相关论文: LREI: A fast numerical solver for quantum Landau-L…

Recent progress in quantum computing is paving the way for the realization of early fault-tolerant quantum computers. To maximize the utility of these devices, it is important to develop quantum algorithms that match their capabilities and…

We consider the question of learning $Q$-function in a sample efficient manner for reinforcement learning with continuous state and action spaces under a generative model. If $Q$-function is Lipschitz continuous, then the minimal sample…

Quantum variational algorithms (QVAs) are increasingly potent tools for simulating quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. This work examines the application of the Variational Quantum Eigensolver (VQE)…

The Landau--Lifshitz--Bloch equation (LLBE) describes the evolution of the magnetic spin field in ferromagnets at high temperatures. In this paper, we study the numerical approximation of the LLBE on bounded polytopal domains in…

Nonequilibrium Green's functions provide a powerful framework for studying quantum many-body dynamics including the laser-induced dynamics in solids. The Non-Equilibrium Systems Simulation package (NESSi) offers an efficient platform for…

The Learning-With-Errors (LWE) problem is a fundamental computational challenge with implications for post-quantum cryptography and computational learning theory. Here we propose a quantum-classical hybrid algorithm with Ising model to…

We introduce a novel, model-independent method for the efficient simulation of low-entropy systems, whose dynamics can be accurately described with a limited number of states. Our method leverages the time-dependent variational principle to…

The non-differentiability of the singular nonlinearity (such as $f=\ln|u|^2$) at $u=0$ presents significant challenges in devising accurate and efficient numerical schemes for the logarithmic Schr\"{o}dinger equation (LogSE). To address…

In this paper, we propose a semi-Lagrangian discontinuous Galerkin method coupled with Runge-Kutta exponential integrators (SLDG-RKEI) for nonlinear Vlasov dynamics. The commutator-free Runge-Kutta (RK) exponential integrators (EI) were…

We consider the problem of approximating the free energy density of a translation-invariant, one-dimensional quantum spin system with finite range. While the complexity of this problem is nontrivial due to its close connection to problems…

Dynamical low-rank approximation (DLRA) is a widely used paradigm for solving large-scale matrix differential equations, as they arise, for example, from the discretization of time-dependent partial differential equations on tensorized…

Low-Rank Adaptation (LoRA) enables efficient fine-tuning of pre-trained language models through low-rank matrix approximation, achieving effectiveness in many scenarios. However, its representation capacity is constrained in complex tasks…

The ground state search problem is central to quantum computing, with applications spanning quantum chemistry, condensed matter physics, and optimization. The Variational Quantum Eigensolver (VQE) has shown promise for small systems but…

Entanglement entropy is an essential metric for characterizing quantum many-body systems, but its numerical evaluation for neural network representations of quantum states has so far been inefficient and demonstrated only for the restricted…

Large Language Models' (LLMs) weight matrices can often be expressed in low-rank form with potential to relax memory and compute resource requirements. Unlike prior efforts that focus on developing novel matrix decompositions, in this work…

We investigate quantum dynamics of the excited electronic states in the double-exchange model at half-filling by solving coupled equations for the quantum evolution of electrons and Landau-Lifshits-Gilbert equation for classical spins. The…

In this paper, we propose a dynamical low-rank (DLR) approximation framework for solving the semiclassical Schrodinger equation with uncertainties. The primary numerical challenges arise from the dual nature of the oscillations: the spatial…

Determining ground state energies of quantum systems by hybrid classical/quantum methods has emerged as a promising candidate application for near-term quantum computational resources. Short of large-scale fault-tolerant quantum computers,…

Quantum algorithms based on the variational principle have found applications in diverse areas with a huge flexibility. But as the circuit size increases the variational landscapes become flattened, causing the so-called Barren plateau…

The eigenvalue problem of quantum many-body systems is a fundamental and challenging subject in condensed matter physics, since the dimension of the Hilbert space (and hence the required computational memory and time) grows exponentially as…