Coherent manipulation of graph states composed of finite-energy Gottesman-Kitaev-Preskill-encoded qubits

Kaushik P. Seshadreesan, Prajit Dhara, Ashlesha Patil, Liang Jiang, and Saikat Guha
Phys. Rev. A 105, 052416 – Published 11 May 2022

Abstract

Graph states are a central resource in measurement-based quantum information processing. In the photonic qubit architecture based on Gottesman-Kitaev-Preskill (GKP) encoding, the generation of high-fidelity graph states composed of realistic, finite-energy approximate GKP-encoded qubits thus constitutes a key task. We consider the finite-energy approximation of GKP-qubit states given by a coherent superposition of shifted finite-squeezed vacuum states, where the displacements are Gaussian distributed. We present an exact description of graph states composed of such approximate GKP qubits as a coherent superposition of a Gaussian ensemble of randomly displaced ideal GKP-qubit graph states. Using standard Gaussian dynamics, we track the transformation of the covariance matrix and the mean-displacement vector elements of the Gaussian distribution of the ensemble under tools such as GKP-Steane error-correction and fusion operations that can be used to grow large high-fidelity GKP-qubit graph states. The covariance matrix elements capture the noise in the graph state due to the finite-energy approximation of GKP qubits, while the mean displacements relate to the possible absolute shift errors on the individual qubits arising conditionally from the homodyne measurements that are a part of these tools. Our work thus pins down an exact coherent error model for graph states generated from truly finite-energy GKP qubits, which can shed light on their error-correction properties.

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  • Received 22 December 2021
  • Accepted 25 April 2022

DOI:https://doi.org/10.1103/PhysRevA.105.052416

©2022 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Kaushik P. Seshadreesan1,2,*, Prajit Dhara1,3, Ashlesha Patil1, Liang Jiang4, and Saikat Guha1

  • 1Wyant College of Optical Sciences, University of Arizona, Tucson, Arizona 85721, USA
  • 2Department of Informatics and Networked Systems, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
  • 3Birla Institute of Technology and Science Pilani, Pilani, Rajasthan 333031, India
  • 4Pritzker School of Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, USA

  • *kausesh@pitt.edu

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Vol. 105, Iss. 5 — May 2022

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