QwaveMPS: An efficient open-source Python package for simulating non-Markovian waveguide-QED using matrix product states

Sofia Arranz Regidor; Matthew Kozma; Stephen Hughes

doi:10.22331/q-2026-11-03-2258

QwaveMPS: An efficient open-source Python package for simulating non-Markovian waveguide-QED using matrix product states

Sofia Arranz Regidor, Matthew Kozma, and Stephen Hughes

Department of Physics, Engineering Physics and Astronomy, Queen's University, Kingston ON K7L 3N6, Canada

Published:	2026-11-03, volume 10, page 2258
Editor:	Francesco Ciccarello
Eprint:	arXiv:2602.15826v3
Doi:	https://doi.org/10.22331/q-2026-11-03-2258
Citation:	Quantum 10, 2258 (2026).

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Abstract

QwaveMPS is an open-source Python library for simulating one-dimensional quantum many-body waveguide systems using matrix product states (MPS). It provides a user-friendly interface for constructing, evolving, and analyzing quantum states and operators, facilitating studies in quantum physics and quantum information with waveguide-QED systems. This approach enables efficient, scalable simulations by focusing computational resources on the most relevant parts of the quantum system. Thus, one can study a wide range of complex dynamical interactions, including time-delayed feedback effects in the non-Markovian regime and deeply nonlinear systems, at a highly reduced computational cost compared to full Hilbert space approaches, making it both practical and convenient to model a variety of open waveguide-QED systems (in Markovian and non-Markovian regimes), treating quantized atoms and quantized photons on an equal footing. The QwaveMPS package automates the waveguide-QED-specific tensor-network operations, including construction of the time-bin evolution operator from physical parameters, the swap network required for delayed interactions, orthogonality-center and truncation management, the matrix-product factorization of $N$-photon Fock-state inputs, and the evaluation of single-time and two-time field observables (such as the second-order quantum correlation function) at chosen points along the waveguide.

Featured image: Schematic of some example cases calculated using QwaveMPS. These can represent various waveguide QED systems, including semiconductors and superconducting circuits: (a) Decay of a TLS in a waveguide; (b) decay of a TLS in a semi-infinite waveguide; (c,d) decay of two TLSs; (e) A TLS perpendicularly driven by a time-dependent classical field; (f) a single TLS driven by a quantum pulse (such as an N-photon Fock state).

The code is available at GitHub.

Popular summary

Light and matter interact in a fundamentally different way when photons are confined to travel along a single line, such as an optical fiber, semiconductor waveguide, or a superconducting wire on a chip. In this waveguide setting, a single atom, or an artificial atom like a quantum dot or a superconducting qubit, can absorb and re-emit a single photon with near-perfect efficiency. This makes such systems a leading candidate for the building blocks of quantum networks and quantum computers, where information is carried between processors by individual particles of light.

Simulating what actually happens in these systems is surprisingly hard. Most theoretical tools assume that once a photon leaves an atom, it is gone for good. But in a real device, a photon can bounce off a mirror or travel to a second atom and come back, arriving after a delay that is long compared with the time the atom takes to emit it. The atom then interacts with its own past, an echo of its earlier emission. Accounting for this retardation means keeping track of the photon everywhere along the waveguide at once, and the number of possibilities to follow grows so quickly that a direct calculation becomes impossible for more than one or two photons.

Our software package, QwaveMPS, makes these calculations tractable. It uses matrix product states (MPS), a technique borrowed from the study of correlated electron systems, which compresses the description of the light field by keeping only the parts that actually matter. The method is exact, not an approximation, yet the examples in our paper — including delayed feedback, strong laser driving, and Fock-state pulses containing an exact number of photons — run in seconds on an ordinary laptop. QwaveMPS is free and open source, and is written so that researchers can use it with only a working knowledge of quantum optics, without needing to learn the underlying tensor-network machinery themselves. We hope it makes a powerful but previously specialized technique available to the whole waveguide-QED community.

► BibTeX data

@article{ArranzRegidor2026qwavempsefficient,
  doi = {10.22331/q-2026-11-03-2258},
  url = {https://doi.org/10.22331/q-2026-11-03-2258},
  title = {Qwave{MPS}: {A}n efficient open-source {P}ython package for simulating non-{M}arkovian waveguide-{QED} using matrix product states},
  author = {Arranz Regidor, Sofia and Kozma, Matthew and Hughes, Stephen},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {10},
  pages = {2258},
  month = nov,
  year = {2026}
}

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Cited by

[1] Robert Meiners Fuchs, Juanjuan Ren, Sebastian Franke, Stephen Hughes, and Marten Richter, "Correlation functions for quantum dynamics of coupled quasinormal modes and quantum emitters interacting via finite-delay propagating photons", Physical Review A 114 2, 023725 (2026).

[2] Sofia Arranz Regidor, Matthew Kozma, and Stephen Hughes, "Matrix Product State Theory of Few-Photon Squeezed Pulses Interacting with a Two-Level Emitter in a Waveguide", arXiv:2608.06590, (2026).

[3] Sofia Arranz Regidor, Matthew Kozma, and Stephen Hughes, "Quantum dynamics of few-photon pulsed waveguide QED with a single artificial atom: Frequency-dependent scattering theory and time-dependent matrix product states", Physical Review Research 8 3, 033260 (2026).

[4] Matias Bundgaard-Nielsen, Matthew Kozma, Sofia Arranz Regidor, and Stephen Hughes, "Decoherence in waveguide quantum electrodynamics using matrix product states", Physical Review Research 8 3, 033109 (2026).

[5] Romain Piron and Akihito Soeda, "Renormalization Treatment of IR and UV Cutoffs in Waveguide QED and Implications to Numerical Model Simulation", arXiv:2601.15945, (2026).

[6] Hong Jiang, Yu Wu, Yue Ban, Xi Chen, and Juan José García-Ripoll, "Programmable Coherent Memory Kernels for Quantum Reservoir Computing in Waveguide QED", arXiv:2609.27072, (2026).

[7] Matthew Kozma and Stephen Hughes, "Pure dephasing destroys two-photon amplitude, not nonlinear phase", arXiv:2610.30098, (2026).

The above citations are from SAO/NASA ADS (last updated successfully 2026-11-03 15:02:36). The list may be incomplete as not all publishers provide suitable and complete citation data.

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