Quantum search algorithms are considered in the context of protein sequence comparison in bioinformatics. Given a sample protein sequence of length m (i.e., m residues), the problem considered is to find an optimal match in a large database containing N residues. Initially, Grover’s quantum search algorithm is applied to a simple illustrative case—namely, where the database forms a complete set of states over the $2^m$ basis states of a m qubit register, and thus is known to contain the exact sequence of interest. This example demonstrates explicitly the typical $O\left(\sqrt{N}\right)$ speedup on the classical $O\left(N\right)\mathrm{}$ requirements. An algorithm is then presented for the (more realistic) case where the database may contain repeat sequences, and may not necessarily contain an exact match to the sample sequence. In terms of minimizing the Hamming distance between the sample sequence and the database subsequences the algorithm finds an optimal alignment, in $O\left(\sqrt{N}\right)$ steps, by employing an extension of Grover’s algorithm, due to Boyer et al. for the case when the number of matches is not a priori known.

• Received 28 February 2000

DOI:https://doi.org/10.1103/PhysRevE.62.7532