Transverse contraction methods are extremely promising tools for the efficient contraction of tensor networks associated with the time evolution of quantum many-body systems, allowing in some cases to circumvent the entanglement barrier that would normally prevent the study of quantum dynamics with classical resources. We present here the ITransverse.jl package, written in Julia and based on ITensors.jl, containing several of these high-level algorithms, including novel prescriptions for efficient truncations of temporal matrix product states.Transverse contraction methods are extremely promising tools for the efficient contraction of tensor networks associated with the time evolution of quantum many-body systems, allowing in some cases to circumvent the entanglement barrier that would normally prevent the study of quantum dynamics with classical resources. We present here the ITransverse.jl package, written in Julia and based on ITensors.jl, containing several of these high-level algorithms, including novel prescriptions for efficient truncations of temporal matrix product states.

arXiv:2509.03699SciPost Physics CodebasesJan 9, 20261 citation

Codebase release 1.5 for PauliStrings.jl

Nicolas Loizeau, J. Clayton Peacock, Dries Sels

We present the Julia package PauliStrings.jl for quantum many-body simulations, which performs fast operations on the Pauli group by encoding Pauli strings in binary. All of the Pauli string algebra is encoded into low-level logic operations on integers, and is made efficient by various truncation methods which allow for systematic extrapolation of the results. We illustrate the effectiveness of our package by (i) performing Heisenberg time evolution through direct numerical integration and (ii) by constructing a Liouvillian Krylov space. We benchmark the results against tensor network methods, and we find our package performs favorably. In addition, we show that this representation allows for easy encoding of any geometry. We present results for chaotic and integrable spin systems in 1D as well as some examples in 2D. Currently, the main limitations are the inefficiency of representing non-trivial pure states (or other low-rank operators), as well as the need to introduce dissipation to probe long-time dynamics.We present the Julia package PauliStrings.jl for quantum many-body simulations, which performs fast operations on the Pauli group by encoding Pauli strings in binary. All of the Pauli string algebra is encoded into low-level logic operations on integers, and is made efficient by various truncation methods which allow for systematic extrapolation of the results. We illustrate the effectiveness of our package by (i) performing Heisenberg time evolution through direct numerical integration and (ii) by constructing a Liouvillian Krylov space. We benchmark the results against tensor network methods, and we find our package performs favorably. In addition, we show that this representation allows for easy encoding of any geometry. We present results for chaotic and integrable spin systems in 1D as well as some examples in 2D. Currently, the main limitations are the inefficiency of representing non-trivial pure states (or other low-rank operators), as well as the need to introduce dissipation to probe long-time dynamics.

SciPost Physics CodebasesMar 24, 20254 citations

Introduction to matrix-product states and tensor networks

Grégoire Misguich

These notes provide an introduction to tensor-network methods in quantum many-body physics, with an emphasis on matrix-product states (MPS). They develop the basic tensor-network language, including graphical notation, virtual indices, bond dimensions, gauge freedom, canonical forms, QR and singular-value decompositions, and the role of entanglement in controlling the efficiency of the representation. The main MPS algorithms are then introduced, including contractions, correlation functions, matrix-product operators, DMRG, and time-evolution methods. The notes also briefly discuss projected entangled-pair states (PEPS) as a higher-dimensional generalization of MPS, together with the basic ideas behind approximate PEPS contraction. Finally, tensor-network representations of mixed states, quantum channels, and Lindblad dynamics are presented, with applications to thermal states and open quantum systems. The presentation is accompanied by short Julia code examples based on ITensor, ITensorMPS, and TensorMixedStates. These notes were written for the 9th Les Houches Summer School on Computational Physics: Open Quantum Systems, held in June 2026.These notes provide an introduction to tensor-network methods in quantum many-body physics, with an emphasis on matrix-product states (MPS). They develop the basic tensor-network language, including graphical notation, virtual indices, bond dimensions, gauge freedom, canonical forms, QR and singular-value decompositions, and the role of entanglement in controlling the efficiency of the representation. The main MPS algorithms are then introduced, including contractions, correlation functions, matrix-product operators, DMRG, and time-evolution methods. The notes also briefly discuss projected entangled-pair states (PEPS) as a higher-dimensional generalization of MPS, together with the basic ideas behind approximate PEPS contraction. Finally, tensor-network representations of mixed states, quantum channels, and Lindblad dynamics are presented, with applications to thermal states and open quantum systems. The presentation is accompanied by short Julia code examples based on ITensor, ITensorMPS, and TensorMixedStates. These notes were written for the 9th Les Houches Summer School on Computational Physics: Open Quantum Systems, held in June 2026.

cond-mat.str-elCross-listedarXiv:2606.24803Jun 24, 20260 citations

Codebase release 1.28 for TensorMixedStates

J. Houdayer, Grégoire Misguich

We introduce TensorMixedStates, a Julia library built on top of ITensor which allows the simulation of quantum systems in the presence of dissipation using matrix product states (MPS). It offers three key features: i) it implements the MPS representation for mixed states along with associated operations, in particular the time evolution according to a Lindblad equation or discrete time evolution using non-unitary gates (quantum channels), ii) it is based on ITensor, which has proven its effectiveness and which gives access to efficient low-level tensor manipulation as well as state-of-the-art algorithms (like DMRG or TDVP), finally iii) it presents a user-friendly interface allowing users to write sophisticated simulations for pure and mixed quantum states in a few lines of code.We introduce TensorMixedStates, a Julia library built on top of ITensor which allows the simulation of quantum systems in the presence of dissipation using matrix product states (MPS). It offers three key features: i) it implements the MPS representation for mixed states along with associated operations, in particular the time evolution according to a Lindblad equation or discrete time evolution using non-unitary gates (quantum channels), ii) it is based on ITensor, which has proven its effectiveness and which gives access to efficient low-level tensor manipulation as well as state-of-the-art algorithms (like DMRG or TDVP), finally iii) it presents a user-friendly interface allowing users to write sophisticated simulations for pure and mixed quantum states in a few lines of code.

SciPost Physics CodebasesJun 5, 20260 citations

Quantum many-body simulations with PauliStrings.jl

Nicolas Loizeau, J. Clayton Peacock, Dries Sels

arXiv:2410.09654SciPost Physics CodebasesMar 24, 202512 citations

PEPSKit.jl: A Julia package for projected entangled-pair state simulations

Paul Brehmer, Lander Burgelman, Zheng-Yuan Yue +3 more

We present PEPSKit $.$ jl, a Julia package for simulating two-dimensional quantum many-body systems with infinite projected entangled-pair states (iPEPS). PEPSKit $.$ jl builds on the TensorKit $.$ jl package for tensor computations and provides high-level algorithms for iPEPS simulations that support both Abelian and non-Abelian symmetries, as well as fermionic systems. This work gives an overview of the main package features, which include support for ground-state, time-evolution, and finite-temperature simulations in systems with different physical symmetries and lattice geometries. These capabilities are illustrated through various examples and technical benchmarks.We present PEPSKit$.$jl, a Julia package for simulating two-dimensional quantum many-body systems with infinite projected entangled-pair states (iPEPS). PEPSKit$.$jl builds on the TensorKit$.$jl package for tensor computations and provides high-level algorithms for iPEPS simulations that support both Abelian and non-Abelian symmetries, as well as fermionic systems. This work gives an overview of the main package features, which include support for ground-state, time-evolution, and finite-temperature simulations in systems with different physical symmetries and lattice geometries. These capabilities are illustrated through various examples and technical benchmarks.

cond-mat.str-elCross-listedarXiv:2605.19960May 20, 20260 citations

We present PEPSKit

.

jl, a Julia package for simulating two-dimensional quantum many-body systems with infinite projected entangled-pair states (iPEPS). PEPSKit

.

jl builds on the TensorKit

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jl package for tensor computations and provides high-level algorithms for iPEPS simulations that support both Abelian and non-Abelian symmetries, as well as fermionic systems. This work gives an overview of the main package features, which include support for ground-state, time-evolution, and finite-temperature simulations in systems with different physical symmetries and lattice geometries. These capabilities are illustrated through various examples and technical benchmarks.