Lindblad Reference

lindblad(H, L)

Construct a Lindblad object from a Hamiltonian H and a collection of jump operators L.

All inputs are materialized as dense matrices.

densitymatrix(ρ)
densitymatrix(ψ)
densitymatrix(i, L; base=2)

Construct a DensityMatrix from an explicit matrix, a pure-state vector, or a basis-state index.

expectation(O, dm::DensityMatrix)

Return the expectation value of observable O in the density matrix dm.

quadraticlindblad(H, L, M=Matrix[])

Construct the quadratic Lindblad generator acting on Majorana covariance matrices from Hamiltonian matrix H, linear jump matrix L, and optional quadratic dissipative terms M.

covariancematrix(Γ)
covariancematrix(n)

Construct a CovarianceMatrix either from an explicit covariance matrix Γ or from a vector of mode occupations n.

majoranaform(A::AbstractMatrix, B::AbstractMatrix)

Return the Majorana quadratic form Ĥ = -i/4 ∑ Hᵢⱼ ωᵢωⱼ from the fermion quadratic form Ĥ = 1/2 ∑(Aᵢⱼ cᵢ⁺cⱼ + Bᵢⱼcᵢ⁺cⱼ⁺ + h.c.).

fermioncorrelation(cm::CovarianceMatrix)
fermioncorrelation(cm::CovarianceMatrix, i)

Recover fermionic correlation blocks from a Majorana covariance matrix.

Returns:

• For the one-argument form, a pair (A, B) of correlation blocks.
• For the two-argument form, one selected correlation block.

Lindblad Equation: ∂ₜρ = -i[H, ρ] + ∑ᵢ LᵢρLᵢ⁺ - 1/2 ∑ᵢ {Lᵢ⁺Lᵢ, ρ} The object Lindblad stores the data needed to apply the corresponding many-body superoperator directly to a density matrix.

DensityMatrix

Wrapper for a many-body density matrix used by the explicit Lindblad workflow.

CovarianceMatrix

Container for a Majorana covariance matrix together with the corresponding number of fermionic modes.