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The NP-complete problem of the travelling salesman (TSP) is considered in the framework of quantum adiabatic computation (QAC). We first derive a remarkable lower bound for the computation time for adiabatic algorithms in general as a…
Routing problems are a common optimization problem in industrial applications, which occur on a large scale in supply chain planning. Due to classical limitations for solving NP-hard problems, quantum computing hopes to improve upon speed…
With progress in quantum technology more sophisticated quantum annealing devices are becoming available. While they offer new possibilities for solving optimization problems, their true potential is still an open question. As the optimal…
The intractability of deterministic solutions in solving $\mathcal{NP}$-Hard Combinatorial Optimisation Problems (COP) is well reported in the literature. One mechanism for overcoming this difficulty has been the use of efficient COP…
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…
Encoding hard-constrained optimization problems into a variational quantum algorithm often turns out to be a challenging task. In this work, we provide a solution for the class of open-shop scheduling problems (OSSPs), which we achieve by…
The Travelling Salesman Problem (TSP) is an important combinatorial optimisation problem, and is usually solved on a quantum computer using a Quadratic Unconstrained Binary Optimisation (QUBO) formulation or a Higher Order Binary…
The Traveling Salesman Problem (TSP) is a fundamental challenge in combinatorial optimization, widely applied in logistics and transportation. As the size of TSP instances grows, traditional algorithms often struggle to produce high-quality…
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…
Several combinatorial optimization problems can be solved with NISQ devices once that a corresponding quadratic unconstrained binary optimization (QUBO) form is derived. The aim of this work is to drastically reduce the variables needed for…
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…
The Traveling Salesman Problem is a classical NP-hard combinatorial optimization problem that has been extensively studied in operations research. A major challenge in Traveling Salesman Problem formulations is the large number of subtour…
Quantum Computing is an emerging paradigm which is gathering a lot of popularity in the current scientific and technological community. Widely conceived as the next frontier of computation, Quantum Computing is still at the dawn of its…
The Traveling Salesperson Problem (TSP), a quintessential NP-hard combinatorial optimisation challenge, is vital for logistics and network design but limited by exponential complexity in large instances. We propose a hybrid…
Quantum algorithms offer an exponential speedup over classical algorithms for a range of computational problems. The fundamental mechanisms underlying quantum computation required the development and construction of quantum computers. These…
In this paper we present a variational algorithm for the Traveling Salesman Problem (TSP) that combines (i) a compact encoding of permutations, which reduces the qubit requirement too, (ii) an optimize-freeze-reuse strategy: where the…
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…
Noisy intermediate-scale quantum (NISQ) hardware is almost universally incompatible with full-scale optimization problems of practical importance which can have many variables and unwieldy objective functions. As a consequence, there is a…
NP-hard problems are not believed to be exactly solvable through general polynomial time algorithms. Hybrid quantum-classical algorithms to address such combinatorial problems have been of great interest in the past few years. Such…
The impressive progress in quantum hardware in the last years has raised the interest of the quantum computing community in harvesting the computational power of such devices. However, in the absence of error correction, these devices can…