. the near-term and the ultimate goals of the circuit-based quantum computation, make requirements on gate fidelities that exceed the state-of-the-art values. For example, both the noisy intermediate-scale quantum (NISQ) application and the fault-tolerant quantum computation, i.e. As to the circuit-based quantum computation, improving the reliability of entire computational tasks is decomposed into a series of subtasks, among which implementing high-fidelity single-qubit gates is an important component. Reliability is an unavoidable crux in the quest for beyond-classical computational capabilities. The demonstration extends the upper limit that the average fidelity of single-qubit gates can reach in a transmon-qubit system, and thus can be an essential step towards practical and reliable quantum computation in the near future. We also observe non-Markovian behavior in the experiment of long-sequence GST, which may provide guidance for further calibration. Moreover, we reconstruct the process matrices for the single-qubit gates by the gate set tomography (GST), with which we simulate RB sequences and obtain single-qubit fidelities consistent with experimental results. To understand the error sources, we experimentally obtain an error budget, consisting of the decoherence errors lower bounded by (4.62 ± 0.04) × 10 −5 and the leakage rate per gate of (1.16 ± 0.04) × 10 −5. In this work, we fabricate a transmon qubit with long coherence times and demonstrate single-qubit gates with the average gate error below 10 −4, i.e. Implementing arbitrary single-qubit gates with near perfect fidelity is among the most fundamental requirements in gate-based quantum information processing.
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