Monte Carlo Stabilizer Rényi Entropy (MC-SRE)

The HadaMAG.jl library provides a Monte Carlo method for estimating the Stabilizer Rényi Entropy of order $q$ for a pure quantum state $|ψ⟩$.

The HadaMAG.MC_SRE(ψ, q; Nsamples=1000, Nβ=13, backend=:auto) function estimates the SRE using a Monte Carlo sampling approach, where Nsamples is the number of samples to draw and Nβ is the number of discrete distribution points used in the estimation.

Under the hood, HadaMAG.MC_SRE(ψ, q) dispatches to one of several backends (:serial, :threads, or :mpi). By default, backend = :auto chooses the fastest available execution engine. For details on available backends and MPI usage, see the Backend Configuration guide.

Usage

julia> using HadaMAG

# Prepare a Haar random state of size L with a specified depth
julia> L = 8; ψ = rand_haar(L; depth=2)

# Compute the exact 2nd-order SRE for reference
julia> SRE(ψ, 2)
[==================================================] 100.0%  (256/256)
(6.005977237090554, 6.661338147750939e-16)

# Estimate the 2nd-order SRE using Monte Carlo with 1000 samples
julia> MC_SRE(ψ, 2; Nsamples=1000)
[==================================================] 100.0%  (1000/1000)
5.9989388155066194

# Estimate the 2nd-order SRE using Monte Carlo with 10000 samples
julia> MC_SRE(ψ, 2; Nsamples=10000)
[==================================================] 100.0%  (10000/10000)
6.00198832046363