# Phonon-induced relaxation and decoherence times of the hybrid qubit in silicon quantum dots

## TL;DR

This paper provides a theoretical analysis of phonon-induced relaxation and decoherence times in silicon-based hybrid qubits, considering valley physics and environmental interactions to inform qubit coherence properties.

## Contribution

It introduces a three-level effective model for hybrid qubits in silicon, incorporating valley effects and environmental interactions to analyze decoherence mechanisms.

## Key findings

- Relaxation and decoherence times depend on bath spectral density and temperature.
- Valley excitations significantly influence qubit energy dispersion and decoherence.
- Results inform fundamental understanding of qubit coherence in silicon quantum dots.

## Abstract

We study theoretically the phonon-induced relaxation and decoherence processes in the hybrid qubit in silicon. Hybrid qubit behaves as a charge qubit when the detuning is close to zero and as spin qubit for large detuning values. It is realized starting from an electrostatically defined double quantum dot where three electrons are confined and manipulated through only electrical tuning. By employing a three-level effective model for the qubit and describing the environment bath as a series of harmonic oscillators in the thermal equilibrium states, we extract the relaxation and decoherence times as a function of the bath spectral density and of the bath temperature using the Bloch-Redfield theory. For Si quantum dots the energy dispersion is strongly affected by the physics of the valley, i.e. the conduction band minima, so we also included the contribution of the valley excitations in our analysis. Our results offer fundamental information on the system decoherence properties when the unavoidable interaction with the environment is included and temperature effects are considered.