State leakage during fast decay and control of a superconducting transmon qubit

TL;DR

This paper investigates state leakage in superconducting transmon qubits, revealing significant short-time leakage effects and demonstrating suppression techniques, thereby clarifying the limits of the two-level approximation in qubit control.

Contribution

It provides a numerically exact analysis of state leakage in transmon qubits, highlighting the impact of higher excited states on decay and gate fidelity, and shows how DRAG control mitigates leakage errors.

Findings

Significant short-time state leakage due to bath coupling.

Quantification of leakage errors in single-qubit gates.

Demonstration of leakage suppression using DRAG control.

Abstract

Superconducting Josephson junction qubits constitute the main current technology for many applications, including scalable quantum computers and thermal devices. Theoretical modeling of such systems is usually done within the two-level approximation. However, accurate theoretical modeling requires taking into account the influence of the higher excited states without limiting the system to the two-level qubit subspace. Here, we study the dynamics and control of a superconducting transmon using the numerically exact stochastic Liouville-von Neumann equation approach. We focus on the role of state leakage from the ideal two-level subspace for bath induced decay and single-qubit gate operations. We find significant short-time state leakage due to the strong coupling to the bath. We quantify the leakage errors in single-qubit gates and demonstrate their suppression with DRAG control for a five-level transmon in the presence of decoherence. Our results predict the limits of accuracy of the two-level approximation and possible intrinsic constraints in qubit dynamics and control for an experimentally relevant parameter set.