# TensorMixedStates.jl 2.0: density matrices as MPS and Lindblad evolution with ITensorMPS

**URL:** <https://itensor.discourse.group/t/tensormixedstates-jl-2-0-density-matrices-as-mps-and-lindblad-evolution-with-itensormps/2643>\
**Category:** General Discussion\
**Created:** [October 26, 2026, 8:45pm UTC](https://itensor.discourse.group/t/tensormixedstates-jl-2-0-density-matrices-as-mps-and-lindblad-evolution-with-itensormps/2643 "2026-10-26T20:45:55Z")\
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**Page:** 1

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**Author:** ![jerhoud](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/jerhoud/32/921_2.png) [@jerhoud](https://itensor.discourse.group/u/jerhoud)\
**Post date:** [October 26, 2026, 8:45pm UTC](https://itensor.discourse.group/t/tensormixedstates-jl-2-0-density-matrices-as-mps-and-lindblad-evolution-with-itensormps/2643/1 "2026-10-26T20:45:55Z")

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I have just released version 2.0 of TensorMixedStates.jl (TMS), a library built on ITensors and ITensorMPS to simulate closed and open quantum systems with matrix product states. It may help with questions that come up here regularly: TDVP on a density matrix, Lindblad equations, steady states, thermal states, logarithmic negativity.

A density matrix is itself an MPS, and a Lindbladian is written as a Julia expression, which TMS turns into an MPO:

```julia
using TensorMixedStates, .Qubits

n = 6
H = -sum(Z(i)Z(i + 1) for i in 1:n-1) - sum(X(i) for i in 1:n)
L = -im * H + sum(Dissipator(sqrt(0.2) * Sm)(i) for i in 1:n) # Lindbladian
ρ = State{Mixed}(System(n, Qubit()), "Up") # density matrix as an MPS
ρ = evolve(L, 2.0, ρ; nsteps = 20) # TDVP
measure(ρ, [Z, Purity])

```

A pure state holds its `MPS` in `state.state`, and the algorithms of TMS call those of ITensorMPS. The page [Coming from QuTiP or ITensors](https://jerhoud.github.io/TensorMixedStates.jl/stable/correspondence/) puts the calls of ITensorMPS and those of TMS side by side.

The full list of features, the documentation and the article are in the announcement on the Julia Discourse: [[ANN] TensorMixedStates.jl 2.0: closed and open quantum systems with matrix product states - Package Announcements - Julia Programming Language](https://discourse.julialang.org/t/ann-tensormixedstates-jl-2-0-closed-and-open-quantum-systems-with-matrix-product-states/140266)

Questions and feedback are very welcome, here or in the GitHub issues.

P.S. The entry of TMS on the Codes page of [itensor.org](http://itensor.org) predates version 2.0: could its description become “A Julia library to simulate closed and open quantum systems, pure and mixed states, using matrix product states.”, and Grégoire Misguich, its co-author, be added as a developer?