Optimal control of a leaking qubit

TL;DR

This paper applies optimal control theory to improve quantum gate fidelity in anharmonic qubits by designing pulse sequences that significantly reduce leakage errors, approaching near-perfect operations.

Contribution

It introduces a method to optimize Rabi pulse envelopes to suppress leakage in anharmonic qubits, enhancing gate fidelity beyond simple pulse shapes.

Findings

Gate error reduced by orders of magnitude

Near-perfect gates achievable for longer pulses

Optimized pulses act as composite sequences refocusing leakage

Abstract

Physical implementations of quantum bits can contain coherent transitions to energetically close non-qubit states. In particular, for anharmonic oscillator systems such as the superconducting phase qubit and the transmon a two-level approximation is insufficient. We apply optimal control theory to the envelope of a resonant Rabi pulse in a qubit in the presence of a single, weakly off-resonant leakage level. The gate error of a spin flip operation reduces by orders of magnitude compared to simple pulse shapes. Near-perfect gates can be achieved for any pulse duration longer than an intrinsic limit given by the nonlinearity. The pulses can be understood as composite sequences that refocus the leakage transition. We also discuss ways to improve the pulse shapes.