Related papers: Grover Adaptive Search with Problem-Specific State…
This paper proposes a quantum algorithm for the capacitated vehicle routing problem with time windows (CVRPTW) based on Grover Search framework. This problem is often faced by Postal services in the context of package delivery or other…
The Traveling Salesman Problem (TSP) is the most popular and most studied combinatorial problem, starting with von Neumann in 1951. It has driven the discovery of several optimization techniques such as cutting planes, branch-and-bound,…
We introduce Limited Rollout Beam Search (LRBS), a beam search strategy for deep reinforcement learning (DRL) based combinatorial optimization improvement heuristics. Utilizing pre-trained models on the Euclidean Traveling Salesperson…
We present a quantum algorithm that has rigorous runtime guarantees for several families of binary optimization problems, including Quadratic Unconstrained Binary Optimization (QUBO), Ising spin glasses ($p$-spin model), and $k$-local…
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…
A generalization of the classical TSP is the so-called quadratic travelling salesman problem (QTSP), in which a cost coefficient is associated with the transition in every vertex, i.e. with every pair of edges traversed in succession. In…
Grover's algorithm is a primary algorithm offered as evidence that quantum computers can provide an advantage over classical computers. It involves an "oracle" specified for a given application whose structure is not part of the formal…
Grover search is a renowned quantum search algorithm that leverages quantum superposition to find a marked item with quadratic speedup. However, when implemented on Noisy Intermediate-scale Quantum (NISQ) hardware, the required repeated…
Recent works using deep learning to solve the Traveling Salesman Problem (TSP) have focused on learning construction heuristics. Such approaches find TSP solutions of good quality but require additional procedures such as beam search and…
Combinatorial optimization is widely applied in a number of areas nowadays. Unfortunately, many combinatorial optimization problems are NP-hard which usually means that they are unsolvable in practice. However, it is often unnecessary to…
In this work, we aim to explore connections between dynamical systems techniques and combinatorial optimization problems. In particular, we construct heuristic approaches for the traveling salesman problem (TSP) based on embedding the…
We propose a different methodology towards approaching a Maze problem. We convert the problem into a Quantum Search Problem (QSP), and its solutions are sought for using the iterative Grover's Search Algorithm. Though the category of mazes…
The Traveling Salesman Problem is a fundamental combinatorial optimization problem widely studied in operations research. Despite its simple formulation, it remains computationally challenging due to the exponential growth of the search…
We derive in this study a Hamiltonian to solve with certainty the analog quantum search problem analogue to the Grover algorithm. The general form of the initial state is considered. Since the evaluation of the measuring time for finding…
Most of the current inference techniques rely upon Bayesian inference on Probabilistic Graphical Models of observations and do predictions and classification on observations. However, there is very little literature on the mining of…
The Traveling Salesman Problem (TSP) is one of the most often-used NP-Hard problems in computer science to study the effectiveness of computing models and hardware platforms. In this regard, it is also heavily used as a vehicle to study the…
Grover's algorithm provides a quadratic speedup over classical algorithms for searching unstructured databases and is known to be strictly optimal in oracle query complexity, with tight bounds on its success probability. Although the…
The Traveling Salesman Problem (TSP) is a well-known combinatorial optimization problem that aims to find the shortest possible route that visits each city exactly once and returns to the starting point. This paper explores the application…
Quantum computing has advanced rapidly in recent years and has shown advantages in a variety of domains. In this paper, we investigate its potential for discrete simulation optimization in the fixed-confidence setting, a fundamental problem…
We introduce the concepts of Grover operators and Grover kernels to systematically analyse Grover's searching algorithms. Then, we investigate a one-parameter family of quantum searching algorithms of Grover's type and we show that the…