Experimental Demonstration of a Brachistochrone Nonadiabatic Holonomic Quantum-Gate Scheme in a Trapped Ion

TL;DR

This paper experimentally demonstrates a brachistochrone nonadiabatic holonomic quantum gate scheme in a trapped ion, showing improved speed and robustness over conventional methods, advancing practical quantum computation.

Contribution

It introduces and experimentally validates a brachistochrone NHQC protocol that enhances speed and robustness of quantum gates in trapped-ion systems.

Findings

BNHQC outperforms conventional NHQC in speed and robustness

High fidelity requires minimizing excited state population

Brachistochrone NHQC balances speed and error resilience

Abstract

Nonadiabatic holonomic quantum computation (NHQC) offers intrinsic resilience to certain control imperfections. However, conventional nonadiabatic holonomic protocols are constrained by the fixed-pulse-area condition, which limits flexibility and prolongs duration of small-angle gates. Here we experimentally demonstrate a universal brachistochrone nonadiabatic holonomic quantum gate scheme in a trapped 40Ca+ ion, and realized the construction of pX gate under the conventional NHQC, brachistochrone NHQC (BNHQC) and composite BNHQC (CBNHQC) protocols. By characterizing the performance of gate performance in the presence of dissipation, Rabi-frequency errors and detuning errors, we show that BNHQC and CBNHQC outperform conventional NHQC, and BNHQC can offer a favorable balance between operation speed and robustness. It further shows that keeping high fidelity and strong robustness need decrease the accumulated population of excited state in the evolution process. These results highlight nonadiabatic holonomic computation as a practical route toward fast and robust quantum gates in trapped-ion platforms.