Simple Pulses for Elimination of Leakage in Weakly Nonlinear Qubits

TLDR

In quantum computing, a qubit is selected from many levels of an anharmonic oscillator, but simple control fails on short timescales due to leakage to higher levels. We aim to provide an analytic formula that suppresses leakage for any single‑control pulse. The method adds a second control proportional to the time derivative of the first. For realistic superconducting qubit parameters, the approach reduces error by an order of magnitude compared to state‑of‑the‑art smooth pulses, showing weak anharmonicity is not a limiting factor.

Abstract

In realizations of quantum computing, a two-level system (qubit) is often singled out from the many levels of an anharmonic oscillator. In these cases, simple qubit control fails on short time scales because of coupling to leakage levels. We provide an easy to implement analytic formula that inhibits this leakage from any single-control analog or pixelated pulse. It is based on adding a second control that is proportional to the time derivative of the first. For realistic parameters of superconducting qubits, this strategy reduces the error by an order of magnitude relative to the state of the art, all based on smooth and feasible pulse shapes. These results show that even weak anharmonicity is sufficient and in general not a limiting factor for implementing quantum gates.