Reducing leakage of single-qubit gates for superconducting quantum processors using analytical control pulse envelopes (2402.17757v1)

Abstract: Improving the speed and fidelity of quantum logic gates is essential to reach quantum advantage with future quantum computers. However, fast logic gates lead to increased leakage errors in superconducting quantum processors based on qubits with low anharmonicity, such as transmons. To reduce leakage errors, we propose and experimentally demonstrate two new analytical methods, Fourier ansatz spectrum tuning derivative removal by adiabatic gate (FAST DRAG) and higher-derivative (HD) DRAG, both of which enable shaping single-qubit control pulses in the frequency domain to achieve stronger suppression of leakage transitions compared to previously demonstrated pulse shapes. Using the new methods to suppress the $ef$-transition of a transmon qubit with an anharmonicity of -212 MHz, we implement $R_X(\pi/2)$-gates with a leakage error below $3.0 \times 10^{-5}$ down to a gate duration of 6.25 ns, which corresponds to a 20-fold reduction in leakage compared to a conventional Cosine DRAG pulse. Employing the FAST DRAG method, we further achieve an error per gate of $(1.56 \pm 0.07)\times 10^{-4}$ at a 7.9-ns gate duration, outperforming conventional pulse shapes both in terms of error and gate speed. Furthermore, we study error-amplifying measurements for the characterization of temporal microwave control pulse distortions, and demonstrate that non-Markovian coherent errors caused by such distortions may be a significant source of error for sub-10-ns single-qubit gates unless corrected using predistortion.

• The paper presents FAST DRAG, which leverages Fourier transform and DRAG to achieve sub-3.0×10⁻⁵ leakage errors in 6.25 ns gate operations.
• The paper introduces HD DRAG, using higher-order derivatives to minimize leakage and achieve an error per gate of (1.56 ± 0.07)×10⁻⁴ in 7.9 ns.
• The study shows that analytical pulse shaping can bypass time-consuming closed-loop optimizations and significantly enhance overall quantum gate performance.

Analytical Pulse Envelopes for Reduced Leakage in Superconducting Quantum Processors

The quest for quantum advantage within the field of quantum computing faces significant challenges associated with improving the fidelity and speed of quantum logic gates. Among these challenges, reducing leakage errors in superconducting quantum processors, particularly those based on transmon qubits with low anharmonicity, is critical. The paper under discussion proposes two novel analytical methods aimed at shaping single-qubit control pulses to achieve enhanced suppression of leakage transitions compared to traditional pulse shapes.

Methodologies

The authors introduce two analytical methods:

1. Fourier Ansatz Spectrum Tuning with Derivative Removal by Adiabatic Gate (FAST DRAG): This method employs the Fourier transform in the frequency domain to adjust pulse shapes. The approach aims to minimize spectral energy at specific frequencies associated with leakage transitions. By incorporating the DRAG framework, this method tunes the quadrature envelope to further suppress leakage while maintaining fast gate operations. Notably, the method achieves a substantial reduction in leakage errors by implementing $R_X(\pi/2)$-gates on a transmon qubit with $6.25$ ns gate durations and leakage errors below $3.0 \times 10^{-5}$.
2. Higher-Derivative (HD) DRAG: The HD DRAG method extends the traditional DRAG technique by using higher-order derivatives in the pulse shaping process. This extension allows for a more robust frequency control, effectively minimizing leakage across multiple transitions. By implementing this method, an error per gate of $(1.56 \pm 0.07)\times 10^{-4}$ was achieved within a 7.9-ns gate duration, significantly outperforming conventional pulse shapes.

Results and Observations

The presented methods yield significant improvements in reducing leakage errors for fast single-qubit gates. The FAST DRAG method, in particular, demonstrates superior performance by reducing the error and leakage per gate over traditional cosine envelopes. Additionally, the ability to avoid time-consuming closed-loop optimizations is a practical advantage of these analytical methods.

The authors also conducted an investigation into temporal microwave control pulse distortions, highlighting the impact of non-Markovian coherent errors as a significant error source for gates lasting under 10 ns. By utilizing error-amplifying measurements, these distortions can be characterized, and correction via predistortion becomes feasible, thereby enhancing the fidelity of the gates.

Implications and Future Directions

This paper has substantial implications for the development of practical quantum computing systems. By addressing the leakage errors that are detrimental to quantum error correction, these methods contribute to enhancing the operational fidelity of qubits, a critical aspect for quantum error-corrected systems. The analytical methods also provide a robust framework for frequency control in pulse shaping, which is vital for deploying gates in frequency-crowded systems or where simultaneous multi-qubit operations are required.

While the paper focuses on single-qubit operations, the framework has potential applications in multi-qubit settings, particularly in optimizing crosstalk suppression and implementing efficient two-qubit gates. Future research could explore integrating these analytical methods with advanced optimization techniques or machine learning algorithms to further refine pulse shapes and enhance overall quantum circuit performance. Additionally, extending the approach to other qubit architectures could broaden its applicability and contribute to the general advancement of quantum technologies.