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The representation of a quantum wave function as a neural network quantum state (NQS) provides a powerful variational ansatz for finding the ground states of many-body quantum systems. Nevertheless, due to the complex variational landscape,…
We propose to solve polynomial hyperbolic partial differential equations (PDEs) with convex optimization. This approach is based on a very weak notion of solution of the nonlinear equation, namely the measure-valued (mv) solution,…
In stochastic modeling, there has been a significant effort towards finding predictive models that predict a stochastic process' future using minimal information from its past. Meanwhile, in condensed matter physics, matrix product states…
We use matrix product techniques to investigate the performance of two algorithms for obtaining the ground state of a quantum many-body Hamiltonian $H = H_A + H_B$ in infinite systems. The first algorithm is a generalization of the quantum…
We introduce a method that ensures efficient computation of one-dimensional quantum systems with long-range interactions across all temperatures. Our algorithm operates within a quasi-polynomial runtime for inverse temperatures up to…
Improving the understanding of strongly correlated quantum many body systems such as gases of interacting atoms or electrons is one of the most important challenges in modern condensed matter physics, materials research and chemistry.…
Understanding non-equilibrium quantum dynamics of many-body systems is one of the most challenging problems in modern theoretical physics. While numerous approximate and exact solutions exist for systems in equilibrium, examples of…
In this work, we present a novel representation of matrix product states (MPS) within the framework of quasi-local algebras. By introducing an enhanced compatibility condition, we enable the extension of finite MPS to an infinite-volume…
We present a new algorithm for finding isolated zeros of a system of real-valued functions in a bounded interval in $\mathbb{R}^n$. It uses the Chebyshev proxy method combined with a mixture of subdivision, reduction methods, and…
We study the applicability of the time-dependent variational principle in matrix product state manifolds for the long time description of quantum interacting systems. By studying integrable and nonintegrable systems for which the long time…
Solving the ground state and the ground-state properties of quantum many-body systems is generically a hard task for classical algorithms. For a family of Hamiltonians defined on an $m$-dimensional space of physical parameters, the ground…
Imaginary-time evolution plays an important role in algorithms for computing ground-state and thermal equilibrium properties of quantum systems, but can be challenging to simulate on classical computers. Many quantum algorithms for…
We propose and simulate a protocol to evolve a quantum particle forward in time such that its trajectory closely matches that of the particle's Newtonian counterpart. Using short bursts of Schr\"odinger time-evolution interleaved with…
In the framework of mapped pseudospectral methods, we introduce a new polynomial-type mapping function in order to describe accurately the dynamics of systems developing almost singular structures. Using error criteria related to the…
We propose a neural-network variational quantum algorithm to simulate the time evolution of quantum many-body systems. Based on a modified restricted Boltzmann machine (RBM) wavefunction ansatz, the proposed algorithm can be efficiently…
In this study, a variety of methods are tested and compared for the numerical solution of the Schr\"odinger equation for few-body systems with explicitely time-dependent Hamiltonians, with the aim to find the optimal one. The configuration…
We compare accuracy of two prime time evolution algorithms involving Matrix Product States - tDMRG (time-dependent density matrix renormalization group) and TDVP (time-dependent variational principle). The latter is supposed to be superior…
Super-moir\'e materials represent a novel playground to engineer states of matter beyond the possibilities of conventional moir\'e materials. However, from the computational point of view, understanding correlated matter in these systems…
We devise a numerical scheme for the time evolution of matrix product operators by adapting the time-dependent variational principle for matrix product states [J. Haegeman et al, Phys. Rev. B 94, 165116 (2016)]. A simple augmentation of the…
We analyse and compare several algorithms to compute numerically periodic solutions of high-dimensional dynamical systems and investigate their Floquet stability without building the monodromy matrix. The solution and its perturbation are…