Comparative analyses of protein-protein interaction networks play important roles in the understanding of biological processes. The growing enormity of available data on the networks becomes a computational challenge for the conventional alignment algorithms. Quantum algorithms generally provide  efficiency over their classical counterparts in solving various problems. One of such algorithms is the quantum phase estimation algorithm which generates the principal eigenvector of a stochastic matrix with probability one. Using this property, in this article, we describe a quantum computing approach for the alignment of protein-protein interaction networks by following the classical algorithm IsoRank which uses the principal eigenvector of the stochastic matrix representing the Kronecker product of the normalized adjacency matrices of networks for the pairwise alignment. We also present a  measurement scheme to efficiently procure the alignment from the output state of the phase estimation algorithm where the eigenvector is encoded as the amplitudes of this state. Furthermore, since the stochastic matrices are generally not Hermitian, we discuss how to approximate such matrices and generate quantum circuits. Finally we discuss the complexity of the quantum approach and show that it is exponentially more efficient .
Comparative analyses of protein-protein interaction networks play important roles in the understanding of biological processes. However, the growing enormity of available data on the networks becomes a computational challenge for the conventional alignment algorithms. Quantum algorithms generally provide greater efficiency over their classical counterparts in solving various problems. One of such algorithms is the quantum phase estimation algorithm which generates the principal eigenvector of a stochastic matrix with probability one. Using the quantum phase estimation algorithm, we introduce a quantum computing approach for the alignment of protein-protein interaction networks by following the classical algorithm IsoRank which uses the principal eigenvector of the stochastic matrix representing the Kronecker product of the normalized adjacency matrices of networks for the pairwise alignment. We also present a greedy quantum measurement scheme to efficiently procure the alignment from the output state of the phase estimation algorithm where the eigenvector is encoded as the amplitudes of this state. The complexity of the quantum approach outperforms the classical running time .
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