A low failure rate quantum algorithm for searching maximum or minimum

Although Durr and Hoyer have proposed state-of-the-art quantum algorithm (DHA) for searching minimum value, the lower limit of DHA’s successful probability is 1/2 . Also, DHA requires approximately \((\log _{2}N)^2\) copies of the initial state. In this paper, we propose a new quantum maximum or minimum searching algorithm (QUMMSA). In big data scenarios, according to sparse sampling with different densities, we can estimate the corresponding precision parameters. QUMMSA can improve the successful probability close to \(100\%\). Furthermore, with the quantum exact search algorithm, QUMMSA only requires approximately \(\log _2 N\) copies of the initial state to solve this problem. Since preparing an arbitrary quantum state is a problem with exponential complexity, our algorithm has a greater advantage with the increasing database size. In addition, we first propose a general method for circuits construction, which can be used in any database. An experiment implemented in an IBM superconducting processor and a numerical simulation of a 6-qubit system to solve a real issue indicate the feasibility and efficiency of QUMMSA. QUMMSA can serve as a subroutine in various quantum algorithms which involves searching maximum or minimum.