Graphical Calculus for Non-Gaussian Quantum States

• URL: http://arxiv.org/abs/2409.07300v1
• Date: Wed, 11 Sep 2024 14:32:26 GMT
• Title: Graphical Calculus for Non-Gaussian Quantum States
• Authors: Lina Vandré, Boxuan Jing, Yu Xiang, Otfried Gühne, Qiongyi He,
• Abstract summary: We provide a graphical method to describe and analyze non-Gaussian quantum states using a hypergraph framework. We present illustrative examples on the preparation of non-Gaussian states rooted in these graph-based formalisms.
• Score: 1.653052113976862
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We provide a graphical method to describe and analyze non-Gaussian quantum states using a hypergraph framework. These states are pivotal resources for quantum computing, communication, and metrology, but their characterization is hindered by their complex high-order correlations. The formalism encapsulates transformation rules for any Gaussian unitary operation and local quadrature measurement, offering a visually intuitive tool for manipulating such states through experimentally feasible pathways. Notably, we develop methods for the generation of complex hypergraph states with more or higher-order hyperedges from simple structures through Gaussian operations only, facilitated by our graphical rules. We present illustrative examples on the preparation of non-Gaussian states rooted in these graph-based formalisms, revealing their potential to advance continuous-variable general quantum computing capabilities.

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