Graphical Framework for Non-Gaussian Quantum States

TL;DR

This paper introduces a graphical hypergraph framework for describing, analyzing, and generating non-Gaussian quantum states, facilitating their manipulation and potential applications in quantum computing and metrology.

Contribution

It develops a novel hypergraph-based graphical method for representing and transforming non-Gaussian quantum states using Gaussian operations and measurements.

Findings

Graphical rules enable manipulation of non-Gaussian states.

Methods for generating complex hypergraph states from simple structures.

Illustrative examples demonstrate the framework's utility in quantum state preparation.

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 framework encapsulates transformation rules for a series of typical 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.