Comparative study on the variations of quantum approximate optimization algorithms to the Traveling Salesman Problem (original) (raw)
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arXiv (Cornell University), 2023
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 feasibility of the quantum computing paradigm for this class of problems. In this paper, we tackle the TSP using the quantum approximate optimization algorithm (QAOA) approach by formulating it as an optimization problem. By adopting an improved qubit encoding strategy and a layerwise learning optimization protocol, we present numerical results obtained from the gate-based digital quantum simulator, specifically targeting TSP instances with 3, 4, and 5 cities. We focus on the evaluations of three distinctive QAOA mixer designs, considering their performances in terms of numerical accuracy and optimization cost. Notably, we find a well-balanced QAOA mixer design exhibits more promising potential for gate-based simulators and realistic quantum devices in the long run, an observation further supported by our noise model simulations. Furthermore, we investigate the sensitivity of the simulations to the TSP graph. Overall, our simulation results show the digital quantum simulation of problem-inspired ansatz is a successful candidate for finding optimal TSP solutions.
A Quantum Genetic Hybrid Algorithm for Solving the Traveling Salesman Problem
2004
In this article we propose a Quantum inspired Genetic Algorithm (GQA) for solving the Traveling Salesman Problem (TSP). The TSP is a known combinatorial optimization problem which aims to find the shortest Hamiltonian cycle linking N cities. This algorithm is an extension of a classical genetic algorithm obtained by introducing some quantum principles such as quantum interference and states superposition. We have obtained excellent solutions in a limited number of iterations (generally about 5000 iterations). Some instances of this algorithm execution on the "gr24" TSP have given the optimal circuit given in the TSP reference site (having the length 1272).
Solving the traveling salesman problem on a quantum annealer
SN Applied Sciences
The paper contains an analysis of four software programs that solve the symmetric traveling salesman problem on a quantum annealer. Three are designed to find approximate solutions. One is designed to find an optimal tour. These programs demonstrate that an application can run across both classical and quantum computing platforms and take advantage of what each can do best. We add value by using a uniform structure for our analysis so that a consistent standard is used to evaluate the software programs. Also we add value by designing a software experiment to test the ability of the D-Wave quantum computer to optimally solve the traveling salesman problem. Our design combines the best attributes of the programs that are reviewed in this paper. Our design assumes that the variables of the traveling salesman problem can be embedded in the qubits, which excludes the problems in the TSP Library until the D-Wave Pegasus computer is available. We note applications of the asymmetric traveling salesman problem that are in the literature and include these problems in the recommendation for an experiment.
Towards Efficiently Solving Quantum Traveling Salesman Problem
2004
We present a framework for efficiently solving Approximate Traveling Salesman Problem (Approximate TSP) for Quantum Computing Models. Existing representations of TSP introduce extra states which do not correspond to any permutation. We present an efficient and intuitive encoding for TSP in quantum computing paradigm. Using this representation and assuming a Gaussian distribution on tour-lengths, we give an algorithm to solve Approximate TSP (Euclidean) within BQP resource bounds. Generalizing this strategy for any distribution, we present an oracle based Quantum Algorithm to solve Approximate TSP. We present a realization of the oracle in the quantum counterpart of PP.
A Realizable GAS-based Quantum Algorithm for Traveling Salesman Problem
arXiv (Cornell University), 2022
The paper proposes a quantum algorithm for the traveling salesman problem (TSP) based on the Grover Adaptive Search (GAS), which can be successfully executed on IBM's Qiskit library. Under the GAS framework, there are at least two fundamental difficulties that limit the application of quantum algorithms for combinatorial optimization problems. One difficulty is that the solutions given by the quantum algorithms may not be feasible. The other difficulty is that the number of qubits of current quantum computers is still very limited, and it cannot meet the minimum requirements for the number of qubits required by the algorithm. In response to the above difficulties, we designed and improved the Hamiltonian Cycle Detection (HCD) oracle based on mathematical theorems. It can automatically eliminate infeasible solutions during the execution of the algorithm. On the other hand, we design an anchor register strategy to save the usage of qubits. The strategy fully considers the reversibility requirement of quantum computing, overcoming the difficulty that the used qubits cannot be simply overwritten or released. As a result, we successfully implemented the numerical solution to TSP on IBM's Qiskit. For the seven-node TSP, we only need 31 qubits, and the success rate in obtaining the optimal solution is 86.71%.
An investigation of IBM Quantum Computing device performance on Combinatorial Optimisation Problems
ArXiv, 2021
The exponential increase in CPU time taken to deterministically solve NP-Hard Combinatorial Optimisation Problems (COP), as the problem size scales, has resulted in a search for non-deterministic optimisation solution techniques to obtain solutions to COP efficiently. This paper juxtaposes classical and quantum optimisation algorithms’ performance to solve two common COP, the Travelling Salesman Problem (TSP) and Quadratic Assignment Problem (QAP). The two classical optimisation techniques applied are Branch and Bound (BNB) and Simulated Annealing (SA), and the two quantum optimisation methods used are the Variational Quantum Eigensolver (VQE) algorithm and Quantum Approximate Optimisation Algorithm (QAOA). These algorithms are respectively executed on classical and IBM’s suite of Noisy Intermediate-Scale Quantum (NISQ) computers. Our experimental results resemble and extend on previously reported results in the literaMaxine T. Khumalo University of the Witwatersrand School of Compu...
Adapting the traveling salesman problem to an adiabatic quantum computer
Quantum Information Processing, 2013
We show how to guide a quantum computer to select an optimal tour for the traveling salesman. This is significant because it opens a rapid solution method for the wide range of applications of the traveling salesman problem, which include vehicle routing, job sequencing and data clustering.
IEEE transactions on quantum engineering, 2023
The vehicle routing problem (VRP) is an NP-hard optimization problem that has been an interest of research for decades in science and industry. The objective is to plan routes of vehicles to deliver goods to a fixed number of customers with optimal efficiency. Classical tools and methods provide good approximations to reach the optimal global solution. Quantum computing and quantum machine learning provide a new approach to solving combinatorial optimization of problems faster due to inherent speedups of quantum effects. Many solutions of VRP are offered across different quantum computing platforms using hybrid algorithms such as quantum approximate optimization algorithm and quadratic unconstrained binary optimization. In this work, we build a basic VRP solver for 3 and 4 cities using the variational quantum eigensolver on a fixed ansatz. The work is further extended to evaluate the robustness of the solution in several examples of noisy quantum channels. We find that the performance of the quantum algorithm depends heavily on what noise model is used. In general, noise is detrimental, but not equally so among different noise sources.
Information Sciences, 2000
We present a quantum algorithm for combinatorial optimization using the cost structure of the search states. Its behavior is illustrated for overconstrained satis®ability (SAT) and asymmetric traveling salesman problems (ATSP). Simulations with randomly generated problem instances show each step of the algorithm shifts amplitude preferentially towards lower cost states, thereby concentrating amplitudes into low-cost states, on average. These results are compared with conventional heuristics for these problems. Ó