相关论文: Stable Optimization of a Tensor Product Variationa…
We investigate the computational hardness of spin-glass instances on a square lattice, generated via a recently introduced tunable and scalable approach for planting solutions. The method relies on partitioning the problem graph into…
The possibility to simulate the properties of many-body open quantum systems with a large number of degrees of freedom is the premise to the solution of several outstanding problems in quantum science and quantum information. The challenge…
We present high-order variational Lagrangian finite element methods for compressible fluids using a discrete energetic variational approach. Our spatial discretization is mass/momentum/energy conserving and entropy stable. Fully implicit…
Modeling dispersed solid phases in fluids still represents a computational challenge when considering a small-scale coupling in wide systems, such as the atmosphere or industrial processes at high Reynolds numbers. A numerical method is…
We introduce the tensor numerical method for solving optimal control problems that are constrained by fractional 2D and 3D elliptic operators with variable coefficients. We solve the governing equation for the control function which…
The rich non-linear dynamics of the coupled oscillators (under second harmonic injection) can be leveraged to solve computationally hard problems in combinatorial optimization such as finding the ground state of the Ising Hamiltonian. While…
We study a class of elastic systems described by a (hyperbolic) partial differential equation. Our working example is the equation of a vibrating string subject to linear disturbance. The main goal is to establish conditions for…
We extend the Slepyan solution of the problem of a steady-state crack in an infinite ideally brittle lattice model to include dissipation in the form of Kelvin viscosity. As a demonstration of this technique, based on the Wiener-Hopf…
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…
This paper deals a continuous-time state-dependent jump linear system, a particular kind of stochastic switching system. In particular, we consider a situation when the transition rate of the random jump process depends on the state…
Quantum processing units boost entanglement at the level of hardware and enable physical simulations of highly correlated electron states in molecules and intermolecular chemical bonds. The variational quantum eigensolver provides a…
This paper studies the adaptive optimal stationary control of continuous-time linear stochastic systems with both additive and multiplicative noises, using reinforcement learning techniques. Based on policy iteration, a novel off-policy…
We consider optimal control of an elliptic two-point boundary value problem governed by functions of bounded variation (BV). The cost functional is composed of a tracking term for the state and the BV-seminorm of the control. We use the…
We study a three-dimensional (3D) classical Ising model that is exactly solvable when some coupling constants take certain imaginary values. The solution combines and generalizes the Onsager-Kaufman solution of the 2D Ising model and the…
Variational quantum metrology represents a powerful tool for optimizing generic estimation strategies, combining the principles of variational optimization with the techniques of quantum metrology. Such optimization procedures result…
Using variational density matrix optimization with two- and three-index conditions we study the one-dimensional Hubbard model with periodic boundary conditions at various filling factors. Special attention is directed to the full…
We derive sufficient conditions for the solvability of the state estimation problem for a class of nonlinear control time-varying systems which includes those, whose dynamics have triangular structure. The state estimation is exhibited by…
We propose a new Monte Carlo algorithm for the numerical study of general lattice models in Hamiltonian form. The algorithm is based on an initial Ansatz for the ground state wave function depending on a set of free parameters which are…
Aiming at the study of critical phenomena in the presence of boundaries with a non-trivial shape we discuss how lattices with an adaptive lattice spacing can be implemented. Since the parameters of the Hamiltonian transform non-trivially…
In this paper, we study stability and instability problem for type-II partitioning problem. First, we make a complete classification of stable type-II stationary hypersurfaces in a ball in a space form as totally geodesic $n$-balls. Second,…