Equivalent noise properties of scalable continuous-variable cluster states

Optical continuous-variable cluster states (CVCSs) in combination with Gottesman-Kitaev-Preskill~(GKP) qubits enable fault-tolerant quantum computation so long as these resources are of high enough quality. Previous studies concluded that a particular CVCS, the quad rail lattice~(QRL), exhibits lowe...

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Bibliographic Details
Published inarXiv.org
Main Authors Walshe, Blayney W, Alexander, Rafael N, Matsuura, Takaya, Baragiola, Ben Q, Menicucci, Nicolas C
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 19.05.2023
Subjects
Clusters
Continuity (mathematics)
Equivalence
Fault tolerance
Optical properties
Physics - Quantum Physics
Quantum computing
Qubits (quantum computing)
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Summary:Optical continuous-variable cluster states (CVCSs) in combination with Gottesman-Kitaev-Preskill~(GKP) qubits enable fault-tolerant quantum computation so long as these resources are of high enough quality. Previous studies concluded that a particular CVCS, the quad rail lattice~(QRL), exhibits lower GKP gate-error rate than others do. We show in this work that many other experimentally accessible CVCSs also achieve this level of performance by identifying operational equivalences to the QRL. Under this equivalence, the GKP Clifford gate set for each CVCS maps straightforwardly from that of the QRL, inheriting its noise properties. Furthermore, each cluster state has at its heart a balanced four-splitter -- the four-mode extension to a balanced beam splitter. We classify all four-splitters, show they form a single equivalence class under SWAP and parity operators, and we give a construction of any four-splitter with linear optics, thus extending the toolbox for theoretical and experimental cluster-state design and analysis.
ISSN:2331-8422
DOI:10.48550/arxiv.2305.11630