Measuring and Suppressing Quantum State Leakage in a Superconducting Qubit (1509.05470v2)

Abstract: Leakage errors occur when a quantum system leaves the two-level qubit subspace. Reducing these errors is critically important for quantum error correction to be viable. To quantify leakage errors, we use randomized benchmarking in conjunction with measurement of the leakage population. We characterize single qubit gates in a superconducting qubit, and by refining our use of Derivative Reduction by Adiabatic Gate (DRAG) pulse shaping along with detuning of the pulses, we obtain gate errors consistently below $10^{-3}$ and leakage rates at the $10^{-5}$ level. With the control optimized, we find that a significant portion of the remaining leakage is due to incoherent heating of the qubit.

Measuring and Suppressing Quantum State Leakage in a Superconducting Qubit

The paper "Measuring and Suppressing Quantum State Leakage in a Superconducting Qubit" addresses a pertinent issue in the field of superconducting qubit technology: the control and reduction of leakage errors. Leakage errors are a type of quantum error where a quantum state leaves the qubit's designated two-level computational subspace, which poses a significant challenge for quantum error correction (QEC) techniques, such as the surface code.

Experimental Methodology and Results

The authors employ randomized benchmarking (RB) to characterize and quantify leakage errors in single qubit gates. Their methodology involves measuring the leakage population to evaluate the effectiveness of gate operations under various pulse shaping techniques. The paper refines the use of Derivative Reduction by Adiabatic Gate (DRAG) pulse shaping and introduces a detuning parameter to enhance gate fidelity while minimizing leakage.

Key metrics achieved in this research include gate errors consistently below $10^{-3}$ and leakage rates at the $10^{-5}$ level, representing significant improvements over previous experimental settings. The RB methodology used not only characterizes overall gate fidelity, but also provides insight into leakage dynamics by modeling the saturation population of the leakage state via rate equations.

Technical Findings and Implications

The paper reveals a trade-off inherent in the simple DRAG pulse shaping technique between minimizing leakage errors and phase errors. The DRAG correction optimizes the spectral weight of control pulses to suppress leakage transitions (notably the $1 \leftrightarrow 2$ transition in the ladder of transmon energy levels) at an optimal weighting parameter $\alpha$. However, $\alpha$ must be refined alongside pulse detuning to concurrently address phase errors from AC Stark shifts.

Detuning of pulse frequencies as a mechanism to mitigate phase errors proves effective, thereby enabling the simultaneous achievement of high-fidelity gate operations with reduced leakage. By optimizing pulse detuning for various values of $\alpha$, gate operations achieved an error per Clifford gate maintained at approximately $9.1 \times 10^{-4}$. This advancement in detuning and DRAG application provides a versatile pathway for constructing functional qubits suitable for error correction.

Furthermore, the paper investigates leakage dependence on pulse length and uncovers the dominance of incoherent processes such as thermal excitation in contributing to leakage at longer pulse times. This highlights an area for potential improvement in qubit designs—to mitigate heating effects and further reduce leakage rates.

Future Directions

This paper sets the foundation for extending the characterization and mitigation strategies for leakage to multi-qubit systems, particularly concerning entangling interactions and complex gate operations. Minimizing leakage remains a pivotal area to advance the practical implementation of quantum error correction and efficient quantum computation architectures.

In terms of future technologies, improving thermal management and coherence aspects of qubit environments can further reduce leakage caused by incoherent heating. The combination of precise pulse shaping and elevated control over qubit interactions holds promise for rapid progress toward scalable quantum processing units. As superconducting qubits remain a leading candidate for quantum computing implementations, continuing studies like these are essential to overcoming longstanding obstacles associated with quantum state stability and fidelity.