Abstract
The algebraic decomposition of a unitary operator is a key operation in the synthesis of quantum circuits. If most methods factorize the matrix into products, there exists a method that allows to reuse already existing optimized circuits to implement linear combinations of them. This paper presents an attempt to extend this method to a general framework of circuit synthesis. The method needs to find suitable groups for the implementation of new quantum circuits. We identify key points necessary for the construction of a comprehensive method and we test potential group candidates.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Simulating quantum computation on a conventional computer is known to be expensive [10] since a linear increase in the number of manipulated qubits yields an exponential increase in the size of the required memory.
References
Barenco, A., Bennett, C.H., Cleve, R., DiVincenzo, D.P., Margolus, N., Shor, P., Sleator, T., Smolin, J.A., Weinfurter, H.: Elementary gates for quantum computation. Phys. Rev. A 52(5), 3457 (1995)
Bullock, S.S., Markov, I.L.: Asymptotically optimal circuits for arbitrary n-qubit diagonal computations. Quant. Inf. Comput. 4(1), 27–47 (2004)
Chi-Chih Yao, A.: Quantum circuit complexity. In: Proceedings of the 34th Annual Symposium on Foundations of Computer Science (SFCS’93), pp. 352–361. IEEE Computer Society, Washington, DC, USA (1993)
De Vos, A., De Baerdemacker, S.: Block-ZXZ synthesis of an arbitrary quantum circuit. Phys. Rev. A 94(5), 052317 (2016)
Deutsch, D., Barenco, A., Ekert, A.: Universality in quantum computation. Proc. R. Soc. Lond. A 449, 669–677 (1995)
JavadiAbhari, A., Patil, S., Kudrow, D., Heckey, J., Lvov, A., Chong, F.T., Martonosi, M.: ScaffCC: Scalable compilation and analysis of quantum programs. Parallel Comput. 45, 2–17 (2015)
Klappenecker, A., Rötteler, M.: Quantum software reusability. Int. J. Found. Comput. Sci. 14(05), 777–796 (2003)
Knill, E.: Approximation by quantum circuits. Technical Report LANL report LAUR-95-2225, Los Alamos National Laboratory (1995)
Maslov, D., Dueck, G.W., Miller, D.M., Negrevergne, C.: Quantum circuit simplification and level compaction. IEEE Trans. Comput.-Aided Des. Integr. Circ. Syst. 27(3), 436–444 (2008)
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2011)
Reck, M., Zeilinger, A., Bernstein, H.J., Bertani, P.: Experimental realization of any discrete unitary operator. Phys. Rev. Lett. 73(1), 58 (1994)
Saeedi, M., Arabzadeh, M., Zamani, M.S., Sedighi, M.: Block-based quantum-logic synthesis. Quant. Inf. Comput. 11(3), 262–277 (2011)
Shende, V.V., Bullock, S.S., Markov, I.L.: Synthesis of quantum-logic circuits. IEEE Trans. Comput.-Aided Des. Integr. Circ. Syst. 25(6), 1000–1010 (2006)
Steane, A.M.: Error correcting codes in quantum theory. Phys. Rev. Lett. 77(5), 793 (1996)
Valiron, B., Ross, N.J., Selinger, P., Alexander, D.S., Smith, J.M.: Programming the quantum future. Commun. ACM 58(8), 52–61 (2015)
Vartiainen, J.J., Möttönen, M., Salomaa, M.M.: Efficient decomposition of quantum gates. Phys. Rev. Lett. 92(17), 177,902 (2004)
Wecker, D., Svore, K.M.: LIQUi\(\vert \rangle \): A software design architecture and domain-specific language for quantum computing (2014). ArXiv:1402.4467
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Allouche, C., Baboulin, M., Goubault de Brugière, T., Valiron, B. (2018). Reuse Method for Quantum Circuit Synthesis. In: Kilgour, D., Kunze, H., Makarov, R., Melnik, R., Wang, X. (eds) Recent Advances in Mathematical and Statistical Methods . AMMCS 2017. Springer Proceedings in Mathematics & Statistics, vol 259. Springer, Cham. https://doi.org/10.1007/978-3-319-99719-3_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-99719-3_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-99718-6
Online ISBN: 978-3-319-99719-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)