Abstract

Nonadiabatic geometric quantum computation (NGQC) has been developed to realize fast and robust geometric gate. However, the conventional NGQC is that all of the gates are performed with exactly the sameamount of time, whether the geometric rotation angle is large or small, due to the limitation of cyclic condition. Here, we propose an unconventional scheme, called nonadiabatic noncyclic geometric quantum computation(NNGQC), that arbitrary single- and two-qubit geometric gate can be constructed via noncyclic non-Abeliangeometric phase. Consequently, this scheme makes it possible to accelerate the implemented geometric gatesagainst the effects from the environmental decoherence. Furthermore, this extensible scheme can be applied invarious quantum platforms, such as superconducting qubit and Rydberg atoms. Specifically, for single-qubit gate,we make simulations with practical parameters in neutral atom system to show the robustness of NNGQC and also compare with NGQC using the recent experimental parameters to show that the NNGQC can significantly suppress the decoherence error. In addition, we also demonstrate that nontrivial two-qubit geometric gate can berealized via unconventional Rydberg blockade regime within current experimental technologies. Therefore, ourscheme provides a promising way for fast and robust neutral-atom-based quantum computation.

Highlights

  • Neutral atoms that interact via dipole-dipole interactions have became a potential platform for quantum computation [1,2]

  • We propose a new scheme, nonadiabatic noncyclic geometric quantum computation (NNGQC), that all of singlequbit geometric gate and nontrivial two-qubit can be realized via noncyclic non-Abelian geometric phase in a Rydberg system

  • To further understand the scheme of our NNGQC, we found that the nondiagonal parts of A and K satisfy the relations of unconventional quantum holonomy [50,85]

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Summary

INTRODUCTION

Neutral atoms that interact via dipole-dipole interactions have became a potential platform for quantum computation [1,2]. Through the laserinduced transitions from ground state to Rydberg state, many two- and multiple-qubit gates in neutral atom based on RRI have been demonstrated in experiments [13,14,15,16,17,18,19,20,21]. These experimental studies show the high-fidelity of single-qubit. Our NNGQC can be conveniently applied to other physical platforms such as superconducting qubits [57] and nitrogen-vacancy centers [66,67]

GENERAL MODEL
GATE PERFORMANCE AND ROBUSTNESS
NONTRIVIAL TWO-QUBIT GATE
Findings
CONCLUSION

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