Single-shot realization of nonadiabatic holonomic gates with a superconducting Xmon qutrit

Zhenxing Zhang,Liang Xiang,Yi Yin,D M Tong,P Z Zhao,Tenghui Wang,Guoping Guo,Peng Duan,Zhilong Jia

doi:10.1088/1367-2630/ab2e26

Zhenxing Zhang, Liang Xiang + Show 7 more

Open Access

https://doi.org/10.1088/1367-2630/ab2e26

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Abstract

Nonadiabatic holonomic quantum computation has received increasing attention due to its robustness against control errors and high-speed realization. The original protocol of nonadiabatic holonomic one-qubit gates has been experimentally demonstrated with a superconducting transmon qutrit. However, it requires two noncommuting gates to complete an arbitrary one-qubit gate, doubling the exposure time of the gate to error sources and thus leaving the gate vulnerable to environment-induced decoherence. Single-shot protocol has been subsequently proposed to realize an arbitrary one-qubit nonadiabatic holonomic gate. In this paper, a single-shot protocol of nonadiabatic holonomic gates is experimentally demonstrated by using a superconducting Xmon qutrit, with all the single-qubit Clifford gates carried out by a single-shot implementation. Characterized by quantum process tomography and randomized benchmarking, the single-shot gates reach a fidelity exceeding 99%.

Highlights

The circuit-based quantum computation requires a universal set of quantum gates, including arbitrary one-qubit gates and a nontrivial two-qubit gate
Nonadiabatic geometric quantum computation [8, 9] based on nonadiabatic Abelian geometric phases [3] and nonadiabatic holonomic quantum computation [10, 11] based on nonadiabatic non-Abelian geometric phases [4] were proposed
The nonadiabatic holonomic quantum computation retains the merits of both robustness against control errors and high-speed realization, receiving increasing attention for practical applications [12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28]

Summary

Introduction

The circuit-based quantum computation requires a universal set of quantum gates, including arbitrary one-qubit gates and a nontrivial two-qubit gate. Geometric quantum computation is an interesting approach to implement the universal quantum gates by using the geometric phases [1,2,3,4] or their non-Abelian counterpart, the holonomies [5]. With the long operation time required in an adiabatic process, the quantum gates are vulnerable to the environment-induced decoherence in the system. To overcome this difficulty, nonadiabatic geometric quantum computation [8, 9] based on nonadiabatic Abelian geometric phases [3] and nonadiabatic holonomic quantum computation [10, 11] based on nonadiabatic non-Abelian geometric phases [4] were proposed. The nonadiabatic holonomic quantum computation retains the merits of both robustness against control errors and high-speed realization, receiving increasing attention for practical applications [12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28]

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