Related papers: A Decomposition Method for the Hybrid Quantum-Clas…
We develop theoretical methods for the implementation of creation and destruction operators in separate registers of a quantum computer, allowing for a transparent and dynamical creation and destruction of particle modes in second…
Quantum annealers offer an efficient way to compute high quality solutions of NP-hard problems when expressed in a QUBO (quadratic unconstrained binary optimization) or an Ising form. This is done by mapping a problem onto the physical…
Emerging quantum computing technologies, such as Noisy Intermediate-Scale Quantum (NISQ) devices, offer potential advancements in solving mathematical optimization problems. However, limitations in qubit availability, noise, and errors pose…
We focus on two central themes in this dissertation. The first one is on decomposing polytopes and polynomials in ways that allow us to perform nonlinear optimization. We start off by explaining important results on decomposing a polytope…
We propose and analyze a set of variational quantum algorithms for solving quadratic unconstrained binary optimization problems where a problem consisting of $n_c$ classical variables can be implemented on $\mathcal O(\log n_c)$ number of…
The Traveling Salesman Problem is a classical NP-hard combinatorial optimization problem that has been extensively studied in operations research. A major challenge in Traveling Salesman Problem formulations is the large number of subtour…
Variational quantum algorithms have emerged as a powerful tool for harnessing the potential of near-term quantum devices to address complex challenges across quantum science and technology. Yet, the robust and scalable quantification of…
The reduction of computational costs in the numerical solution of nonstationary problems is achieved through splitting schemes. In this case, solving a set of less computationally complex problems provides the transition to a new level in…
For linearly constrained least-squares problems that depend on a vector of parameters, this paper proposes techniques for reducing the number of involved optimization variables. After first eliminating equality constraints in a numerically…
To approximate solutions of complex nonlinear partial differential equations remains a computational challenge, especially for sets of equations relevant in industry, such as Euler or Navier-Stokes equations. Even the most sophisticated…
A series of hybrid quantum-classical generalized Benders decomposition (GBD) algorithms are proposed to address unit commitment (UC) problems under centralized, distributed, and partially distributed frameworks. In the centralized approach,…
Quantum annealing provides a promising route for the development of quantum optimization devices, but the usefulness of such devices will be limited in part by the range of implementable problems as dictated by hardware constraints. To…
We introduce an algorithm for combinatorial search on quantum computers that is capable of significantly concentrating amplitude into solutions for some NP search problems, on average. This is done by exploiting the same aspects of problem…
We introduce an algorithm for combinatorial search on quantum computers that is capable of significantly concentrating amplitude into solutions for some NP search problems, on average. This is done by exploiting the same aspects of problem…
Identifying computational tasks suitable for (future) quantum computers is an active field of research. Here we explore utilizing quantum computers for the purpose of solving differential equations. We consider two approaches: (i) basis…
Quantum optimization holds promise for addressing classically intractable combinatorial problems, yet a standardized framework for benchmarking its performance, particularly in terms of solution quality, computational speed, and scalability…
In this paper three heuristic algorithms using the Divide-and-Conquer paradigm are developed and assessed for three integer optimizations problems: Multidimensional Knapsack Problem (d-KP), Bin Packing Problem (BPP) and Travelling Salesman…
The Sequential Multiple Knapsack Problem is a special case of Multiple knapsack problem in which the items sizes are divisible. A characterization of the optimal solutions of the problem and a description of the convex hull of all the…
Efficiently solving large-scale optimal power flow (OPF) problems is challenging due to the high dimensionality and interconnectivity of modern power systems. Decomposition methods offer a promising solution via partitioning large problems…
Quantum algorithms can deliver asymptotic speedups over their classical counterparts. However, there are few cases where a substantial quantum speedup has been worked out in detail for reasonably-sized problems, when compared with the best…