Quantum Counting with Decoherence Errors — Influence of Circuits’ Order —

— Influence of Circuits’ Order — Jun Hasegawa Fumitaka Yura Department of Computer Science, Graduate School of Information Science and Technology, University of Tokyo. 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan. ERATO Quantum Computation and Information Project, JST. Hongo White Building, 5-28-3 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan. Abstract. Quantum counting algorithm can estimate the number of solutions in a database. In this paper, we analyze its behaviors in the presence of decoherence errors. We construct two counting circuits in which the order of commutative gates are altered and show that the behaviors of circuits are different when decoherence errors occur. On one circuit, almost correct number of solutions are obtained and on the other circuit, the estimated numbers of solutions are mostly distributed over the correct one and wrong counts zero and , the number of elements. We analyze that these phenomena result from the rotation outside the Grover space due to decoherence.