Benchmarking of dynamically corrected gates for the exchange-only spin qubit in $1/f$ noise environment

TL;DR

This paper evaluates the effectiveness of dynamically corrected gates in reducing noise-induced errors in exchange-only spin qubits under 1/f noise, showing significant improvements for certain noise correlation levels.

Contribution

It provides a theoretical analysis and numerical benchmarking of dynamically corrected gates' performance against hyperfine noise in exchange-only spin qubits, highlighting the critical noise correlation exponent for error reduction.

Findings

Dynamically corrected gates reduce errors by about two orders of magnitude for noise exponent α ≥ 1.5.

No significant improvement is observed for α ≤ 1.5.

The critical noise correlation exponent α_c is approximately 1.5, higher than in singlet-triplet qubits.

Abstract

We study theoretically the responses of the dynamically corrected gates to time-dependent noises in the exchange-only spin qubit system. We consider $1/f$ noises having spectra proportional to $1/\omega^\alpha$, where the exponent $\alpha$ indicates the strength of correlation within the noise. The quantum gate errors due to noises are extracted from a numerical simulation of Randomized Benchmarking, and are compared between the application of uncorrected operations and that of dynamically corrected gates robust against the hyperfine noise. We have found that for $\alpha\gtrsim1.5$, the dynamically corrected gates offer considerable reduction in the gate error and such reduction is approximately two orders of magnitude for the experimentally relevant noise exponent. On the other hand, no improvement of the gate fidelity is provided for $\alpha\lesssim1.5$. This critical value $\alpha_c\approx1.5$ is comparatively larger than that for the cases for the singlet-triplet qubits. The filter transfer functions corresponding to the dynamically corrected gates are also computed and compared to those derived from uncorrected pulses. Our results suggest that the dynamically corrected gates are useful measures to suppress the hyperfine noise when operating the exchange-only qubits.