Related papers: Quantum Langevin Dynamics for Optimization
Variational quantum algorithms, optimized using gradient-based methods, often exhibit sub-optimal convergence performance due to their dependence on Euclidean geometry. Quantum natural gradient descent (QNGD) is a more efficient method that…
A recent promising arena for quantum advantage is simulating exponentially large classical systems. Here, we show how this advantage can be used to calculate the dynamics of open classical systems experiencing dissipation, including the…
We study a generic open quantum system where the coupling between the system and its environment is of an energy-preserving quantum nondemolition (QND) type. We obtain the general master equation for the evolution of such a system under the…
In the case of quantum systems interacting with multiple environments, the time-evolution of the reduced density matrix is described by the Liouvillian. For a variety of physical observables, the long-time limit or steady state solution is…
Quantum annealing is a computational paradigm in which optimisation problems are mapped onto the energy landscape of an interacting quantum system and explored through its dynamical evolution. By continuously transforming a simple initial…
Continuous-time models provide important insights into the training dynamics of optimization algorithms in deep learning. In this work, we establish a non-asymptotic convergence analysis of stochastic gradient Langevin dynamics (SGLD),…
Feedback-based methods have gained significant attention as an alternative training paradigm for the Quantum Approximate Optimization Algorithm (QAOA) in solving combinatorial optimization problems such as MAX-CUT. In particular, Quantum…
A generalized Langevin equation with quantum baths (QMD) for thermal transport is derived with the help of nonequilibrium Green's function (NEGF) formulation. The exact relationship of the quasi-classical approximation to NEGF is…
As an example of the nonlinear Fokker-Planck equation, the mean field Langevin dynamics recently attracts attention due to its connection to (noisy) gradient descent on infinitely wide neural networks in the mean field regime, and hence the…
We propose Quantum Riemannian Hamiltonian Descent (QRHD), a quantum algorithm for continuous optimization on Riemannian manifolds that extends Quantum Hamiltonian Descent (QHD) by incorporating geometric structure of the parameter space via…
The training of Quantum Neural Networks (QNNs) is hindered by the high computational cost of gradient estimation and the barren plateau problem, where optimization landscapes become intractably flat. To address these challenges, we…
A quantum thermodynamic system is described by a Hamiltonian and a list of conserved, non-commuting charges, and a fundamental goal is to determine the minimum energy of the system subject to constraints on the charges. Recently, [Liu et…
Classical molecular dynamics (MD) has been shown to be effective in simulating heat conduction in certain molecular junctions since it inherently takes into account some essential methodological components which are lacking with quantum…
Computational fluid dynamics (CFD) is a cornerstone of classical scientific computing, and there is growing interest in whether quantum computers can accelerate such simulations. To date, the existing proposals for fault-tolerant quantum…
Gradient Langevin dynamics and a variety of its variants have attracted increasing attention owing to their convergence towards the global optimal solution, initially in the unconstrained convex framework while recently even in convex…
We introduce a novel algorithm for gradient-based optimization of stochastic objective functions. The method may be seen as a variant of SGD with momentum equipped with an adaptive learning rate automatically adjusted by an 'energy'…
This work proposes a simple yet effective sampling framework for combinatorial optimization (CO). Our method builds on discrete Langevin dynamics (LD), an efficient gradient-guided generative paradigm. However, we observe that directly…
Generalized Langevin Equation (GLE) thermostats have been used very effectively as a tool to manipulate and optimize the sampling of thermodynamic ensembles and the associated static properties. Here we show that a similar, exquisite level…
We introduce a quantum approximate optimization algorithm (QAOA) for continuous optimization. The algorithm is based on the dynamics of a quantum system moving in an energy potential which encodes the objective function. By approximating…
We employ the principle of minimum pressure gradient to transform problems in unsteady computational fluid dynamics (CFD) into a convex optimization framework subject to linear constraints. This formulation permits solving, for the first…