{"id":20669523,"url":"https://github.com/iitis/statisticalverificationofisingenergies","last_synced_at":"2026-03-19T17:02:26.976Z","repository":{"id":141460744,"uuid":"402394095","full_name":"iitis/StatisticalVerificationOfIsingEnergies","owner":"iitis","description":"implementation of cumulant's based method to verify whether the Ising output contains a ground state 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StatisticalVerificationOfIsingEnergies\nimplementation of cumulant's based method to verify whether the Ising output contains a ground state energy\n\n\n# Analysing Ising energy spectrum\n\n### Estimating ground state energy\n\n\nTo estimate ground state energy from data\n\n```julia\n\nestimate_ground_state_energy(energies::Vector{Float64}, α::Float64)\n\n\njulia\u003e energies = [0.1, 1., 1.2, 2., 2.2, 3., 3.1, 3.5];\n\njulia\u003e estimate_ground_state_energy(energies, 0.19)\n9.745023110079497\n\n```\n\n### Bootstrap series of samples of estimated minimal energies\n\nStatistics and histogram can be computed from these\n\n\n```julia\n\nbootstrap_hists_of_mins(energies::Vector{Float64}, α::Float64, s::Int, l::Int=length(x))\n\njulia\u003e energies = [1. ,1.5, 2., 3., 4.];\n\njulia\u003e Random.seed!(1234);\n\njulia\u003e h = bootstrap_hists_of_mins(energies, 0.19, 3)\n3-element Vector{Float64}:\n 10.327274688631618\n -4.407048476374387\n -4.721357273543485\n```\n\n### Squared error of estimated minimal energy, for comparison with bootstrap\n\n```julia\n\njulia\u003e squared_error(energies::Vector{Float64}, α::Float64)\n\njulia\u003e energies = [1. ,1.5, 2., 3., 4.];\n\n\njulia\u003e squared_error(energies, 0.19)\n8.633622351519547\n\n```\n\n\n### Testing energy spectrum\n\nTo get the p-value, the probability that the minimal enegry can be the ground state energy (using the Boodstad resampling):\n\n```julia\n\n bootstrap_get_pvalue(energies::Vector{Float64}, α::Float64, s::Int = 1_000)\n\n\n julia\u003e Random.seed!(1234);\n\n julia\u003e energies = [0.1, 1., 1.2, 2., 2.2, 3., 3.1, 3.5];\n\n julia\u003e bootstrap_get_pvalue(energies, 0.19)\n 0.655\n\n\n```\n\n\n### Estimate temperature, given a ground state energy\n\n```julia\n\nestiamte_temperature(energies::Vector{Float64}, ground_energy::Float64)\n\n\njulia\u003e energies = [1. ,1.5, 2., 3., 4.];\n\n\njulia\u003e estiamte_temperature(x, -5.)\n3.4826659310464034\n\n\n\n```\n\n## Citing this work\n\nKrzysztof Domino, Mátyás Koniorczyk, Zbigniew Puchała,  Domino, K., M. Koniorczyk, and Z. Puchała, \"Statistical quality assessment of Ising-based annealer outputs\", Quantum Information Processing, vol. 21, issue Article number: 288 (2022), 08/2022, https://link.springer.com/article/10.1007/s11128-022-03623-5\n\nThis project was supported by the Foundation for Polish Science (FNP) under grant number TEAM NET POIR.04.04.00-00-17C1/18-00\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fiitis%2Fstatisticalverificationofisingenergies","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fiitis%2Fstatisticalverificationofisingenergies","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fiitis%2Fstatisticalverificationofisingenergies/lists"}