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Lindblad Workflows

EDKit includes two different open-system layers:

  • a many-body Lindblad representation acting on density matrices,
  • a quadratic-fermion covariance-matrix representation for free or quadratic problems.

They solve related physical questions, but they are meant for different regimes.

Many-Body Lindblad Evolution

Use lindblad when you already have a Hamiltonian and jump operators as explicit matrices and want to evolve a density matrix directly.

using EDKit

H = Array(trans_inv_operator(spin((1.0, "xx"), (1.0, "yy")), 1:2, 4))
Lops = [Array(operator(spin("+" ), [i], 4)) for i in 1:4]

lb = lindblad(H, Lops)
rho0 = densitymatrix(1, 4)
rho1 = lb(rho0, 0.01)

This layer is the natural open-system companion to exact diagonalization, but it scales with the full density-matrix dimension.

Density Matrices And Observables

The helper densitymatrix constructs density matrices from:

  • an explicit matrix,
  • a pure-state vector,
  • or a basis-state index.

Use expectation(O, dm) to evaluate observables and entropy(dm) for density-matrix entropy.

Quadratic Lindblad Evolution

Use quadraticlindblad when the model can be expressed in quadratic Majorana or fermionic form and you want covariance-matrix evolution rather than full density-matrix evolution.

The related helpers are:

  • covariancematrix to construct covariance matrices,
  • majoranaform to build Majorana quadratic forms from fermionic data,
  • fermioncorrelation to recover correlation blocks.

This layer is usually far more scalable than the many-body Lindblad path, but only applies when the model structure permits it.

Which One Should You Use

Use the many-body lindblad path when:

  • your system is small enough for explicit density matrices,
  • you want a direct, general representation,
  • or your problem is not quadratic.

Use quadraticlindblad when:

  • the model is quadratic,
  • covariance-matrix evolution is the natural language,
  • you need much larger system sizes than many-body density matrices allow.

Practical Advice

If you are unsure, start from the physical representation of your problem:

  • explicit finite Hilbert-space Hamiltonian and jump matrices suggests lindblad,
  • quadratic fermion or Majorana data suggests quadraticlindblad.