# Achieving High Fidelity Single Qubit Gates in a Strongly Driven Silicon Quantum Dot Hybrid Qubit

## TL;DR

This paper analyzes fast resonant X rotations in silicon quantum dot hybrid qubits under strong driving, providing analytic formulas for optimal parameters and demonstrating the potential for gate fidelities exceeding 99.99% without decoherence.

## Contribution

It introduces a dressed-state formalism beyond the rotating wave approximation to optimize strong-driving qubit gates in silicon quantum dots.

## Key findings

- Analytic formulas for optimal driving frequency and Rabi frequency.
- Gate fidelities above 99.99% are achievable without decoherence.
- Strong driving effects can be suppressed to improve gate performance.

## Abstract

Performing qubit gate operations as quickly as possible can be important to minimize the effects of decoherence. For resonant gates, this requires applying a strong ac drive. However, strong driving can present control challenges by causing leakage to levels that lie outside the qubit subspace. Strong driving can also present theoretical challenges because preferred tools such as the rotating wave approximation can break down, resulting in complex dynamics that are difficult to control. Here we analyze resonant $X$ rotations of a silicon quantum double dot hybrid qubit within a dressed-state formalism, obtaining results beyond the rotating wave approximation. We obtain analytic formulas for the optimum driving frequency and the Rabi frequency, which both are affected by strong driving. While the qubit states exhibit fast oscillations due to counter-rotating terms and leakage, we show that they can be suppressed to the point that gate fidelities above $99.99\%$ are possible, in the absence of decoherence. Hence decoherence mechanisms, rather than strong-driving effects, should represent the limiting factor for resonant-gate fidelities in quantum dot hybrid qubits.