Abstract
The synthesis of Boolean functions, as they are found in many quantum algorithms, is usually conducted in two steps. First, the function is realized in terms of a reversible circuit followed by a mapping into a corresponding quantum realization. During this process, the number of lines and the quantum costs of the resulting circuits have mainly been considered as optimization objectives thus far. However, beyond that also the depth of a quantum circuit is vital. Although first synthesis approaches that consider depth have recently been introduced, the majority of design methods did not consider this metric.
In this paper, we introduce an optimization approach aiming for the reduction of depth in the process of mapping a reversible circuit into a quantum circuit. For this purpose, we present an improved (local) mapping of single gates as well as a (global) optimization scheme considering the whole circuit. In both cases, we incorporate the idea of exploiting additional circuit lines which are used in order to split a chain of serial gates. Our optimization techniques enable a concurrent application of gates which significantly reduces the depth of the circuit. Experiments show that reductions of approx. 40% on average can be achieved when following this scheme.
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
Preview
Unable to display preview. Download preview PDF.
References
Fazel, K., Thornton, M., Rice, J.: ESOP-based toffoli gate cascade generation. In: Pacific Rim Conference on Communications, Computers and Signal Processing, PacRim 2007, pp. 206–209 (2007)
Miller, D.M., Maslov, D., Dueck, G.W.: A transformation based algorithm for reversible logic synthesis. In: Design Automation Conf., pp. 318–323 (2003)
Wille, R., Drechsler, R.: BDD-based synthesis of reversible logic for large functions. In: Design Automation Conf., pp. 270–275 (2009)
Soeken, M., Wille, R., Otterstedt, C., Drechsler, R.: A synthesis flow for sequential reversible circuits. In: Int’l Symposium on Multiple-Valued Logic, pp. 299–304 (2012)
Soeken, M., Wille, R., Hilken, C., Przigoda, N., Drechsler, R.: Synthesis of reversible circuits with minimal lines for large functions. In: ASP Design Automation Conf., pp. 85–92 (2012)
Barenco, A., Bennett, C.H., Cleve, R., DiVinchenzo, D., Margolus, N., Shor, P., Sleator, T., Smolin, J., Weinfurter, H.: Elementary gates for quantum computation. The American Physical Society 52, 3457–3467 (1995)
Arabzadeh, M., Saheb Zamani, M., Sedighi, M., Saeedi, M.: Depth-optimized reversible circuit synthesis. Quantum Information Processing, 1–23 (2012)
Maslov, D., Dueck, G., Miller, D., Negrevergne, C.: Quantum circuit simplification and level compaction. Transactions on Computer-Aided Design of Integrated Circuits and Systems 27(3), 436–444 (2008)
Bocharov, A., Svore, K.M.: A depth-optimal canonical form for single-qubit quantum circuits arXiv preprint arXiv:1206.3223 (2012)
Amy, M., Maslov, D., Mosca, M., Roetteler, M.: A meet-in-the-middle algorithm for fast synthesis of depth-optimal quantum circuits arXiv preprint arXiv:1206.0758 (2012)
Arabzadeh, M., Zamani, M., Sedighi, M., Saeedi, M.: Logical-depth-oriented reversible logic synthesis. In: Int’l Workshop on Logic and Synthesis (2011)
Toffoli, T.: Reversible computing. In: de Bakker, J., van Leeuwen, J. (eds.) Automata, Languages and Programming. LNCS, vol. 85, pp. 632–644. Springer, Heidelberg (1980)
Shende, V.V., Prasad, A.K., Markov, I.L., Hayes, J.P.: Synthesis of reversible logic circuits. Transactions on Computer-Aided Design of Integrated Circuits and Systems 22(6), 710–722 (2003)
Nielsen, M., Chuang, I.: Quantum Computation and Quantum Information. Cambridge Univ. Press (2000)
Miller, D.M., Wille, R., Sasanian, Z.: Elementary quantum gate realizations for multiple-control Toffolli gates. In: Int’l Symp. on Multi-Valued Logic, pp. 217–222 (May 2011)
Meter, R.V., Oskin, M.: Architectural implications of quantum computing technologies. J. Emerg. Technol. Comput. Syst. 2(1), 31–63 (2006)
Miller, D.M., Wille, R., Drechsler, R.: Reducing reversible circuit cost by adding lines. In: Int’l Symp. on Multi-Valued Logic, pp. 217–222 (2010)
Zahra, S.: Technology Mapping and Optimization for Reversible and Quantum. PhD thesis, University of Victoria (2012)
Soeken, M., Frehse, S., Wille, R., Drechsler, R.: Revkit: an open source toolkit for the design of reversible circuits. In: De Vos, A., Wille, R. (eds.) RC 2011. LNCS, vol. 7165, pp. 64–76. Springer, Heidelberg (2012), RevKit is available at http://www.revkit.org
Wille, R., Große, D., Teuber, L., Dueck, G.W., Drechsler, R.: RevLib: an online resource for reversible functions and reversible circuits. In: Int’l Symp. on Multi-Valued Logic, pp. 220–225 (2008), RevLib is available at http://www.revlib.org
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Abdessaied, N., Wille, R., Soeken, M., Drechsler, R. (2013). Reducing the Depth of Quantum Circuits Using Additional Circuit Lines. In: Dueck, G.W., Miller, D.M. (eds) Reversible Computation. RC 2013. Lecture Notes in Computer Science, vol 7948. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38986-3_18
Download citation
DOI: https://doi.org/10.1007/978-3-642-38986-3_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38985-6
Online ISBN: 978-3-642-38986-3
eBook Packages: Computer ScienceComputer Science (R0)