Filter function formalism beyond pure dephasing and non-Markovian noise in singlet-triplet qubits

TL;DR

This paper extends the filter function formalism to handle non-commuting noise in qubits, enabling better modeling of realistic noise environments like nuclear and charge noise in singlet-triplet qubits, with validation against experiments.

Contribution

It introduces a generalized filter function approach for non-commuting noise, applicable to slow noise fluctuations, enhancing the modeling of qubit decoherence beyond pure dephasing.

Findings

Good agreement with experimental data on singlet-triplet qubits

Demonstrates the formalism's ability to model complex noise types

Highlights challenges in distinguishing noise sources in experiments

Abstract

The filter function formalism quantitatively describes the dephasing of a qubit by a bath that causes Gaussian fluctuations in the qubit energies with an arbitrary noise power spectrum. Here, we extend this formalism to account for more general types of noise that couple to the qubit through terms that do not commute with the qubit's bare Hamiltonian. Our approach applies to any power spectrum that generates slow noise fluctuations in the qubit's evolution. We demonstrate our formalism in the case of singlet-triplet qubits subject to both quasistatic nuclear noise and $1/\omega^\alpha$ charge noise and find good agreement with recent experimental findings. This comparison shows the efficacy of our approach in describing real systems and additionally highlights the challenges with distinguishing different types of noise in free induction decay experiments.