State representation in HadaMAG.jl

In HadaMAG.jl, the StateVec{T,q} type provides a representation of an $n$-qudit quantum state in the computational basis (with local dimension $q$), and offers support for constructing from raw amplitude vectors, generating Haar-random states, loading from common on-disk formats and other utilities.

Constructing a StateVec{T,q}

Create a state from an existing amplitude vector of length = $q^n$:

julia> using HadaMAG

julia> amplitudes = randn(ComplexF64, 2^4);

julia> ψ = StateVec(amplitudes) # defaults to q=2 (qubits)
StateVec{ComplexF64,2}(n=4, dim=16, mem=296.0 B)

Or specify a non-qubit local dimension q (e.g., for qutrits, q=3):

julia> amplitudes = randn(ComplexF64, 3^3);

julia> ψ = StateVec(amplitudes; q=3) # qutrits
StateVec{ComplexF64,3}(n=3, dim=27, mem=472.0 B)

Density Matrices

HadaMAG.jl also provides with the DensityMatrix{T,q} struct to represent mixed states. Additionally, you can compute the reduced density matrix of a pure state ψ::StateVec{T,q} using the reduced_density_matrix function:

julia> ψ = StateVec(amplitudes)
StateVec{ComplexF64,2}(n=4, dim=16, mem=296.0 B)

julia> ρA = reduced_density_matrix(ψ, 2; side=:right)
DensityMatrix{ComplexF64,2}(n=2, size=(4, 4), mem=304.0 B)

Generating quantum circuit states

HadaMAG.jl provides the rand_haar function to generate pure states obtained with quantum circuits from computational basis state by applying Haar random 2-qudit gates in a brickwall pattern with an specified depth. For example, let's generate a state on N=4 qubits, corresponding to depth=3 layers of random 2-qubit gates:

julia> using HadaMAG

julia> N = 4
4

julia> depth = 3
3

julia> ψ = rand_haar(N; depth)
StateVec{ComplexF64,2}(n=4, dim=16, mem=296.0 B)

You can also generate states evolved with quantum circuits for qutrits:

julia> ψ_qutrit = rand_haar(3; q=3, depth=2)
StateVec{ComplexF64,3}(n=3, dim=27, mem=472.0 B)

Loading a state vector from disk

You can load amplitude data from various on-disk formats into a StateVec. The data is not renormalized automatically, so make sure your file encodes a unit-norm state.

Supported formats (by extension):

• .jld2: JLD2 format (with JLD2.jl)
• .npy: NumPy format (with NPZ.jl)
• .txt and other text formats: Whitespace-delimited real and imaginary parts.

julia> using LinearAlgebra

julia> ψ = load_state("state_L_12.txt")
StateVec{ComplexF64,2}(n=12, dim=4096, mem=64.0 KiB)

julia> norm(ψ)
1.0

API Reference

rand_haar(n::Int, depth::Int; rng::AbstractRNG = Random.GLOBAL_RNG)

load_state(path::AbstractString; q::Int = 2) -> StateVec