Quantum-control approach to realizing a Toffoli gate in circuit QED

TL;DR

This paper demonstrates a quantum-control method to implement a high-fidelity Toffoli gate in circuit QED with superconducting qubits, achieving over 90% fidelity in 75 ns and over 99% in 140 ns, considering realistic control constraints.

Contribution

It introduces an optimized quantum-control protocol for Toffoli gate realization in circuit QED, accounting for control field filtering and leakage suppression, with theoretical fidelity predictions.

Findings

Achieves >90% fidelity in 75 ns

Fidelity exceeds 99% in about 140 ns

Control field filtering minimally impacts gate fidelity

Abstract

We study the realization of a Toffoli gate with superconducting qubits in a circuit-QED setup using quantum-control methods. Starting with optimized piecewise-constant control fields acting on all qubits and typical strengths of XY-type coupling between the qubits, we demonstrate that the optimal gate fidelities are affected only slightly by a "low-pass" filtering of these fields with the typical cutoff frequencies of microwave driving. Restricting ourselves to the range of control-field amplitudes for which the leakage to the non-computational states of a physical qubit is heavily suppressed, we theoretically predict that in the absence of decoherence and leakage, within 75 ns a Toffoli gate can be realized with intrinsic fidelities higher than 90%, while fidelities above 99% can be reached in about 140 ns.