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Variational quantum algorithms (VQAs) utilize a hybrid quantum-classical architecture to recast problems of high-dimensional linear algebra as ones of stochastic optimization. Despite the promise of leveraging near- to intermediate-term…
Quantum computing is a promising technology because of the ability of quantum computers to process vector spaces with dimensions that increase exponentially with the simulated system size. Extracting the solution, however, is challenging as…
Variational quantum algorithms (VQAs) offer a promising path toward using near-term quantum hardware for applications in academic and industrial research. These algorithms aim to find approximate solutions to quantum problems by optimizing…
Quantum algorithms offer a compelling new avenue for addressing difficult NP-complete optimization problems, such as the Generalized Assignment Problem (GAP). Given the operational constraints of contemporary Noisy Intermediate-Scale…
Variational quantum algorithms are poised to have significant impact on high-dimensional optimization, with applications in classical combinatorics, quantum chemistry, and condensed matter. Nevertheless, the optimization landscape of these…
We present a hybrid classical-quantum computing paradigm where the quantum part strictly runs within the coherence time of a quantum annealer, a method we call variational coherent quantum annealing (VCQA). It involves optimizing the…
A broad class of hybrid quantum-classical algorithms known as "variational algorithms" have been proposed in the context of quantum simulation, machine learning, and combinatorial optimization as a means of potentially achieving a quantum…
The ADAPT-VQE algorithm is a promising method for generating a compact ansatz based on derivatives of the underlying cost function, and it yields accurate predictions of electronic energies for molecules. In this work we report the…
This paper presents a methodology for using varying sample sizes in sequential quadratic programming (SQP) methods for solving equality constrained stochastic optimization problems. The first part of the paper deals with the delicate issue…
Quantum sensing harnesses the unique properties of quantum systems to enable precision measurements of physical quantities such as time, magnetic and electric fields, acceleration, and gravitational gradients well beyond the limits of…
Variational Quantum Algorithms (VQAs) have emerged as promising methods for tackling complex problems on near-term quantum devices. Among these algorithms, the Variational Quantum Linear Solver (VQLS) addresses linear systems of the form…
In this paper, we introduce stochastic simulated quantum annealing (SSQA) for large-scale combinatorial optimization problems. SSQA is designed based on stochastic computing and quantum Monte Carlo, which can simulate quantum annealing (QA)…
We study the costs and benefits of different quantum approaches to finding approximate solutions of constrained combinatorial optimization problems with a focus on Maximum Independent Set. In the Lagrange multiplier approach we analyze the…
Variational quantum algorithms (VQAs) promise efficient use of near-term quantum computers. However, training VQAs often requires an extensive amount of time and suffers from the barren plateau problem where the magnitude of the gradients…
Approximate Nearest Neighbor Search (ANNS) plays a critical role in applications such as search engines, recommender systems, and RAG for LLMs. Vector quantization (VQ), a crucial technique for ANNS, is commonly used to reduce space…
Kolmogorov-Arnold Network (KAN) is a novel multi-layer neuromorphic network. Many groups worldwide have studied this network, including image processing, time series analysis, solving physical problems, and practical applications such as…
Variational quantum algorithms (VQAs) can potentially solve practical problems using contemporary Noisy Intermediate Scale Quantum (NISQ) computers. VQAs find near-optimal solutions in the presence of qubit errors by classically optimizing…
Variational quantum algorithms (VQAs) constitute a prominent framework for exploring the capabilities of near-term quantum computers. As the effectiveness of VQAs depends heavily on the design of variational quantum circuits, Quantum…
Variational Quantum Algorithms (VQAs) employ parameterized quantum circuits optimized using classical methods to minimize a cost function. While VQAs have found broad applications, certain challenges persist. Notably, a significant…
Algorithmic discrepancy theory seeks efficient algorithms to find those two-colorings of a set that minimize a given measure of coloring imbalance in the set, its {\it discrepancy}. The {\it Euclidean discrepancy} problem and the problem of…