Smoking-gun signatures of non-Markovianity of a superconducting qubit

TL;DR

This paper investigates non-Markovian noise effects in superconducting qubits, revealing how temporally correlated noise causes coherence revivals and frequency shifts, impacting qubit control and fidelity.

Contribution

It models non-Markovian noise in superconducting qubits using quantum circuit theory and derives a master equation demonstrating persistent non-Markovian dynamics.

Findings

Revealed periodic coherence revivals due to non-Markovian noise.

Identified additional frequency components affecting qubit precession.

Showed non-Markovian effects influence single-qubit gate operations.

Abstract

We describe temporally correlated noise processes that influence the idle evolution of a superconducting transmon qubit. To model the composite qubit-environment system we use quantum circuit theory, and we show how a circuit Hamiltonian can be derived for transverse noise affecting the qubit. Based on the time-convolutionless projection operator method, we construct a time-local master equation which, when transformed to its canonical Lindblad form, exhbitis a decay rate that is negative at all times, corresponding to eternally non-Markovian dynamics. By expressing the solution of the master equation in the Kraus representation, we identify two crucial non-Markovian phenomena: periodic revivals of coherence, and the appearance of additional frequencies far from the qubit frequency in the precession of the qubit state. When a single qubit gate acts on the qubit state, these extra frequency terms rotate undesirably and they effectively act as the memory of the state prior to the rotation around the Bloch sphere.