Quantum Algorithms for Optimization

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

Abstract:

This abstract provides an overview of quantum algorithms for optimization, emphasizing their revolutionary potential for tackling difficult optimization problems. We discuss the applications of quantum techniques in binary, integer, and combinatorial optimization, including the Variational Quantum Eigensolver (VQE), quantum annealing, and the Quantum Approximate Optimization Algorithm (QAOA). The abstract establishes the framework for an investigation of the ways in which quantum optimization algorithms could revolutionize computer methods employed in numerous sectors.

Introduction:

In the struggle for supremacy in computing, quantum computing has emerged as a paradigm-shifting technology that can address challenging issues that conventional computers are unable to. Quantum algorithms for optimization issues stand out as a potential direction among the many applications.[1] Various industries, such as finance, logistics, and artificial intelligence, have optimization challenges.[2] In this piece, the topic of Quantum Algorithms for Optimization is explored. This is a novel approach that uses quantum physics to rethink

problem-solving methods.

QAOA (Quantum Approximate Optimization Algorithm):

A flexible quantum technique for resolving combinatorial optimization problems is the Quantum Approximate Optimization approach (QAOA).[3] Using a sequence of quantum gates, QAOA creates a quantum state to approximate answers to optimization problems. Examining the foundations of QAOA and its applications to graph partitioning, Max-Cut, and traveling salesman problems is essential.

Quantum Annealing:

One specific quantum computing paradigm created for optimization issues is called quantum annealing. This tactic looks for a cost function’s global minimum using ideas from quantum physics. [4] Employed by companies like D-Wave Systems, quantum annealing shows promise for applications in resource allocation, logistics, and other fields. It also may lead to advances in solving optimization problems.

Variational Quantum Eigensolver (VQE):

Originally developed for quantum chemistry simulations, the Variational Quantum Eigensolver (VQE) now handles optimization problems. VQE combines quantum and conventional computation to find the smallest eigenvalue of a given Hamiltonian. This section examines how VQE can be applied to optimization problems, namely parameter optimization inside a quantum circuit and ground state energy optimization.

Quantum Integer Programming:

Finding integer values that maximize a given objective function is the purpose of integer programming, an area in which quantum algorithms are making great strides. Quantum methods to this class of optimization issues could have significant implications not only for scheduling and planning but also for logistics and resource allocation.

Quantum Unconstrained Binary Optimization (QUBO):

The Quantum Unconstrained Binary Optimization (QUBO) concept approaches optimization problems with binary variables from a quantum perspective. Quantum algorithms built for QUBO issues find applications in banking, logistics, and machine learning by seeking optimal binary values for a given objective function.

Conclusion

Finally, Quantum Algorithms for Optimization offer an exciting area where the unique capabilities of quantum computing promise to change problem-solving methodologies. The quantum landscape provides a wide toolkit for handling optimization difficulties across numerous industries, ranging from generic algorithms like QAOA to specialist approaches like quantum annealing. The influence of these algorithms on addressing complicated optimization issues becomes increasingly evident as research improves and quantum hardware matures, indicating a critical step toward the realization of quantum advantage in practical applications.

References:

1. Cerezo, M., Arrasmith, A., Babbush, R., Benjamin, S. C., Endo, S., Fujii, K., … & Coles, P. J. (2021). Variational quantum algorithms. Nature Reviews Physics, 3(9), 625-644.
2. Chakrabarti, S., Childs, A. M., Li, T., & Wu, X. (2020). Quantum algorithms and lower bounds for convex optimization. Quantum, 4, 221.
3. Farhi, E., Goldstone, J., & Gutmann, S. (2014). A quantum approximate optimization algorithm. arXiv preprint arXiv:1411.4028.
4. Morita, S., & Nishimori, H. (2008). Mathematical foundation of quantum annealing. Journal of Mathematical Physics, 49(12).
5. Memos, V. A., Psannis, K. E., Ishibashi, Y., Kim, B. G., & Gupta, B. B. (2018). An efficient algorithm for media-based surveillance system (EAMSuS) in IoT smart city framework. Future Generation Computer Systems, 83, 619-628.
6. Yu, C., Li, J., Li, X., Ren, X., & Gupta, B. B. (2018). Four-image encryption scheme based on quaternion Fresnel transform, chaos and computer generated hologram. Multimedia Tools and Applications, 77, 4585-4608.
7. Li, D., Deng, L., Gupta, B. B., Wang, H., & Choi, C. (2019). A novel CNN based security guaranteed image watermarking generation scenario for smart city applications. Information Sciences, 479, 432-447.

Cite As

Hasan A. (2023) Quantum Algorithms for Optimization, Insights2Techinfo, pp.1

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