Single-loop realization of arbitrary non-adiabatic holonomic single-qubit quantum gates in a superconducting circuit

TL;DR

This paper demonstrates a single-loop method to implement arbitrary non-adiabatic holonomic single-qubit gates in superconducting circuits, achieving high fidelities and paving the way for robust quantum manipulation.

Contribution

It introduces a novel single-loop scheme for non-adiabatic holonomic gates in superconducting qubits and cavities, with high experimental fidelities.

Findings

Transmon qubit gate fidelity of 0.996

Cavity gate fidelity of 0.978

Potential for two-qubit holonomic gates

Abstract

Geometric phases are noise-resilient, and thus provide a robust way towards high fidelity quantum manipulation. Here we experimentally demonstrate arbitrary non-adiabatic holonomic single-qubit quantum gates for both a superconducting transmon qubit and a microwave cavity in a single-loop way. In both cases, an auxiliary state is utilized, and two resonant microwave drives are simultaneously applied with well-controlled but varying amplitudes and phases for the arbitrariness of the gate. The resulting gates on the transmon qubit achieve a fidelity of 0.996 characterized by randomized benchmarking and the ones on the cavity show an averaged fidelity of 0.978 based on a full quantum process tomography. In principle, a nontrivial two-qubit holonomic gate between the qubit and the cavity can also be realized based on our presented experimental scheme. Our experiment thus paves the way towards practical non-adiabatic holonomic quantum manipulation with both qubits and cavities in a superconducting circuit.