Decomposition of unitary matrices for finding quantum circuits: Application to molecular Hamiltonians

Anmer Daskin, Purdue University
Sabre Kais, Birck Nanotechnology Center and Department of Chemistry, Purdue University

Date of this Version



J. Chem. Phys. 134, 144112 (2011)


Copyright (2011) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in J. Chem. Phys. 134, 144112 (2011) and may be found at The following article has been submitted to/accepted by The Journal of Chemical Physics. Copyright (2011) Anmer Daskin and Sabre Kais. This article is distributed under a Creative Commons Attribution 3.0 Unported License.


Constructing appropriate unitary matrix operators for new quantum algorithms and finding the minimum cost gate sequences for the implementation of these unitary operators is of fundamental importance in the field of quantum information and quantum computation. Evolution of quantum circuits faces two major challenges: complex and huge search space and the high costs of simulating quantum circuits on classical computers. Here, we use the group leaders optimization algorithm to decompose a given unitary matrix into a proper-minimum cost quantum gate sequence. We test the method on the known decompositions of Toffoli gate, the amplification step of the Grover search algorithm, the quantum Fourier transform, and the sender part of the quantum teleportation. Using this procedure, we present the circuit designs for the simulation of the unitary propagators of the Hamiltonians for the hydrogen and the water molecules. The approach is general and can be applied to generate the sequence of quantum gates for larger molecular systems. (C) 2011 American Institute of Physics. [doi:10.1063/1.3575402]


Nanoscience and Nanotechnology