  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.
