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Quantum many-body systems pose a formidable computational challenge due to the exponential growth of their Hilbert space. While machine learning (ML) has shown promise as an alternative paradigm, most applications remain at the…
One of the main challenges of quantum many-body physics is that the dimensionality of the Hilbert space grows exponentially with the system size, which makes it extremely difficult to solve the Schr\"{o}dinger equations of the system. But…
Non-equilibrium steady states are a focal point of research in the study of open quantum systems. Previous variational algorithms for searching these steady states have suffered from resource-intensive implementations due to vectorization…
We present an expression for the spectral gap, opening up new possibilities for performing and accelerating spectral calculations of quantum many-body systems. We develop and demonstrate one such possibility in the context of tensor network…
This is a concise, pedagogical introduction to the dynamic field of open quantum systems governed by Markovian master equations. We focus on the mathematical and physical origins of the widely used Lindblad equation, its unraveling in terms…
The phenomenon of quantum entanglement underlies several important protocols that enable emerging quantum technologies. Entangled states, however, are extremely delicate and often get perturbed by tiny fluctuations in their external…
A long-standing open problem in non-Markovian quantum state diffusion (QSD) approach to open quantum systems is to establish the non-Markovian QSD equations for multiple qubit systems. In this paper, we settle this important question by…
We develop a computationally and numerically efficient method to calculate binding energies and corresponding wave functions of quantum mechanical three-body problems in low dimensions. Our approach exploits the tensor structure of the…
The spectral theorem is proven for the quantum dynamics of quadratic open systems of n fermions described by the Lindblad equation. Invariant eigenspaces of the many-body Liouvillean dynamics and their largest Jordan blocks are explicitly…
Tensor network methods as presented in our open source Matrix Product States software have opened up the possibility to study many-body quantum physics in one and quasi-one-dimensional systems in an easily accessible package similar to…
In experimentally realistic situations, quantum systems are never perfectly isolated and the coupling to their environment needs to be taken into account. Often, the effect of the environment can be well approximated by a Markovian master…
Embedding non-Markovian open quantum dynamics into an enlarged Markovian space offers a powerful route to nonperturbative simulations, where the dynamics of the extended space can be governed by multiple distinct Markovian equations. We…
We present a compendium of numerical simulation techniques, based on tensor network methods, aiming to address problems of many-body quantum mechanics on a classical computer. The core setting of this anthology are lattice problems in low…
The Lindblad equation is commonly used for studying quantum dynamics in open systems that cannot be completely isolated from an environment, relevant to a broad variety of research fields, such as atomic physics, materials science, quantum…
We demonstrate a surprising connection between pure steady state entanglement and relaxation timescales in an extremely broad class of Markovian open systems, where two (possibly many-body) systems $A$ and $B$ interact locally with a common…
This text is a short introduction to the physics of driven-dissipative many-body systems, focusing on a few selected topics. Beyond its more ``historical'' interest in the study of atomic physics and quantum optics, presently the modeling…
Tensor network states and methods have erupted in recent years. Originally developed in the context of condensed matter physics and based on renormalization group ideas, tensor networks lived a revival thanks to quantum information theory…
Nonequilibrium dynamics of quantum many-body systems is challenging for classical computing, providing opportunities for demonstrating practical quantum computational advantage with analogue quantum simulators. Owing to the intimate…
We investigate the monitored dynamics of many-body quantum systems in which projective measurements of extensive operators are alternated with unitary evolution. Focusing on mean-field models characterized by all-to-all interactions, we…
We investigate the relation between non-Hermitian Hamiltonian and Lindblad dynamics in nonequilibrium open quantum systems. Non-Hermitian models can extend phase diagrams and enable sensing advantages, but such effects often rely on…