Exact Stabilizer Rényi Entropy (SRE)

The Stabilizer Rényi Entropy (SRE) of order $q$ is a measure of the non-stabilizer content of a pure quantum state $| ψ ⟩$. Under the hood, HadaMAG.SRE(ψ, q) dispatches to one of several backends (:serial, :threads, or :mpi) and uses a sequence of Fast Hadamard Transforms to reduce the naive $O(4^n)$ sum down to $O(n2^n)$ work.

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 2nd-order SRE with automatic backend selection (in this case, muli-threaded)
julia> SRE(ψ, 2)
[==================================================] 100.0%  (256/256)
(6.009572767520443, 4.440892098500626e-16)

# Force the serial backend (not multi-threaded)
julia> SRE(ψ, 2; backend = :serial)
[==================================================] 100.0%  (256/256)
(6.0095727675204405, 6.661338147750939e-16)

In each call you get a tuple (entropy, lost_norm), where lost_norm is the numerical deviation (in absolute value) from unit norm after applying the algorithm.

Backends

The backend keyword argument lets you choose the execution engine. The available backends for SRE are:

• :serial: Single-threaded CPU execution.
• :threads: Multi-threaded CPU execution using Julia Threads.
• :mpi: Hybrid MPI + threads execution (requires MPI.jl).
• cuda: GPU execution using CUDA (requires HadaMAGCUDAExt.jl).
• mpi_cuda: Hybrid MPI + GPU execution (requires both MPI.jl and HadaMAGCUDAExt.jl).

For more details on backend configuration and MPI/CUDA usage, see the Backend Configuration guide.

API Reference

SRE(ψ::StateVec{T,2}; backend = :auto)