Advances in Evolutionary Optimization of Quantum Operators

Keywords: Evolution Strategy, Differential Evolution, Self-adaptation of Control Parameters, Quantum Operator, Unitary Matrix


A comparative study is presented regarding the evolutionary design of quantum operators in the form of unitary matrices.A comparative study is presented regarding the evolutionary design of quantum operators in the form of unitary matrices.    Three existing techniques (representations) which allow generating unitary matrices are used in various evolutionary algorithms in order to optimize their coefficients.    The objective is to obtain as precise quantum operators (the resulting unitary matrices) as possible for given quantum transformations.    Ordinary evolution strategy, self-adaptive evolution strategy and differential evolution are applied with various settings as the optimization algorithms for the quantum operators.    These algorithms are evaluated on the tasks of designing quantum operators for the 3-qubit and 4-qubit maximum amplitude detector and a solver of a logic function of three variables in conjunctive normal form.    These tasks require unitary matrices of various sizes.    It will be demonstrated that the self-adaptive evolution strategy and differential evolution are able to produce remarkably better results than the ordinary evolution strategy.    Moreover, the results can be improved by selecting a proper settings for the evolution as presented by a comparative evaluation.


Acampora, G., and Vitiello, A. Implementing evolutionary optimization on actual quantum processors. Information Sciences 575 (2021), 542–562.

Bang, J., and Yoo, S. A genetic-algorithmbased method to find unitary transformations for any desired quantum computation and application to a one-bit oracle decision problem. Journal of the Korean Physical Society 65, 12 (2014), 2001–2008.

Bidlo, M., and Zufan, P. On comparison of some representations for the evolution of quantum operators. In 2020 IEEE Symposium Series on Computational Intelligence (SSCI) (2020), IEEE, pp. 2101–2108.

Brabazon, A., O’Neill, M., and McGarraghy, S. Natural computing algorithms, vol. 554. Springer, 2015.

Caires, L. F. V., Neto, O. P. V., and Noronha, T. F. Evolutionary synthesis of robust qca circuits. In 2013 IEEE Congress on Evolutionary Computation (2013), IEEE, pp. 2802–2808.

Chuang, I. L., Gershenfeld, N., and Kubinec, M. Experimental implementation of fast quantum searching. Physical review letters 80, 15 (1998), 3408.

Gander, W. Algorithms for the qr decomposition. Res. Rep 80, 02 (1980), 1251–1268.

Gepp, A., and Stocks, P. A review of procedures to evolve quantum algorithms. Genetic programming and evolvable machines 10, 2 (2009), 181–228.

Gregor, C. Construction of Unitary Matrices and Bounding Minimal Quantum Gate Fidelity Using Genetic Algorithms. PhD thesis, The University of Guelph, Guelph, Ontario, CA, 2018.

Hota, A. R., and Pat, A. An adaptive quantum-inspired differential evolution algorithm for 0–1 knapsack problem. In 2010 Second World Congress on Nature and Biologically Inspired Computing (NaBIC) (2010), IEEE, pp. 703–708.

Hutsell, S. R., and Greenwood, G. W. Applying evolutionary techniques to quantum computing problems. In 2007 IEEE Congress on Evolutionary Computation (2007), IEEE, pp. 4081–4085.

Krawec, W. O. An algorithm for evolving multiple quantum operators for arbitrary quantum computational problems. In Proceedings of the Companion Publication of the 2014 Annual Conference on Genetic and Evolutionary Computation (2014), pp. 59–60.

Krylov, G., and Lukac, M. Quantum encoded quantum evolutionary algorithm for the design of quantum circuits. In Proceedings of the 16th ACM International Conference on Computing Frontiers (2019), pp. 220–225.

Li, B., Li, P., et al. Quantum inspired differential evolution algorithm. Open Journal of Optimization 4, 02 (2015), 31.

Li, K., Elsayed, S., Sarker, R., and Essam, D. Quantum differential evolution: an investigation. In 2019 IEEE Congress on Evolutionary Computation (CEC) (2019), IEEE, pp. 3022–3029.

MacKinnon, D. Evolving Quantum Algorithms with Genetic Programming. PhD thesis, University of Guelph, Guelph, Ontario, CA, 2017.

Nielsen, M. A., and Chuang, I. Quantum computation and quantum information. Cambridge University Press, 2011.

Omran, M. G., Salman, A., and Engelbrecht, A. P. Self-adaptive differential evolution. In International conference on computational and information science (2005), Springer, pp. 192–199.

Press, W. H., Flannery, B. P., Teukolsky, S. A., Vetterling, W. T., et al. Numerical recipes, 2007.

Reid, T. On the evolutionary design of quantum circuits. Master’s thesis, University of Waterloo, Ontario, CA, 2005.

Sarvaghad-Moghaddam, M., Niemann, P., and Drechsler, R. Multi-objective synthesis of quantum circuits using genetic programming. In International Conference on Reversible Computation (2018), Springer, pp. 220–227.

Surkan, A. J., and Khuskivadze, A. Evolution of quantum computer algorithms from reversible operators. In Proceedings 2002 NASA/DoD Conference on Evolvable Hardware (2002), IEEE, pp. 186–187.

Szwarcman, D., Civitarese, D., and Vellasco, M. Quantum-inspired neural architecture search. In 2019 International Joint Conference on Neural Networks (IJCNN) (2019), IEEE, pp. 1–8.

Tang, D., Liu, Z., Zhao, J., Dong, S., and Cai, Y. Memetic quantum evolution algorithm for global optimization. Neural Computing and Applications (2019), 1–31.

Van Loan, C. F., and Golub, G. Matrix computations (johns hopkins studies in mathematical sciences).

Zyczkowski, K., and Kus, M. Random unitary matrices. Journal of Physics A: Mathematical and General 27, 12 (1994), 4235.

How to Cite
Žufan, P. and Bidlo, M. 2021. Advances in Evolutionary Optimization of Quantum Operators. MENDEL. 27, 2 (Dec. 2021), 12-22. DOI:
Research articles