Related papers: Universal Quantum Speedup for Branch-and-Bound, Br…
Designing faster algorithms for solving Mixed-Integer Linear Programming (MILP) problems is highly desired across numerous practical domains, as a vast array of complex real-world challenges can be effectively modeled as MILP formulations.…
Quadratic programming (QP) is a well-studied fundamental NP-hard optimization problem which optimizes a quadratic objective over a set of linear constraints. In this paper, we reformulate QPs as a mixed-integer linear problem (MILP). This…
Constraint programming (CP) is a paradigm used to model and solve constraint satisfaction and combinatorial optimization problems. In CP, problems are modeled with constraints that describe acceptable solutions and solved with backtracking…
Quantum linear system algorithms (QLSAs) have the potential to speed up algorithms that rely on solving linear systems. Interior Point Methods (IPMs) yield a fundamental family of polynomial-time algorithms for solving optimization…
Linear regression is one of the most fundamental linear algebra problems. Given a dense matrix $A \in \mathbb{R}^{n \times d}$ and a vector $b$, the goal is to find $x'$ such that $ \| Ax' - b \|_2^2 \leq (1+\epsilon) \min_{x} \| A x - b…
In Noisy Intermediate-Scale Quantum (NISQ) era, quantum processing units (QPUs) suffer from, among others, highly limited connectivity between physical qubits. To make a quantum circuit effectively executable, a circuit transformation…
Integer programming (IP) is an NP-hard combinatorial optimization problem that is widely used to represent a diverse set of real-world problems spanning multiple fields, such as finance, engineering, logistics, and operations research. It…
In this paper, we present a Branch and Bound algorithm called QuickBB for computing the treewidth of an undirected graph. This algorithm performs a search in the space of perfect elimination ordering of vertices of the graph. The algorithm…
This paper investigates the potential of quantum acceleration in addressing infinite horizon Markov Decision Processes (MDPs) to enhance average reward outcomes. We introduce an innovative quantum framework for the agent's engagement with…
Computing nonlinear functions over multilinear forms is a general problem with applications in risk analysis. For instance in the domain of energy economics, accurate and timely risk management demands for efficient simulation of millions…
Recent years have seen significant advances in quantum/quantum-inspired technologies capable of approximately searching for the ground state of Ising spin Hamiltonians. The promise of leveraging such technologies to accelerate the solution…
In hybrid Model Predictive Control (MPC), a Mixed-Integer Quadratic Program (MIQP) is solved at each sampling time to compute the optimal control action. Although these optimizations are generally very demanding, in MPC we expect…
Classification is at the core of data-driven prediction and decision-making, representing a fundamental task in supervised machine learning. Recently, several quantum machine learning algorithms that use quantum kernels as a measure of…
The problem of {\em efficiently} finding the best match for a query in a given set with respect to the Euclidean distance or the cosine similarity has been extensively studied in literature. However, a closely related problem of efficiently…
We propose a new approach to utilize quantum computers for binary linear programming (BLP), which can be extended to general integer linear programs (ILP). Quantum optimization algorithms, hybrid or quantum-only, are currently general…
The maximum-cut problem is one of the fundamental problems in combinatorial optimization. With the advent of quantum computers, both the maximum-cut and the equivalent quadratic unconstrained binary optimization problem have experienced…
A combinatorial optimization problem is to find an optimal solution under the constraints. This is one of the potential applications for quantum computers. Quantum Random Access Optimization (QRAO) is the quantum optimization algorithm that…
In this paper we provide new quantum algorithms with polynomial speed-up for a range of problems for which no such results were known, or we improve previous algorithms. First, we consider the approximation of the frequency moments $F_k$ of…
The finite element method is used to approximately solve boundary value problems for differential equations. The method discretises the parameter space and finds an approximate solution by solving a large system of linear equations. Here we…
In this paper, we present a novel formulation of traditional sampling-based motion planners as database-oracle structures that can be solved via quantum search algorithms. We consider two complementary scenarios: for simpler sparse…