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The design of a good algorithm to solve NP-hard combinatorial approximation problems requires specific domain knowledge about the problems and often needs a trial-and-error problem solving approach. Graph coloring is one of the essential…
Variational quantum algorithms (VQAs) are promising hybrid quantum-classical methods designed to leverage the computational advantages of quantum computing while mitigating the limitations of current noisy intermediate-scale quantum (NISQ)…
The traveling salesman problem is a fundamental combinatorial optimization problem with strong exact algorithms. However, as problems scale up, these exact algorithms fail to provide a solution in a reasonable time. To resolve this, current…
Combinatorial optimization is the field devoted to the study and practice of algorithms that solve NP-hard problems. As Machine Learning (ML) and deep learning have popularized, several research groups have started to use ML to solve…
Quantum computers have long been expected to efficiently solve complex classical differential equations. Most digital, fault-tolerant approaches use Carleman linearization to map nonlinear systems to linear ones and then apply quantum…
Variational quantum algorithms involve training parameterized quantum circuits using a classical co-processor. An important variational algorithm, designed for combinatorial optimization, is the quantum approximate optimization algorithm.…
We propose the variational quantum singular value decomposition based on encoding the elements of the considered { $N\times N$} matrix into the state of a quantum system of appropriate dimension. This method doesn't use the expansion of…
Current universal quantum computers have a limited number of noisy qubits. Because of this, it is difficult to use them to solve large-scale complex optimization problems. In this paper we tackle this issue by proposing a quantum…
In the era of Noisy Intermediate Scale Quantum (NISQ) computing, available quantum resources are limited. Many NP-hard problems can be efficiently addressed using hybrid classical and quantum computational methods. This paper proposes a…
In recent years, there has been much interest in phase transitions of combinatorial problems. Phase transitions have been successfully used to analyze combinatorial optimization problems, characterize their typical-case features and locate…
We show how to find a Hamiltonian cycle in a graph of degree at most three with n vertices, in time O(2^{n/3}) ~= 1.260^n and linear space. Our algorithm can find the minimum weight Hamiltonian cycle (traveling salesman problem), in the…
Quantum variational optimization has been posed as an alternative to solve optimization problems faster and at a larger scale than what classical methods allow. In this paper we study systematically the role of entanglement, the structure…
With applications to many disciplines, the traveling salesman problem (TSP) is a classical computer science optimization problem with applications to industrial engineering, theoretical computer science, bioinformatics, and several other…
Situations involving competition for resources among entities can be modeled by the competitive multi-armed bandit (CMAB) problem, which relates to social issues such as maximizing the total outcome and achieving the fairest resource…
We analyze two classic variants of the Traveling Salesman Problem using the toolkit of fine-grained complexity. Our first set of results is motivated by the Bitonic TSP problem: given a set of $n$ points in the plane, compute a shortest…
This paper presents a powerful genetic algorithm(GA) to solve the traveling salesman problem (TSP). To construct a powerful GA, I use edge swapping(ES) with a local search procedure to determine good combinations of building blocks of…
Solving real-world optimization problems with quantum computing requires choosing between a large number of options concerning formulation, encoding, algorithm and hardware. Finding good solution paths is challenging for end users and…
This paper introduces a non-variational quantum algorithm designed to solve a wide range of combinatorial optimisation problems, including constrained and non-binary problems. The algorithm leverages an engineered interference process…
Entanglement is a fundamental property of quantum mechanics, and is a primary resource in quantum information systems. Its manipulation remains a central challenge in the development of quantum technology. In this work, we demonstrate a…
In this short note, the dual problem for the traveling salesman problem is constructed through the classic Lagrangian. The existence of optimality conditions is expressed as a corresponding inverse problem. A general 4-cities instance is…