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arXiv:2302.08690 · npj Quantum Information

Error per single-qubit gate below 10−4 in a superconducting qubit

Zhiyuan Li, Pei Liu, Peng Zhao, Zhenyu Mi, Huikai Xu, Xuehui Liang, Tang Su, Weijie Sun, Guangming Xue, Jing-Ning Zhang, Weiyang Liu, Yirong Jin, Haifeng Yu

Published Nov 3, 2023• 57 citations
arXivHTMLPDF

Abstract

Abstract Implementing arbitrary single-qubit gates with near perfect fidelity is among the most fundamental requirements in gate-based quantum information processing. 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. (7.42 ± 0.04) × 10 −5 by randomized benchmarking (RB). 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 . 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. We also observe non-Markovian behavior in the experiment of long-sequence GST, which may provide guidance for further calibration. 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.

DOI
10.1038/s41534-023-00781-x

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Abstract Implementing arbitrary single-qubit gates with near perfect fidelity is among the most fundamental requirements in gate-based quantum information processing. 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. (7.42 ± 0.04) × 10 −5 by randomized benchmarking (RB). 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 . 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. We also observe non-Markovian behavior in the experiment of long-sequence GST, which may provide guidance for further calibration. 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.
Quantum computers have the potential to solve problems which are classically intractable. Superconducting qubits present a promising path to building such a computer. Recent experiments with these qubits have demonstrated the principles of quantum error correction, quantum simulation, quantum annealing, and more. Current research with superconducting qubits is focused on two primary goals: creating a fully fault tolerant logical qubit out of many physical qubits using surface code error correction, and demonstrating an exponential speedup over any classical computer for a well-defined computational problem. To achieve either of these goals requires high precision control of three components: single qubit gates, two qubit gates, and qubit measurement. In this thesis, we use randomized benchmarking to characterize single qubit gates with 99.95\\% fidelity and two qubit gates wiht 99.5\\% fidelity in superconducting transmon qubits. In addition, we use standard decoherence measurements as well as newly developed extensions of randomized benchmarking to determine the limiting sources of error. Finally, we explore the surprisingly complicated dynamics of measuring the transmon state through a coupled resonator, and show that fully understanding this process requires breaking a few "standard" assumptions.
Abstract Universal quantum computation will require qubit technology based on a scalable platform1, together with quantum error correction protocols that place strict limits on the maximum infidelities for one- and two-qubit gate operations2, 3. Although various qubit systems have shown high fidelities at the one-qubit level4–10, the only solid-state qubits manufactured using standard lithographic techniques that have demonstrated two-qubit fidelities near the fault-tolerance threshold6 have been in superconductor systems. Silicon-based quantum dot qubits are also amenable to large-scale fabrication and can achieve high single-qubit gate fidelities (exceeding 99.9 per cent) using isotopically enriched silicon11, 12. Two-qubit gates have now been demonstrated in a number of systems13–15, but as yet an accurate assessment of their fidelities using Clifford-based randomized benchmarking, which uses sequences of randomly chosen gates to measure the error, has not been achieved. Here, for qubits encoded on the electron spin states of gate-defined quantum dots, we demonstrate Bell state tomography with fidelities ranging from 80 to 89 per cent, and two-qubit randomized benchmarking with an average Clifford gate fidelity of 94.7 per cent and an average controlled-rotation fidelity of 98 per cent. These fidelities are found to be limited by the relatively long gate times used here compared with the decoherence times of the qubits. Silicon qubit designs employing fast gate operations with high Rabi frequencies16, 17, together with advanced pulsing techniques18, should therefore enable much higher fidelities in the near future.
We present benchmarking results for single-qubit gates implemented on a neutral atom quantum processor using Direct Randomized Benchmarking (DRB) and Gate Set Tomography (GST). The DRB protocol involves preparing stabilizer states, applying mmm layers of native single-qubit gates, and measuring in the computational basis, providing an efficient error characterization under a stochastic Pauli noise model. GST enables the full, self-consistent reconstruction of quantum processes, including gates, input states, and measurements. Both protocols provide robust to state preparation and measurement (SPAM) errors estimations of gate performance, offering complementary perspectives on quantum gate fidelity. For single-qubit gates, DRB yields an average fidelity of 99.963%99.963 \%99.963%. The protocol was further applied to a 25-qubit array under global single-qubit control. GST results are consistent with those obtained via DRB. We also introduce a gauge optimization procedure for GST that brings the reconstructed gates, input states, and measurements into a canonical frame, enabling meaningful fidelity comparisons while preserving physical constraints. These constraints of the operators -- such as complete positivity and trace preservation -- are enforced by performing the optimization over the Stiefel manifold. The combined analysis supports the use of complementary benchmarking techniques for characterizing scalable quantum architectures.
Abstract Nonadiabatic holonomic quantum computation has received increasing attention due to its robustness against control errors and high-speed realization. The original protocol of nonadiabatic holonomic one-qubit gates has been experimentally demonstrated with a superconducting transmon qutrit. However, it requires two noncommuting gates to complete an arbitrary one-qubit gate, doubling the exposure time of the gate to error sources and thus leaving the gate vulnerable to environment-induced decoherence. Single-shot protocol has been subsequently proposed to realize an arbitrary one-qubit nonadiabatic holonomic gate. In this paper, a single-shot protocol of nonadiabatic holonomic gates is experimentally demonstrated by using a superconducting Xmon qutrit, with all the single-qubit Clifford gates carried out by a single-shot implementation. Characterized by quantum process tomography and randomized benchmarking, the single-shot gates reach a fidelity exceeding 99%.
With improved gate calibrations reducing unitary errors, we achieve a benchmarked single-qubit gate fidelity of $0.9995\ifmmode\pm\else\textpm\fi{}0.0002$ with superconducting qubits in a circuit quantum electrodynamics system. We present a method for distinguishing between unitary and nonunitary errors in quantum gates by interleaving repetitions of a target gate within a randomized benchmarking sequence. The benchmarking fidelity decays quadratically with the number of interleaved gates for unitary errors but linearly for nonunitary errors, allowing us to separate systematic coherent errors from decoherent effects. With this protocol, we show that the fidelity of the gates is not limited by unitary errors.