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Mathematica notebook for "Nonclassical nullifiers for quantum hypergraph states"

Abhijith Ravikumar, Darren W. Moore, Radim Filip

Published Apr 27, 2026• 0 citations
Publisher

Abstract

Mathematica notebook with equations and data which were used to create figures 1-8 in the paper "Nonclassical nullifiers for quantum hypergraph states".
DOI
10.5281/zenodo.19813993

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Quantum hypergraph states form a generalisation of the graph state formalism that goes beyond the pairwise (dyadic) interactions imposed by remaining inside the Gaussian approximation. Networks of such states are able to achieve universality for continuous variable measurement based quantum computation with only Gaussian measurements. For normalised states, the simplest hypergraph states are formed from k -adic interactions among a collection of k harmonic oscillator ground states. However such powerful resources have not yet been observed in experiments and their robustness and scalability have not been tested. Here we develop and analyse necessary criteria for hypergraph nonclassicality based on simultaneous nonlinear squeezing in the nullifiers of hypergraph states. We put forward an essential analysis of their robustness to realistic scenarios involving thermalisation or loss and suggest several basic proof-of-principle options for experiments to observe nonclassicality in hypergraph states.
This repository contains the computational data and source code required to reproduce the numerical validations and figures presented in the manuscript "Exact Microcanonical Density of States and Fibonacci Convolutions in the 1D Ising Model" and its accompanying Supplemental Material. The dataset includes the following files: Numerical Validation.nb: This Wolfram Mathematica notebook contains the complete numerical verification of the exact combinatorial degeneracy formulas derived in the study. It implements three independent computational approaches—brute-force enumeration via the full Ising Hamiltonian, analytical combinatorial formulas based on Fibonacci/Lucas convolutions, and the algebraic transfer-matrix formalism. The code validates the exact macroscopic degeneracies across the full excitation spectrum for both open-chain and closed-ring topologies. Thermodynamic Quantities.nb: This Wolfram Mathematica notebook contains the numerical routines used to compute and generate the plots of the thermodynamic quantities presented in the appendix of the main manuscript. Software Requirements: To execute and modify the provided .nb files, Wolfram Mathematica is required.