Related papers: Two-Step Quantum Search Algorithm for Solving Trav…
Quantum Computing is considered as the next frontier in computing, and it is attracting a lot of attention from the current scientific community. This kind of computation provides to researchers with a revolutionary paradigm for addressing…
In this paper, we present an implementation of a Job Selection Problem (JSP) -- a generalization of the well-known Travelling Salesperson Problem (TSP) -- of $N=9$ jobs on its Quadratic Unconstrained Binary Optimization (QUBO) form, using…
The Traveling Salesperson Problem (TSP) is a fundamental NP-hard optimisation challenge with widespread applications in logistics, operations research, and network design. While classical algorithms effectively solve small to medium-sized…
We present a map from the travelling salesman problem (TSP), a prototypical NP-complete combinatorial optimisation task, to the ground state associated with a system of many-qudits. Conventionally, the TSP is cast into a quadratic…
In our pursuit of quantum supremacy during the NISQ era, this research introduces a novel approach rooted in the Quantum Approximate Optimization Algorithm (QAOA) framework to address the Traveling Salesman Problem (TSP). By strategically…
Unstructured search remains as one of the significant challenges in computer science, as classical search algorithms become increasingly impractical for large-scale systems due to their linear time complexity. Quantum algorithms, notably…
The search problem is to find a state satisfying certain properties out of a given set. Grover's algorithm drives a quantum computer from a prepared initial state to the target state and solves the problem quadratically faster than a…
Quantum computing is offering a novel perspective for solving combinatorial optimization problems. To fully explore the possibilities offered by quantum computers, the problems need to be formulated as unconstrained binary models, taking…
One of the significant breakthroughs in quantum computation is Grover's algorithm for unsorted database search. Recently, the applications of Grover's algorithm to solve global optimization problems have been demonstrated, where unknown…
Quantum computing has noteworthy speedup over classical computing by taking advantage of quantum parallelism, i.e., the superposition of states. In particular, quantum search is widely used in various computationally hard problems. Grover's…
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…
Ising formulation is important for many NP problems (Lucas, 2014). This formulation enables implementing novel quantum computing methods including Quantum Approximate Optimization Algorithm and Variational Quantum Eigensolver (VQE). Here,…
Quantum algorithms use the principles of quantum mechanics, as for example quantum superposition, in order to solve particular problems outperforming standard computation. They are developed for cryptography, searching, optimisation,…
We propose a new Quadratic Unconstrained Binary Optimization (QUBO) formulation of the Travelling Salesman Problem (TSP), with which we overcame the best formulation of the Vehicle Routing Problem (VRP) in terms of the minimum number of…
Searching large databases is an important problem with broad applications. The Grover search algorithm provides a powerful method for quantum computers to perform searches with a quadratic speedup in the number of required database queries…
TSP (Traveling Salesman Problem), a classic NP-complete problem in combinatorial optimization, is of great significance in multiple fields. Exact algorithms for TSP are not practical due to their exponential time cost. Thus, approximate…
Quantum computation has attracted much attention since it was shown by Shor and Grover the possibility to implement quantum algorithms able to realize, respectively, factoring and searching in a faster way than any other known classical…
Hybrid quantum-classical algorithms can help mitigating the physical limitations of current quantum devices, particularly the low qubit count and the reduced topological connectivity. In this paper, we propose a hybrid technique to solve a…
This paper introduces a novel edge-based encoding technique for solving the Traveling Salesman Problem (TSP) on a quantum computer, reducing the required number of qubits. For implementation in real quantum devices, we applied the subspace…
Traveling salesman problems (TSP) are one of the well-known combinatorial optimization problems that many groups tackle to solve. This problem appears in many types of combinational optimization, such as scheduling, route optimization, and…