Related papers: A quantum central path algorithm for linear optimi…
In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…
Variational quantum algorithms dominate contemporary gate-based quantum enhanced optimisation, eigenvalue estimation and machine learning. Here we establish the quantum computational universality of variational quantum computation by…
This paper proposes a novel combination of constraint encoding methods for the Quantum Approximate Optimization Ansatz (QAOA). Real-world optimization problems typically consist of multiple types of constraints. To solve these optimization…
In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly…
Executing quantum circuits on currently available quantum computers requires compiling them to a representation that conforms to all restrictions imposed by the targeted architecture. Due to the limited connectivity of the devices' physical…
A reinforcement algorithm solves a classical optimization problem by introducing a feedback to the system which slowly changes the energy landscape and converges the algorithm to an optimal solution in the configuration space. Here, we use…
In this work we study quantum algorithms for Hopcroft's problem which is a fundamental problem in computational geometry. Given $n$ points and $n$ lines in the plane, the task is to determine whether there is a point-line incidence. The…
Quantum algorithms require a universal set of gates that can be implemented in a physical system. For these, an optimal decomposition into a sequence of available operations is desired. Here, we present a method to find such sequences for a…
Randomized quantum algorithms have been proposed in the context of quantum simulation and quantum linear algebra with the goal of constructing shallower circuits than methods based on block encodings. While the algorithmic complexities of…
We propose a novel quantum algorithm for solving linear autonomous ordinary differential equations (ODEs) using the Pad\'e approximation. For linear autonomous ODEs, the discretized solution can be represented by a product of matrix…
This paper presents and analyzes the first matrix optimization model which allows general coordinate and spectral constraints. The breadth of problems our model covers is exemplified by a lengthy list of examples from the literature,…
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…
This paper describes a quantum algorithm for finding the maximum among N items. The classical method for the same problem takes O(N) steps because we need to compare two numbers in one step. This algorithm takes O(sqrt(N)) steps by…
We present a new interior-point potential-reduction algorithm for solving monotone linear complementarity problems (LCPs) that have a particular special structure: their matrix $M\in{\mathbb R}^{n\times n}$ can be decomposed as $M=\Phi U +…
Quantum computing is currently strongly limited by the impact of noise, in particular introduced by the application of two-qubit gates. For this reason, reducing the number of two-qubit gates is of paramount importance on noisy…
We present a new hybrid, local search algorithm for quantum approximate optimization of constrained combinatorial optimization problems. We focus on the Maximum Independent Set problem and demonstrate the ability of quantum local search to…
Constrained optimization problems are ubiquitous in science and industry. Quantum algorithms have shown promise in solving optimization problems, yet none of the current algorithms can effectively handle arbitrary constraints. We introduce…
A specialized algorithm for quadratic optimization (QO, or, formerly, QP) with disjoint linear constraints is presented. In the considered class of problems, a subset of variables are subject to linear equality constraints, while variables…
We introduce an algorithm which can be directly used to feasible and optimum search in linear programming. Starting from an initial point the algorithm iteratively moves a point in a direction to resolve the violated constraints. At the…
In this paper, we study an infeasible interior-point method for linear optimization with full-Newton step. The introduced method uses an algebraic equivalent transformation on the centering equation of the system which defines the central…