Quantum Algorithms for Optimization Problems: Quantum Computing for Problem-Solving

By: Aiyaan Hasan, International Center for AI and Cyber Security Research and Innovations (CCRI), Asia University, Taiwan, rayhasan114@gmail.com

Abstract:

The article showcases the novel area of quantum algorithms for optimization issues, showcasing the unparalleled computational capability of quantum computing. In the area of quantum-inspired optimization, the Quantum Approximate Optimisation Algorithm (QAOA) is a useful tool that demonstrates its capacity to resolve combinatorial optimisation issues. Beyond their theoretical applications, quantum algorithms’ claims of enhanced optimization, risk assessment, and option pricing efficiency are confusing the financial sector.

Introduction:

The study of optimization problems is one of the most promising fields in the quickly emerging science of quantum computing.[1] Conventional computer techniques, despite their efficacy, are limited in their ability to tackle complex optimization problems that emerge across diverse sectors including finance, artificial intelligence, and logistics.[2] Quantum algorithms designed expressly for optimization tasks demonstrate the revolutionary potential of quantum computing, where the ideas of superposition and entanglement become powerful tools for unlocking previously unheard-of computational efficiency.[3]

Quantum Advantage in Optimization:

Quantum algorithms leverage the unique characteristics of quantum bits, or qubits, for optimization. Unlike conventional bits, which can only exist in states of 1, qubits can represent 0 and 1 simultaneously when they are in a state of superposition.[4] Because quantum algorithms are inherently parallel, they can investigate several solutions at once, potentially leading to exponential speedups over classical algorithms.

This quantum advantage is particularly apparent in optimization jobs, where the goal is to find the best option out of a wide range of possibilities. In particular, quantum algorithms excel in concurrently analyzing multiple choices, exploring solution spaces, and rapidly converging to the optimal solutions.

The Algorithm for Quantum Approximate Optimisation (QAOA):

One popular quantum technique for optimization tasks is the Quantum Approximate Optimisation approach (QAOA). QAOA is an approximation-based method for solving combinatorial optimization problems. To approach the optimal solution, it employs a parameterized quantum circuit that evolves iteratively.[5]

Potential fixes for the QAOA approach have been shown for the travelling salesman problem, a well-known route optimisation challenge, and the graph optimization problem MaxCut. As quantum technology develops, QAOA provides proof that quantum algorithms have the ability to completely transform the way optimization problems are solved.

Rapid Acceleration in Financial Optimisation:

The finance sector is using quantum algorithms because optimization is crucial. Quantum computing’s processing advantages could be used to complex problems like portfolio optimization, risk assessment, and option pricing. Quantum algorithms have the potential to optimize investment portfolios more successfully since they can modify tactics to changing market conditions and consider multiple factors at once.

Challenges and Considerations:

Although quantum algorithms hold great promise for optimisation, there are obstacles in the way of realising their full potential. The development of quantum hardware is still in its early stages, and creating error-resistant quantum computers with a large enough qubit count is still a significant challenge. Furthermore, the structure of the issue and the properties of the quantum algorithms must be carefully taken into account when converting conventional optimisation problems to their quantum counterparts.

Conclusion:

The use of quantum algorithms to solve optimisation issues is where the power of quantum computing can transform the effectiveness of problem-solving in a variety of fields. Potential applications for algorithms such as QAOA extend across several areas, including banking, logistics, and artificial intelligence. These algorithms show the quantum edge in tackling complex optimisation problems.

The creation of quantum hardware and the conversion of classical issues to quantum algorithms continue to provide hurdles, although the direction of quantum computing research is encouraging. The age of quantum-inspired optimisation algorithms is opening up new possibilities for more effective, quicker, and ground-breaking solutions to challenging real-world issues as research and development in this area progresses.

References:

1. Childs, A. M., & Van Dam, W. (2010). Quantum algorithms for algebraic problems. Reviews of Modern Physics, 82(1), 1.
2. Han, K. H., & Kim, J. H. (2000, July). Genetic quantum algorithm and its application to combinatorial optimization problem. In Proceedings of the 2000 congress on evolutionary computation. CEC00 (Cat. No. 00TH8512) (Vol. 2, pp. 1354-1360). IEEE.
3. Jörg, T., Krzakala, F., Semerjian, G., & Zamponi, F. (2010). First-order transitions and the performance of quantum algorithms in random optimization problems. Physical review letters, 104(20), 207206.
4. Lykov, D., Wurtz, J., Poole, C., Saffman, M., Noel, T., & Alexeev, Y. (2023). Sampling frequency thresholds for the quantum advantage of the quantum approximate optimization algorithm. npj Quantum Information, 9(1), 73.
5. Choi, J., & Kim, J. (2019, October). A tutorial on quantum approximate optimization algorithm (QAOA): Fundamentals and applications. In 2019 International Conference on Information and Communication Technology Convergence (ICTC) (pp. 138-142). IEEE.
6. Deveci, M., Pamucar, D., Gokasar, I., Köppen, M., & Gupta, B. B. (2022). Personal mobility in metaverse with autonomous vehicles using Q-rung orthopair fuzzy sets based OPA-RAFSI model. IEEE Transactions on Intelligent Transportation Systems.
7. Cvitić, I., Perakovic, D., Gupta, B. B., & Choo, K. K. R. (2021). Boosting-based DDoS detection in internet of things systems. IEEE Internet of Things Journal, 9(3), 2109-2123.
8. Lv, L., Wu, Z., Zhang, L., Gupta, B. B., & Tian, Z. (2022). An edge-AI based forecasting approach for improving smart microgrid efficiency. IEEE Transactions on Industrial Informatics, 18(11), 7946-7954.
9. Stergiou, C. L., Psannis, K. E., & Gupta, B. B. (2021). InFeMo: flexible big data management through a federated cloud system. ACM Transactions on Internet Technology (TOIT), 22(2), 1-22.
10. Almomani, A., Alauthman, M., Shatnawi, M. T., Alweshah, M., Alrosan, A., Alomoush, W., & Gupta, B. B. (2022). Phishing website detection with semantic features based on machine learning classifiers: a comparative study. International Journal on Semantic Web and Information Systems (IJSWIS), 18(1), 1-24.

Cite As

Hasan A. (2023) Quantum Algorithms for Optimization Problems: Quantum Computing for Problem-Solving, Insights2Techinfo, pp.1

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