Related papers: A Model-Based Derivative-Free Optimization Algorit…
The quantum approximate optimization algorithm (QAOA) is a leading iterative variational quantum algorithm for heuristically solving combinatorial optimization problems. A large portion of the computational effort in QAOA is spent by the…
With the rapid advancement of quantum computing, Quantum Approximate Optimization Algorithm (QAOA) is considered as a promising candidate to demonstrate quantum supremacy, which exponentially solves a class of Quadratic Unconstrained Binary…
Multifidelity forward uncertainty quantification (UQ) problems often involve multiple quantities of interest and heterogeneous models (e.g., different grids, equations, dimensions, physics, surrogate and reduced-order models). While…
We introduce a novel quantum optimization paradigm: the Fixed-Parameter-Count Quantum Approximate Optimization Algorithm (FPC-QAOA). It is a scalable variational framework that maintains a constant number of trainable parameters regardless…
Neural operators (NOs) provide fast, resolution-invariant surrogates for mapping input fields to PDE solution fields, but their predictions can exhibit significant epistemic uncertainty due to finite data, imperfect optimization, and…
Recent advances in quantum computing and the increasing availability of quantum hardware have substantially enhanced the practical relevance of quantum approaches to discrete optimization. Among these, the Quadratic Unconstrained Binary…
Variational quantum algorithms (VQAs) have the potential of utilizing near-term quantum machines to gain certain computational advantages over classical methods. Nevertheless, modern VQAs suffer from cumbersome computational overhead,…
Solving optimization problems with high performance is the target of existing works of Quantum Approximate Optimization Algorithm (QAOA). With this intention, we propose an advanced QAOA based on incremental learning, where the training…
Feedback-based adaptive quantum optimization (FALQON) is a promising approach for solving combinatorial problems on noisy intermediate-scale quantum (NISQ) devices, requiring only single circuit evaluations per layer. However, standard…
Quantum computers promise a great computational advantage over classical computers, yet currently available quantum devices have only a limited amount of qubits and a high level of noise, limiting the size of problems that can be solved…
Parametric uncertainty in nonlinear dynamical systems can fundamentally alter bifurcation behaviour, leading to qualitative response changes. Predicting operating margins/envelopes under such uncertainties is critical but challenging:…
In this paper, we propose a hybrid framework to solve large-scale permutation-based combinatorial problems effectively using a high-performance quadratic unconstrained binary optimization (QUBO) solver. To do so, transformations are…
We have recently proposed a rigorous framework for Uncertainty Quantification (UQ) in which UQ objectives and assumption/information set are brought into the forefront, providing a framework for the communication and comparison of UQ…
In this paper, we combine the operator splitting methodology for abstract evolution equations with that of stochastic methods for large-scale optimization problems. The combination results in a randomized splitting scheme, which in a given…
We propose a method to reduce the computational effort to solve a partial differential equation on a given domain. The main idea is to split the domain of interest in two subdomains, and to use different approximation methods in each of the…
We consider the problem of providing optimal uncertainty quantification (UQ) --- and hence rigorous certification --- for partially-observed functions. We present a UQ framework within which the observations may be small or large in number,…
Local quantum annealing (LQA), an iterative algorithm, is designed to solve combinatorial optimization problems. It draws inspiration from QA, which utilizes adiabatic time evolution to determine the global minimum of a given objective…
Data-driven approaches to predict-then-optimize decision-making problems seek to mitigate the risk of uncertainty region misspecification in safety-critical settings. Current approaches, however, suffer from considering overly conservative…
QAOA is a hybrid quantum-classical algorithm to solve optimization problems in gate-based quantum computers. It is based on a variational quantum circuit that can be interpreted as a discretization of the annealing process that quantum…
We are interested in numerically approximating the solution ${\bf U}(t)$ of the large dimensional semilinear matrix differential equation $\dot{\bf U}(t) = { \bf A}{\bf U}(t) + {\bf U}(t){ \bf B} + {\cal F}({\bf U},t)$, with appropriate…