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Quantum random walks on graphs have been shown to display many interesting properties, including exponentially fast hitting times when compared with their classical counterparts. However, it is still unclear how to use these novel…
Grover's quantum algorithm improves any classical search algorithm. We show how random Gaussian noise at each step of the algorithm can be modelled easily because of the exact recursion formulas available for computing the quantum amplitude…
Random walks describe diffusion processes, where movement at every time step is restricted to only the neighbouring locations. We construct a quantum random walk algorithm, based on discretisation of the Dirac evolution operator inspired by…
We present a trajectory optimization algorithm for the traveling salesman problem (TSP) in graphs of convex sets (GCS). Our framework uses an augmented graph of convex sets to encode the TSP specification and solve it exactly as a shortest…
Consider the following generalization of the classic binary search problem: A searcher is required to find a hidden target vertex $x$ in a graph $G$. To do so, they iteratively perform queries to an oracle, each about a chosen vertex $v$.…
We introduce SamBa-GQW, a novel quantum algorithm for solving binary combinatorial optimization problems of arbitrary degree with no use of any classical optimizer. The algorithm is based on a continuous-time quantum walk on the solution…
This paper explores the application of Quadratic Unconstrained Binary Optimization (QUBO) models in solving the Travelling Salesman Problem (TSP) through Quantum Annealing algorithms and Graph Neural Networks. Quantum Annealing (QA), a…
Routing in wireless communication networks is shaped by mobility, interference, congestion, and competing service requirements, making route selection a high-dimensional constrained optimization problem rather than a simple shortest-path…
Quantum search algorithms are crucial for exploring large solution spaces, but their robustness to environmental perturbations, such as noise or disorder, remains a critical challenge. We examine the impact of biased disorder potentials…
Gaussian variational approximation is a popular methodology to approximate posterior distributions in Bayesian inference especially in high dimensional and large data settings. To control the computational cost while being able to capture…
A quantum computer encodes information in quantum states and runs quantum algorithms to surpass the classical counterparts by exploiting quantum superposition and quantum correlation. Grover's quantum search algorithm is a typical quantum…
Quantum variational circuits have gained significant attention due to their applications in the quantum approximate optimization algorithm and quantum machine learning research. This work introduces a novel class of classical probabilistic…
We present a novel quantum algorithm for solving the unstructured search problem with one marked element. Our algorithm allows generating quantum circuits that use asymptotically fewer additional quantum gates than the famous Grover's…
The containment of malware in computing networks may be naturally formulated as a network influence minimisation problem, in which one seeks to limit the expected spread of an infection while balancing the operational cost of disabling…
This paper examines the performance of spatial search where the Grover diffusion operator is replaced by continuous-time quantum walks on a class of interdependent networks. We prove that for a set of optimal quantum walk times and marked…
Probabilistic graphs are an abstraction that allow us to study randomized propagation in graphs. In a probabilistic graph, each edge is "active" with a certain probability, independent of the other edges. For two vertices $u,v$, a classic…
In this article, we propose a distributed quantum algorithm for solving counting problem using Grover operator and a classical post-processing procedure. We apply the proposed algorithm to estimate inner products and Hamming distances.…
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…
The $n$-point amplitudes of gauge and gravity theory are given as a series in the coupling. The recursive derivative expansion is used to find all of the coupling coefficients. Initial conditions to any bare Lagrangian, or of an improved…
Many combinatorial optimization problems admit a maximin fairness variant, where the aim is to find a distribution over possible solutions which maximizes an expected worst-case outcome. However, the support for an optimal distribution may…