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

TL;DR

QwaveMPS is an open-source Python library for simulating one-dimensional quantum many-body waveguide systems using matrix product states (MPS), facilitating studies in quantum physics and quantum information with waveguide QED systems.

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.

Figures (14)

• 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 in a semi-infinite waveguide with a side mirror at a distance $d= v_g \tau /2$, with $v_g$ the group velocity and $\tau$ the roundtrip delay time. (c) Decay of two TLSs, where one is initially excited, and the other one is in the ground state (linear regime). (d) Decay of two TLSs initially excited (non-linear regime). (e) A TLS in a waveguide perpendicularly driven by a time-dependent classical field $\Omega(t)$. (f) Single TLS driven by a quantum pulse (such as an $n$-photon Fock state) with an envelope shape $f(t)$.
• 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 orthogonality center (grey bin).
• Figure 3: Diagrammatic representation of a state written as a matrix product state The grey bin represents the emitter subspace and contains the OC, and the magenta bins are right-normalized tensors containing the field discretized in time, with each bin corresponding to a time step. In this diagram, $i_s i_1...i_N$ represent the physical indices of the MPS.
• Figure 4: Diagrammatic representation of a single site operator written as an MPO. Here, $i_1$ and $j_1$ represent the physical indices of the MPO.
• Figure 5: Diagrammatic representation of a Markovian time evolution operator $U$ operating at a time step $t_k$ on the system bin (grey bin) and the corresponding present bin (magenta bin). Here, $i_s$ is the system physical index and $i_k$ is the time bin one.