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

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-energymore » GKP qubits, which can shed light on their error-correction properties.« less

Authors:

Seshadreesan, Kaushik P. ^[1]; Dhara, Prajit  ^[2];

• Search DOE PAGES for author "Dhara, Prajit"
• Search DOE PAGES for ORCID "0000-0002-4672-5117"

Patil, Ashlesha ^[3]; Jiang, Liang  ^[4];

• Search DOE PAGES for author "Jiang, Liang"
• Search DOE PAGES for ORCID "0000-0002-0000-9342"

Guha, Saikat ^[3]

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+ Show Author Affiliations

1. Univ. of Arizona, Tucson, AZ (United States); Univ. of Pittsburgh, PA (United States)
2. Univ. of Arizona, Tucson, AZ (United States); Birla Inst. of Technology and Science Pilani (India)
3. Univ. of Arizona, Tucson, AZ (United States)
4. Univ. of Chicago, IL (United States)

Publication Date:

Wed May 11 00:00:00 EDT 2022

Research Org.:

Univ. of Arizona, Tucson, AZ (United States)

Sponsoring Org.:

USDOE; National Science Foundation (NSF); US Army Research Office (ARO); US Air Force Office of Scientific Research (AFOSR); Packard Foundation

OSTI Identifier:

1982752

Grant/Contract Number:  

AC05-00OR22725; 4000178321; 1941583; W911NF-18-1- 0020; W911NF-18-1-0212; W911NF-16-1- 0349; FA9550-19-1-0399; EFMA- 1640959; OMA-1936118; EEC-1941583; 2013-39273

Resource Type:

Accepted Manuscript

Journal Name:

Physical Review A

Additional Journal Information:

Journal Volume: 105; Journal Issue: 5; Journal ID: ISSN 2469-9926

Publisher:

American Physical Society (APS)

Country of Publication:

United States

Language:

English

Subject:

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Optics; Physics; Measurement-based quantum computing; Quantum error correction; Quantum information processing; Quantum information processing with continuous variables; Quantum repeaters