Composite Short-path Nonadiabatic Holonomic Quantum Gates

TL;DR

This paper introduces a fast, robust, and high-fidelity nonadiabatic holonomic quantum gate scheme using inverse Hamiltonian engineering and composite pulses, suitable for implementation with Rydberg atoms, advancing quantum computation.

Contribution

It presents a shortest-path NHQC scheme with inverse Hamiltonian engineering and composite dynamical decoupling pulses, improving fidelity and robustness over previous methods.

Findings

Higher fidelity and robustness than previous NHQC schemes.

Outperforms the optimal dynamical scheme in certain parameters.

Feasible implementation with Rydberg atoms and simplified CNOT gate.

Abstract

Nonadiabatic holonomic quantum computation (NHQC) has attracted significant attention due to its fast evolution and the geometric nature induced resilience to local noises. However, its long operation time and complex physical implementation make it hard to surpass the dynamical scheme, and thus hindering its wide application. Here, we present to implement NHQC with the shortest path under some conditions, through the inverse Hamiltonian engineering technique, which posseses higher fidelity and stronger robustness than previous NHQC schemes. Meanwhile, the gate performance in our scheme can be further improved by using the proposed composite dynamical decoupling pulses, which can efficiently improve both the gate fidelity and robustness, making our scheme outperform the optimal dynamical scheme in certain parameters range. Remarkably, our scheme can be readily implemented with Rydberg atoms, and a simplified implementation of the controlled-not gate in the Rydberg blockade regime can be achieved. Therefore, our scheme represents a promising progress towards future fault-tolerant quantum computation in atomic systems.