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HadaMAG.jl Documentation

arXiv

HadaMAG.jl is an optimized Julia library for computing the Stabilizer Rényi Entropy (SRE) on pure quantum states. Most notably, it contains:

  • Exact SRE: Computes the SRE exactly, which applies a sequence of Fast Hadamard Transforms (FHT) to reduce the naive $O(8^N)$ cost down to $O(N 4^N)$ for $N$ qubits (see Exact SRE).
  • Monte Carlo SRE: Estimates the SRE using stochastic sampling (see Monte Carlo SRE).
  • Mana for qutrit systems: Computes the exact mana of pure qutrit states, with complexity $O(N 9^N)$ (see Mana Computation).
  • Mana for mixed states of qutrits: Computes the exact mana for mixed qutrit states represented as density matrices, with complexity $O(N 9^N)$ (see Mana for Mixed States).

Paper: Computing quantum magic of state vectors, arXiv:2601.07824.

Performance tip

If you are dealing with significant number of qubits ($N > 16$), you can get around 30 % speed-up by compiling and linking your own optimized FFHT library. See the Custom FHT Library guide for how to build, enable and revert your own .so.

Quickstart

julia> using Pkg; Pkg.add(url="https://github.com/bsc-quantic/HadaMAG.jl/")

julia> using HadaMAG

# Haar-random 16-qubit state
julia> ψ = rand_haar(16; depth=2)
StateVec{ComplexF64,2}(n=16, dim=65536, mem=1.0 MiB)

# Compute the 2nd-order Stabilizer Rényi Entropy
julia> (sre2, lost_norm) = SRE(ψ, 2)
[==================================================] 100.0%  (65536/65536)
(8.213760134602566, 3.9968028886505635e-15)

# Estimate the 2nd-order SRE using Monte Carlo with 10000 samples
julia> sre2_mc = MC_SRE(ψ, 2; Nsamples=10000)
[==================================================] 100.0%  (10000/10000)
8.218601276704227

Manuals

For detailed guides on how to use HadaMAG.jl, see the following sections:

  • State Representation: StateVec and DensityMatrix structs for representing pure and mixed quantum states.
  • Exact SRE: Stabilizer Rényi Entropy computation via efficient SRE(ψ, q) function.
  • Monte Carlo SRE: Estimation of SRE using stochastic sampling with MC_SRE(ψ, q; Nsamples).
  • Mana Computation: Exact mana computation for pure and mixed qutrit states using Mana(ψ) and Mana(ρ).
  • Backend Configuration: Configuration of different execution backends for optimal performance, including some instructions for MPI and CUDA usage.