Robust composite two-qubit gates for silicon-based spin qubits

TL;DR

This paper introduces a Hamiltonian inverse engineering approach for constructing robust, high-fidelity two-qubit gates in silicon-based spin qubits, simplifying implementation and enhancing error resilience.

Contribution

It presents a universal, efficient method for designing composite two-qubit gates with fewer operations, applicable to various physical systems, and combines geometric and dynamic principles for robustness.

Findings

Achieved a high-fidelity fSim gate with 99.95% fidelity in 50 ns

Demonstrated stronger robustness against systematic errors using a hybrid geometric-dynamic scheme

Proposed a one-step pulse switch method for silicon double quantum dots

Abstract

We propose a universal approach based on Hamiltonian inverse engineering to realize a set of parameterized two-qubit gates. This method possesses unique advantages to simultaneous control of transitions among four energy levels, providing a simpler and effective way to construct composite two-qubit gates with fewer operations than traditional methods. Applied to silicon double quantum dots (DQDs), one can realize a one-step fSim gate and a B gate with only one pulse switch. Of note, the method can be further integrated with various optimization theories to enhance gate performance. Based on quantum optimal control theory, we develop a high-fidelity fSim gate scheme with experimentally feasible pulse shapes, featuring an average gate time of 50 ns and a theoretical fidelity of 99.95% in the presence of decoherence and approximation error. By incorporating geometric quantum gate principles, we propose a combined geometric and dynamic fSim gate scheme. Numerical simulations demonstrate that this hybrid scheme exhibits stronger robustness against systematic errors compared to the purely dynamic approach. Our method is generalizable to arbitrary two-qubit physical systems, offering a feasible pathway for rapidly and robustly constructing composite two-qubit gates.