Resonant Quantum Search with Monitor Qubits**B.W. is supported by the National Key R&D Program of China (Grant Nos. 2017YFA0303302 and 2018YFA0305602), the National Natural Science Foundation of China (Grant No. 11921005), and Shanghai Municipal Science and Technology Major Project (Grant No. 2019SHZDZX01). F.W. is supported by the Swedish Research Council (Contract No. 335–2014-7424), U.S. Department of Energy (Contract No. de-sc0012567),

Abstract

We present an algorithm for the generalized search problem (searching k marked items among N items) based on a continuous Hamiltonian and exploiting resonance. This resonant algorithm has the same time complexity as the Grover algorithm. A natural extension of the algorithm, incorporating auxiliary “monitor” qubits, can determine k precisely, if it is unknown. The time complexity of our counting algorithm is , similar to the best quantum approximate counting algorithm, or better, given appropriate physical resources.