Journal
PHYSICAL REVIEW A
Volume 105, Issue 5, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevA.105.052416
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Funding
- Department of Energy [4000178321]
- National Science Foundation (NSF) ERC, Center for Quantum Networks [1941583]
- ARO [W911NF-18-1-0020, W911NF-18-1-0212]
- ARO MURI [W911NF-16-1-0349, W911NF-21-1-0325]
- AFOSR MURI [FA9550-19-1-0399]
- NSF [EFMA-1640959, OMA-1936118, EEC-1941583, OMA-2137642]
- NTT Research
- Packard Foundation [2013-39273]
- Div Of Engineering Education and Centers
- Directorate For Engineering [1941583] Funding Source: National Science Foundation
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This study focuses on the generation of high-fidelity graph states composed of realistic, finite-energy approximate GKP-encoded qubits in the photonic qubit architecture. The researchers track the transformation of the graph states under GKP-Steane error-correction and fusion operations using standard Gaussian dynamics, and provide an exact coherent error model to shed light on the error-correction properties of these graph states.
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 transfor-mation 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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