Related papers: Universal Quantum Speedup for Branch-and-Bound, Br…
Demonstrating quantum advantage has been a pressing challenge in the field. Most claimed quantum speedups rely on a subroutine in which classical information can be accessed in a coherent quantum manner, which imposes a crucial constraint…
This research explores the integration of the Quantum Approximate Optimization Algorithm (QAOA) into Hybrid Quantum-HPC systems for solving the Max-Cut problem, comparing its performance with classical algorithms like brute-force search and…
Recent works on quantum algorithms for solving semidefinite optimization (SDO) problems have leveraged a quantum-mechanical interpretation of positive semidefinite matrices to develop methods that obtain quantum speedups with respect to the…
The minimisation of cost functions is crucial in various optimisation fields. However, identifying their global minimum remains challenging owing to the huge computational cost incurred. This work analytically expresses the computational…
Small-scale Mixed-Integer Quadratic Programming (MIQP) problems often arise in embedded control and estimation applications. Driven by the need for algorithmic simplicity to target computing platforms with limited memory and computing…
We propose quantum algorithms that provide provable speedups for Markov Chain Monte Carlo (MCMC) methods commonly used for sampling from probability distributions of the form $\pi \propto e^{-f}$, where $f$ is a potential function. Our…
Efficient sampling from a classical Gibbs distribution is an important computational problem with applications ranging from statistical physics over Monte Carlo and optimization algorithms to machine learning. We introduce a family of…
We study some extensions of Grover's quantum searching algorithm. First, we generalize the Grover iteration in the light of a concept called amplitude amplification. Then, we show that the quadratic speedup obtained by the quantum searching…
The principle of majorization-minimization (MM) provides a general framework for eliciting effective algorithms to solve optimization problems. However, they often suffer from slow convergence, especially in large-scale and high-dimensional…
Leverage score sampling is crucial to the design of randomized algorithms for large-scale matrix problems, while the computation of leverage scores is a bottleneck of many applications. In this paper, we propose a quantum algorithm to…
The advent of quantum algorithms has initiated a discourse on the potential for quantum speedups for optimization problems. However, several factors still hinder a practical realization of the potential benefits. These include the lack of…
We propose a mixed-integer quadratic programming (QP) solver that is suitable for use in embedded applications, for example, hybrid model predictive control (MPC). The solver is based on the branch-and-bound method, and uses a recently…
Integer Linear Programs (ILPs) are a flexible and ubiquitous model for discrete optimization problems. Solving ILPs is \textsf{NP-Hard} yet of great practical importance. Super-quadratic quantum speedups for ILPs have been difficult to…
Mixed-integer programming (MIP) has emerged as a powerful framework for learning optimal decision trees. Yet, existing MIP approaches for regression tasks are either limited to purely binary features or become computationally intractable…
Quantum machine learning has the potential for broad industrial applications, and the development of quantum algorithms for improving the performance of neural networks is of particular interest given the central role they play in machine…
Identifying optimal basic feasible solutions to linear programming problems is a critical task for mixed integer programming and other applications. The crossover method, which aims at deriving an optimal extreme point from a suboptimal…
In this paper, we surveyed the existing literature studying different approaches and algorithms for the four critical components in the general branch and bound (B&B) algorithm, namely, branching variable selection, node selection, node…
Mixed-integer linear programming problems are extensively used in industry for a wide range of optimization tasks. However, as they get larger, they present computational challenges for classical solvers within practical time limits.…
Optimization problems become fundamentally challenging as the number of variables increases. Because the volume of the search space grows exponentially, classical algorithms frequently fail to locate the global minimum of non-convex…
Quadratically Constrained Quadratic Programs (QCQPs) are an important class of optimization problems with diverse real-world applications. In this work, we propose a variational quantum algorithm for general QCQPs. By encoding the variables…