Analytic control methods for high fidelity unitary operations in a weakly nonlinear oscillator

TL;DR

This paper introduces a general adiabatic expansion-based method to design pulse shapes that reduce leakage errors in weakly nonlinear oscillators, improving upon the DRAG technique for high-fidelity qubit operations.

Contribution

It develops a flexible scheme for creating tailored pulse shapes that correct leakage errors, extending and enhancing the DRAG method for various nonlinear oscillators.

Findings

Developed a family of pulse solutions for leakage correction.

Improved upon the existing DRAG technique.

Applicable to oscillators with multiple leakage transitions.

Abstract

In qubits made from a weakly anharmonic oscillator the leading source of error at short gate times is leakage of population out of the two dimensional Hilbert space that forms the qubit. In this paper we develop a general scheme based on an adiabatic expansion to find pulse shapes that correct this type of error. We find a family of solutions that allows tailoring to what is practical to implement for a specific application. Our result contains and improves the previously developed DRAG technique [F. Motzoi, et. al., Phys. Rev. Lett. 103, 110501 (2009)] and allows a generalization to other non-linear oscillators with more than one leakage transition.