This thesis investigates quantum many-body systems in and out of equilibrium, with a dual focus on open-system theory and advanced computational methods. Taken together, the results articulate a unifying perspective: in both classical/analog simulations and digital algorithms for many-body quantum systems, the relevant physics often concentrates in small, dynamically selected pockets of the Liouville or Hilbert space. By exposing this structure - whether as noise-protected logical manifolds in bosonic modes, low-rank sectors of the density operator during open evolution, or expressive submanifolds learned by neural networks - and by designing algorithms that operate within these reduced subspaces, the thesis advances hardware-aware encoding strategies, scalable open-system simulation, and dependable neural-network-based variational Monte Carlo methods. The manuscript presents three original contributions: (i) a Liouville-space framework that leverages symmetries and spectral diagnostics to engineer dissipation as a resource for bosonic quantum information; (ii) a low-rank, time-dependent variational method for simulating Lindblad dynamics with adaptive error control; and (iii) methodological advances for Neural Quantum States that stabilize Monte-Carloâ driven optimization and enable reliable ground-state and dynamical calculations. These three directions structure the three main chapters of the thesis. Each chapter includes a focused, self-contained review of the necessary background, not as a textbook survey but as a coherent theoretical scaffold framing the proposed advances.
This thesis investigates quantum many-body systems in and out of equilibrium, with a dual focus on open-system theory and advanced computational methods. Taken together, the results articulate a unifying perspective: in both classical/analog simulations and digital algorithms for many-body quantum systems, the relevant physics often concentrates in small, dynamically selected pockets of the Liouville or Hilbert space. By exposing this structure - whether as noise-protected logical manifolds in bosonic modes, low-rank sectors of the density operator during open evolution, or expressive submanifolds learned by neural networks - and by designing algorithms that operate within these reduced subspaces, the thesis advances hardware-aware encoding strategies, scalable open-system simulation, and dependable neural-network-based variational Monte Carlo methods. The manuscript presents three original contributions: (i) a Liouville-space framework that leverages symmetries and spectral diagnostics to engineer dissipation as a resource for bosonic quantum information; (ii) a low-rank, time-dependent variational method for simulating Lindblad dynamics with adaptive error control; and (iii) methodological advances for Neural Quantum States that stabilize Monte-Carloâ driven optimization and enable reliable ground-state and dynamical calculations. These three directions structure the three main chapters of the thesis. Each chapter includes a focused, self-contained review of the necessary background, not as a textbook survey but as a coherent theoretical scaffold framing the proposed advances.
This thesis is devoted to the theoretical study of driven-dissipative many-body quantum systems with a particular focus on advanced computational methods. After reviewing several state-of-the-art numerical methods to determine the steady-state and dynamics of open quantum systems described by a Lindblad master equation for the density matrix, this thesis manuscript presents two original methods: (i) an optimal unraveling of stochastic quantum trajectories for disordered systems; (ii) a variational neural network method. The stochastic methods have been applied to investigate the driven-dissipative Bose-Hubbard lattice model that can for instance describe lattices of coupled nonlinear electromagnetic resonators such those obtained with semiconductor microcavities or superconducting quantum circuits. Our study has shown that a critical slowing down of the dynamics occurs for some parameters in dimensions higher than one. The phenomena is linked to a first-order dissipative phase transition and to lattice-level collective bistability. Furthermore, we reveal the role of disorder on the spatial correlation properties of these phenomena. In the last part of the thesis, we present the strong connection between fundamental concepts of machine learning and variational approaches in quantum physics. We present a novel computational method for open quantum systems based on neural network ans\"{a}tze that is compatible with a stochastic minimisation of a cost function through Monte Carlo sampling. As a first application, we have applied this method to the dissipative transverse quantum Ising model. Exciting perspectives and possible developments are also drawn in the concluding remarks.
Neural quantum states provide flexible variational representations of quantum many-body wave functions by combining neural-network parametrizations with Monte Carlo sampling. In this perspective, we review recent advances in their application to condensed-matter systems, focusing on frustrated quantum magnets, interacting lattice fermions, and non-equilibrium dynamics. We discuss the architectures, symmetry constraints, optimization methods, and sampling strategies underlying state-of-the-art calculations, and summarize practical guidelines for reliable simulations. We also examine the principal remaining challenges, including learning non-trivial sign and phase structures, controlling variational bias, enforcing physical symmetries, scaling optimization to large networks, and achieving stable real-time evolution. Finally, we outline promising directions in which neural quantum states may extend the reach of classical simulations of strongly correlated quantum matter.
This thesis focuses on the development, application, and high-performance implementation of numerical methods for simulating quantum many-body systems. In the first chapter, I provide an overview of several most successful conventional approaches for simulating quantum many-body systems, along with their current limitations. Then, the basic properties of the quantum spin model, which will be the subject of study in the following chapters, and its ground state are briefly summarized. Additionally, I discuss the background and the motivations of the research projects carried out during my PhD research. Chapter 2 introduces two numerical algorithms that are extensively used in this thesis, which are exact diagonalization (ED) and variational Monte Carlo. I outline the process of constructing a Hamiltonian matrix and employing iterative methods for exact diagonalization. Subsequently, I introduce the mechanism of the four important components in the ``standard" variational Monte Carlo that are widely used in the most recent research. In Chapter 3, we propose a symmetry-projected variational ansatz in the form of linear combinations of simple restricted Boltzmann machines. This construction allows one to explore states outside of the original variational manifold and increase the representation power with moderate computational effort. Besides allowing one to restore spatial symmetries, an expansion in terms of Krylov states using a Lanczos recursion offers a solution that can further improve the quantum state accuracy. We illustrate these ideas with an application to the Heisenberg J1−J2 model on the square lattice, a paradigmatic problem under debate in condensed matter physics,and achieve state-of-the-art accuracy in the representation of the ground state. In Chapter 4, we present a variational approach based on a Chebyshev expansion of the spectral function, and each Chebyshev polynomial is represented by a neural network quantum state. The Chebyshev moments are obtained by recursively applying the Hamiltonian and projecting on the space of variational states using a modified natural gradient descent method. We compare this approach with a modified approximation of the spectral function which uses a Krylov subspace constructed from the "Chebyshev wave functions." We present results for the one-dimensional and two-dimensional Heisenberg models on the square lattice and compare them with those obtained by other methods in the literature. In Chapter 5, we describe a method to carry out thermodynamic simulations of quantum many-body models using typicality and variational representations of quantum states. Minimally entangled typical thermal states (METTS) are a construction that allows one to solve for the imaginary time evolution of quantum many-body systems. By using wave functions that are weakly entangled, one can take advantage of efficient representations in the form of matrixproduct states. We generalize these ideas to arbitrary variational wave functions and we focus, as an illustration, on the particular case of restricted Boltzmann machines. We demonstrate the application of the method to quantum spin systems in one and two spatial dimensions. In Chapter 6, we study the properties of the impurity band in heavily doped nonmagnetic semiconductors using the Jacobi-Davidson algorithm and the supervised deep learning method. The disorder averaged inverse participation ratio and Thouless number calculation show us the rich structure inside the impurity band. A convolutional neural network model, which is trained to distinguish the extended/localized phase of the Anderson model with high accuracy, shows us the results in good agreement with the conventional approach. Together, we find that there are three mobility edges in the impurity band for a specific on-site impurity potential, which means the presence of the extended states while filling the impurity band. In the final chapter, Chapter 7, we discuss the implementation of architecture-aware optimizations for spin dynamics simulations on x86 CPUs and Nvidia GPUs. The time cost of evaluating the spin-spin correlation functions in real space increases quadratically as the number of spins N, leading to significant computational effort, making the simulation of large spin systems very challenging. We propose to use a highly optimized general matrix multiply (GEMM) subroutine to calculate the dynamical spin-spin correlation function that can achieve near-optimal hardware utilization. Furthermore, we fuse the element-wise operations in the calculation of S(q,t) into the in-house GEMM kernel to reduce memory latency. On Nvidia GPU, we perform the on-the-fly calculation in the epilogue of the GEMM subroutine to avoid saving intermediate results on global memory, which significantly reduces memory usage and achieves better performance than cuBLAS.--Author's abstract
Theoretical investigations of open quantum systems have uncovered a wide variety of unique dynamical phenomena. For instance, current research in quantum information technology aims to control and utilize time-delayed system-reservoir interactions and phonon-induced dynamical dissipative processes for the design of novel chip-integrated quantum optical devices. This thesis develops and advances multiple theoretical approaches for the accurate and efficient description of open quantum systems, where a high degree of information compression is essential to extract crucial information from the open system degrees of freedom which scale exponentially with the system size. The presented methods range from correlation expansions to second-order perturbative master equations, real-time path integral formulations, numerical realizations of high-dimensional tensor networks and, based on the most recent theoretical developments, machine learning implementations in the form of artificial neural networks. We explore all of these techniques with respect to their compression efficiency, performance and representational limits by applying them to a variety of physical setups and scenarios. Firstly, emerging non-Markovian memory effects in open quantum systems are investigated, e.g., resulting from interactions with a structured phonon environment or time-discrete coherent quantum feedback, leading to information exchange and a time-delayed dynamical interplay between system and reservoir. Examined systems range from solid state p-wave topological superconductors coupled to a structured phonon environment, where a memory-induced stabilization and recovery of topological properties is observed, to semiconductor quantum dot nanostructures exhibiting complete population inversion and unidirectional quantum transport as a result of dissipation-induced non-Markovian system-reservoir interactions, and quantum emitters simultaneously subjected to coherent quantum feedback and a decoherence-inducing structured phonon reservoir, leading to the formation of dynamical dissipative structures and population trapping. Secondly, novel machine learning techniques based on artificial neural networks are investigated, enabling simulations of symmetric open quantum spin-1/2 systems with Markovian dynamics. Combining their potential for parallelization and efficient Hilbert space truncation, they facilitate unmatched degrees of information compression and numerical performance for large systems. In this thesis, we expand the representational limits of the restricted Boltzmann machine neural network architecture by developing novel hybrid sampling strategies for a highly customizable compression of configuration space, rendering accurate and efficient simulations of asymmetric systems feasible. Finally, the applicability of the neural network is extended beyond pure spin-1/2 systems by introducing a neural bit encoding scheme for Fock number states, facilitating high performing calculations of large hybrid open quantum systems with bosonic degrees of freedom.
This dissertation develops quantum computing methods for two fundamental aspects of nature: electronic structure in molecules and materials, and the dynamics of open quantum systems. Framed by the theme of moving from structure to dynamics, the work explores how quantum computers can be utilized to compute both the stationary properties of many-body systems and their evolution in realistic environments. Throughout, the emphasis is on physically grounded algorithms that are compatible with noisy intermediate-scale quantum hardware.On the electronic-structure side, this dissertation develops hybrid quantum-classical workflows for chemistry and condensed-matter problems. Sample-based quantum diagonalization and its extended variant are used to recover low-energy molecular states from quantum samples, with application to a reactive molecular system. For materials, a quantum computing workflow is constructed for defect-containing LixCoO2 by combining first-principles electronic-structure calculations, Wannier downfolding, and quantum many-body solvers, including variational and neural-network-based approaches.On the dynamics side, this dissertation presents several complementary methods for simulating open quantum systems on quantum computers. A dilation-based framework is introduced to embed non-unitary reduced dynamics into enlarged unitary evolutions, first for Kraus-map dynamics and then for dynamics generated by the generalized quantum master equation. Two additional near-term strategies are also developed: an adaptive variational method for dissipative many-body dynamics, demonstrated for Dicke superradiance, and a stochastic Schr\"odinger equation approach based on quantum trajectories, applied to excitation transport in the Fenna-Matthews-Olson complex.Taken together, these results establish a set of quantum algorithmic tools that traverse scales and descriptions, from electronic structure to dynamical processes, and from molecular chemistry to complex quantum environments. In this way, the dissertation advances the use of quantum computers as a framework for probing the interconnected fabric of nature.
Numerous variational methods have been proposed for solving quantum many-body systems, but they often face exponentially increasing computational complexity as the Hilbert space dimension grows. To address this, we introduce a novel approach using quantum neural networks to simulate the dissipative dynamics of many-body open quantum systems. This method combines neural-network quantum state representation with the time-dependent variational principle, both implemented via quantum algorithms. This results in accurate open quantum dynamics described by the Lindblad quantum master equation, exemplified by the spin-boson and transverse field Ising models. Our approach avoids the computational expense of classical algorithms and demonstrates the potential advantages of quantum computing for many-body simulations. To reduce measurement errors, we introduce a projection reset procedure, which could benefit other quantum simulations. In addition, our approach can be extended to simulate non-Markovian quantum dynamics.