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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. Also, if you are using an ARM-based Apple Silicon machine (or a platform that is not x86_64), the default JLL-provided library will not have optimized binaries, which will lead to significantly slower performance. In that case, you may specially want to consider compiling FFHT yourself for much better performance. See the Custom FHT Library guide for how to build, enable and revert your own .so file.

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.