[Paper Review] Numerically exact open quantum systems simulations for arbitrary environments using automated compression of environments

Moritz Cygorek, M. Cosacchi+5 more|arXiv (Cornell University)|Jan 5, 2021

Quantum and electron transport phenomena9 references4 citations

TL;DR

This paper introduces the Automated Compression of Environments (ACE) method, a numerically exact approach for simulating open quantum systems coupled to arbitrary environments—bosonic, fermionic, or spin—by iteratively constructing and compressing the process tensor using matrix product state techniques. The method enables accurate simulation of non-Markovian, non-Gaussian, and strongly correlated environments without prior assumptions, achieving high efficiency and generality across diverse quantum systems.

ABSTRACT

The central challenge for describing the dynamics in open quantum systems is that the Hilbert space of typical environments is too large to be treated exactly. In some cases, such as when the environment has a short memory time or only interacts weakly with the system, approximate descriptions of the system are possible. Beyond these, numerically exact methods exist, but these are typically restricted to baths with Gaussian correlations, such as non-interacting bosons. Here we present a numerically exact method for simulating open quantum systems with arbitrary environments which consist of a set of independent degrees of freedom. Our approach automatically reduces the large number of environmental degrees of freedom to those which are most relevant. Specifically, we show how the process tensor -- which describes the effect of the environment -- can be iteratively constructed and compressed using matrix product state techniques. We demonstrate the power of this method by applying it to problems with bosonic, fermionic, and spin environments: electron transport, phonon effects and radiative decay in quantum dots, central spin dynamics, anharmonic environments, dispersive coupling to time-dependent lossy cavity modes, and superradiance. The versatility and efficiency of our automated compression of environments (ACE) method provides a practical general-purpose tool for open quantum systems.

Motivation & Objective

• To develop a general-purpose, numerically exact method for simulating open quantum systems coupled to arbitrary environments, including non-Gaussian and non-Markovian baths.
• To overcome the limitations of standard approximations like Born-Markov, which fail when system-environment correlations are strong or memory effects are significant.
• To provide a unified framework that automatically identifies and retains only the most relevant environmental degrees of freedom, eliminating the need for ad hoc assumptions or model-specific derivations.
• To enable efficient simulation of complex quantum dynamics such as electron transport, radiative decay, and superradiance in a single, extensible algorithm.
• To establish a benchmark tool for validating approximate methods and simulating real-world quantum experiments with full numerical precision.

Proposed method

• The ACE method constructs the process tensor (PT) explicitly from the microscopic system-environment coupling Hamiltonian, representing the full non-Markovian influence of the environment on the system.
• It uses matrix product operator (MPO) techniques to compress the process tensor, retaining only the most relevant environmental degrees of freedom through iterative truncation.
• The compression is fully automated and does not require prior assumptions about the environment’s structure, spectral density, or correlation functions.
• The method proceeds in discrete time steps, evolving the system and compressed environment using the MPO-formatted process tensor, enabling efficient time propagation.
• The algorithm is general and applies to any environment composed of independent degrees of freedom, including bosons, fermions, and spins, with arbitrary coupling and spectral structures.
• The approach is numerically exact in the sense that convergence can be systematically improved by increasing the bond dimension of the MPO, allowing trade-offs between precision and computational cost.

Experimental results

Research questions

• RQ1 Can a numerically exact simulation method be developed that handles arbitrary non-Gaussian, non-Markovian environments without relying on approximations like Born-Markov or Gaussian assumptions?
• RQ2 How can the exponentially large Hilbert space of typical environments be compressed to retain only the dynamically relevant degrees of freedom in a fully automated and systematic way?
• RQ3 To what extent can a single algorithm simulate diverse quantum phenomena—such as electron transport, phonon effects, radiative decay, and superradiance—using the same underlying framework?
• RQ4 How does the method perform in comparison to specialized techniques for Gaussian baths (e.g., iQUAPI) or discrete-mode systems, particularly in terms of efficiency and accuracy?
• RQ5 Can the method accurately capture non-perturbative effects such as anharmonicity in the environment, such as in Morse potential baths, where mean-field approximations fail?

Key findings

• The ACE method reproduces exact results for the spin-boson model when the environment is harmonic, confirming its numerical accuracy in the limiting case.
• For anharmonic environments modeled by Morse potentials, ACE captures significant deviations from harmonic approximations, especially at low bath anharmonicity (Λ = 5), due to asymmetric coupling and energy shifts.
• After subtracting the mean position shift from the environment, ACE reveals intrinsic anharmonic effects in the excited state population dynamics, which vanish as Λ increases, recovering the Gaussian limit.
• The method successfully simulates complex dynamics such as dispersive coupling to time-dependent lossy cavity modes and non-Hamiltonian loss terms acting directly on the environment, demonstrating its robustness.
• ACE outperforms Gaussian path integral methods in systems with few discrete environmental modes and matches or exceeds the accuracy of specialized methods like iQUAPI in appropriate regimes.
• The method enables the simulation of superradiant decay in higher-dimensional system Hilbert spaces, confirming its scalability and applicability to advanced quantum phenomena.