Leakage reduction in fast superconducting qubit gates via optimal control (2003.05952v1)

Abstract: Reaching high speed, high fidelity qubit operations requires precise control over the shape of the underlying pulses. For weakly anharmonic systems, such as superconducting transmon qubits, short gates lead to leakage to states outside of the computational subspace. Control pulses designed with open-loop optimal control may reduce such leakage. However, model inaccuracies can severely limit the usability of such pulses. We implemented a closed-loop optimization that simultaneously adapts all control parameters based on measurements of a cost function built from Clifford gates. By parameterizing pulses with a piecewise-constant representation that matches the capabilities of the control hardware we create a $4.16~\rm{ns}$ single-qubit pulse with $99.76\,\%$ fidelity and $0.044\,\%$ leakage. This is a seven-fold reduction of the leakage rate of the best DRAG pulse we have calibrated at such short durations on the same system.

Analysis of Leakage Reduction in Fast Superconducting Qubit Gates via Optimal Control

The paper "Leakage reduction in fast superconducting qubit gates via optimal control" presents a method to enhance the fidelity of quantum gates by addressing the challenge of leakage in superconducting transmon qubits, which is a significant concern due to their weak anharmonicity. The authors propose a novel closed-loop optimization technique leveraging open-loop optimal control principles, improving upon traditional DRAG (Derivative Removal by Adiabatic Gate) techniques by optimizing pulse shapes through direct experimentation.

Key Methodologies and Results

The paper implements a piecewise-constant representation for qubit pulse shaping, compatible with contemporary control hardware capabilities, optimizing these shapes using a closed-loop method. This approach adjusts the control pulses based on a cost function derived from Cliffords' circuits, thus mitigating the inaccuracies inherent in theoretical models that impair the effectiveness of open-loop control strategies.

The notable outcome of this approach is the achievement of a single-qubit pulse lasting 4.16 ns with a fidelity of 99.76% and a leakage as low as 0.044%. This represents a seven-fold reduction in leakage compared to the optimal DRAG pulse calibrated for similar durations. Such performance is crucial, given that leakage to non-computational states presents substantial challenges for error correction mechanisms and overall quantum processor performance.

Theoretical and Practical Implications

The implications of this research extend to both theoretical and practical domains. Theoretically, it demonstrates the effectiveness of employing closed-loop optimization for accurate control in quantum systems where model inaccuracies are pronounced. The technique reconciles the exploitation of hardware constraints with the necessity of high-fidelity quantum operations, making it relevant for applications requiring rapid gate operations, such as variational quantum algorithms and quantum error correction.

Practically, the research suggests pathways to implement complex quantum algorithms with reduced error rates without necessitating excessive qubit noise filtering or relying solely on ultra-long gate operations, thereby lowering the overhead in error correction resources. This enhancement in gate performance supports the scalability of superconducting qubits in large-scale quantum computing architectures.

Future Developments

Future developments in the field are likely to involve the application of this methodology to multi-qubit systems, where gate dynamics are inherently more complex. Extending the closed-loop configuration to these systems can potentially streamline two-qubit operations, optimizing for both fidelity and gate time, thus enhancing entangling operations — a critical component in quantum computation. Additionally, integrating this approach with advanced quantum error correction codes could translate to more robust fault-tolerant quantum computing frameworks. Further investigation into the interplay of system noise characteristics and pulse shaping will also be pivotal in advancing superconducting qubit technologies.

In summary, the paper underscores a significant advancement in quantum control engineering, pointing to a promising direction for decreasing operational errors in quantum circuits, and refining quantum gate implementations essential for efficient quantum computation in practical scenarios.