Designing gate operations for single ion quantum computing in rare-earth-ion-doped crystals

TL;DR

This paper investigates the design of single and two-qubit gate operations in rare-earth-ion-doped crystals for quantum computing, analyzing error sources, parameter sensitivities, and realistic error rates through simulations.

Contribution

It provides a detailed simulation-based analysis of gate errors, bandwidth requirements, and parameter sensitivities for single and two-qubit gates in rare-earth-ion-doped crystal quantum computers.

Findings

Single-qubit gate errors of 2.1×10^{-4} without ISD and 3.4×10^{-4} with ISD considered.

Two-qubit gate errors ranging from 5×10^{-4} to 3×10^{-3} across various dipole-dipole interactions.

Analysis of how system uncertainties influence gate fidelity.

Abstract

Quantum computers based on rare-earth-ion-doped crystals show promising properties in terms of scalability and connectivity if single ions can be used as qubits. Through simulations, we investigate gate operations on such qubits and discuss how gate and system parameters affect gate errors, the required frequency bandwidth per qubit, and the risk of instantaneous spectral diffusion (ISD) occurring. Furthermore, we examine how uncertainties in the system parameters affect the gate errors, and how precisely the system needs to be known. We find gate errors for arbitrary single-qubit gates of $2.1\cdot 10^{-4}$ when ISD is not considered and $3.4\cdot 10^{-4}$ when we take heed to minimize it. Additionally, we construct two-qubit gates with errors ranging from $5\cdot 10^{-4} \rightarrow 3\cdot 10^{-3}$ over a broad range of dipole-dipole interaction strengths.