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

Sofia Arranz Regidor, Matthew Kozma+1 more|arXiv (Cornell University)|Feb 17, 2026

Cold Atom Physics and Bose-Einstein Condensates0 citations

TL;DR

QwaveMPS is an open-source Python library that uses matrix product states to simulate one-dimensional waveguide-QED systems, including non-Markovian time-delayed feedback and strongly nonlinear dynamics, with a user-friendly interface and scalable performance.

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 non-linear 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.

Motivation & Objective

• Motivate the need for numerically exact simulations of waveguide-QED beyond Markovian approximations.
• Provide an accessible, open-source tool that implements tensor-network methods for waveguide-QED.
• Enable studies of time-delayed feedback, nonlinearity, and multi-quanta dynamics in 1D systems.
• Demonstrate applicability across Markovian and non-Markovian regimes with practical benchmarks.

Proposed method

• Use matrix product states (MPS) to represent the system plus discretized time-bin waveguide fields.
• Discretize the waveguide into time bins and formulate the time evolution with matrix product operators (MPO).
• Represent the initial state as a matrix product state and evolve with time-step MPOs for Markovian and non-Markovian dynamics.
• Define initial states (e.g., TLS excited, vacuum, Fock pulses) and Hamiltonians (including multi-emitter cases) within an MPO/MPS framework.
• Compute observables from the evolved bins, including populations, photon fluxes, two-time correlations, spectra, and entanglement.
• Provide pre-defined Hamiltonians (e.g., 1TLS, 1TLS with feedback, 2TLS) and evolution routines for Markovian and non-Markovian regimes.

Figure 1: 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, where $\gamma_{L}$ and $\gamma_{R}$ are the left/right coupling rates. (b) Decay of a TLS

Experimental results

Research questions

• RQ1 How can non-Markovian waveguide-QED dynamics with time-delayed feedback be simulated efficiently beyond the Markov approximation?
• RQ2 Can MPS-based methods accurately capture nonlinear and multi-photon dynamics in waveguide-QED systems?
• RQ3 What is the performance and scalability of QwaveMPS for multi-emitter and delayed-feedback configurations across Markovian and non-Markovian regimes?
• RQ4 How well do MPS-based observables (populations, fluxes, correlations, entanglement) reproduce known benchmarks and analytical solutions?

Key findings

• QwaveMPS enables numerically exact simulations of waveguide-QED systems with delay lines and nonlinearities using MPS, offering scalable performance.
• The package supports Markovian and non-Markovian regimes, including time-delayed feedback and loop photon dynamics.
• Examples demonstrate linear and nonlinear dynamics, multiple emitters, and quantized pulses, with observables such as populations, fluxes, correlations, spectra, and entanglement.
• Run times on a standard workstation are in the order of a second for the presented examples, with modest memory usage, illustrating practicality on typical hardware.
• The results include conservation checks (quanta conservation) and agreement with analytical/ODE benchmarks in representative cases.

Figure 2: Diagrammatic representation of an SVD, where $U$ represents a left-normalized tensor (green bins), $V$ is a right-normalized (magenta bin) and $S$ represents the diagonal matrix with the Schmidt coefficients (blue bin), and its subsequent contraction, where $OC$ represents the orthogonalit