## 1 Introduction  
Searching for an intelligent algorithm inspired by nature has always been a research hotspot [1]. All practical but computationally challenging problems are often addressed by heuristic algorithms using classical computers. However, these algorithms were empirically shown to be effective but not analytically proven to be the best approaches to outperform previous approaches. Due to the growing research in quantum computing and the promising development of quantum hardware, quantum computing will soon help us experiment and solve many problems, obtaining results even beyond those reachable by today's largest supercomputers [2]. We are in the era of quantum computing, which holds the potential to be the next industrial revolution and help solve existential challenges. Quantum computing is a promising technology based on the unique properties of quantum physics such as superposition, entanglement, and quantum interference. Quantum computers consist of qubits that can be either 0 or 1 or a superposition of both 0 and 1, which provides them with a computational power that grows exponentially as the number of qubits increases. There has been considerable effort in building quantum-centric supercomputers by large corporations such as IBM, Google, Microsoft, Intel, IonQ, D-Wave systems, etc. In addition, to foster their adoption and improve their computation capacity, numerous improvements are being made to the middleware applications to streamline hybrid quantum-classical integrations. Primarily, there have been two approaches to building quantum computers, one of which is quantum gate-based, while the other is based on quantum annealing. In quantum gate-based quantum computers, qubits are initialized to a known state, and gates are used for manipulating the states, encoding the problem, and performing the computations. In contrast, in quantum computers based on quantum annealing, the formulation starts off with a set of qubits, whose interactions at their lowest energy state, called the ground state, represent the optimal answer that we are attempting to solve. Notably, quantum annealing is mainly used for optimization problems, and D-Wave has been following this approach and released quantum computers with 500 qubits [3]. In contrast, the IBM Osprey quantum processor released in November 2022 has 433 qubits and is based on superconducting transmon qubits. Optimization problems with discrete variables are classified as combinatorial optimization problems and typically involve finding a grouping, ordering, or assignment of a discrete, finite set of objects that satisfies given conditions. In other words, in any given discrete but large configuration space, combinatorial optimization is the process of searching either _maxima_ or _minima_, based on the goal of an objective function \(F\). It has important applications in several fields including Artificial Intelligence (AI) and Machine Learning (ML). A few popular examples of problems in this category are the travelling salesman problem (TSP), the minimum spanning tree problem (MST), the knapsack problem, the job-shop scheduling problem, protein structure prediction, etc. In this paper, we focused on solving large-scale combinational optimization problems, specifically the TSP, employing hybrid quantum and classical computing environments. While quantum computing has the potential to optimally solve the TSP, which is an NP-hard problem, the number of qubits needed for an \(n\)-node TSP is O(\(n^{2}\)). So far, the number of reliable quantum operations have been limited by noise and decoherence as well as by the available qubit size, and therefore, hybrid quantum-classical algorithms have been introduced in recent years. Thus, efficient algorithms that partition a TSP with a large number of nodes and combine the optimized partitioned solutions via metaheuristics, such that the overall solution is near optimal, are of fundamental importance. Ant Colony Optimization (ACO) is a population-based metaheuristic for solving hard computational problems.