# Hyperfine-assisted decoherence of a phosphorus nuclear-spin qubit in silicon

## TL;DR

This paper investigates the decoherence mechanisms affecting a phosphorus nuclear-spin qubit in silicon, focusing on electric noise sources like phonons and charge noise, and identifies parameter regimes for fast, coherent control.

## Contribution

It provides a detailed analysis of electric noise-induced decoherence in electrically controlled nuclear-spin qubits in silicon, guiding optimized nanostructure design for quantum operations.

## Key findings

- Decoherence times are limited by phonons and 1/f charge noise.
- Electrical single-qubit operations can be an order of magnitude faster than decoherence.
- Dephasing due to 1/f charge noise dominates in optimal parameter regimes.

## Abstract

The nuclear spin of a phosphorus atom in silicon has been used as a quantum bit in various quantum-information experiments. It has been proposed that this nuclear-spin qubit can be efficiently controlled by an ac electric field, when embedded in a two electron dot-donor setup subject to intrinsic or artificial spin-orbit interaction. Exposing the qubit to control electric fields in that setup exposes it to electric noise as well. In this work, we describe the effect of electric noise mechanisms, such as phonons and $1/f$ charge noise, and estimate the corresponding decoherence time scales of the nuclear-spin qubit. We identify a promising parameter range where the electrical single-qubit operations are at least an order of magnitude faster then the decoherence. In this regime, decoherence is dominated by dephasing due to $1/f$ charge noise. Our results facilitate the optimized design of nanostructures to demonstrate electrically driven nuclear spin resonance.