Resonant Quantum Search with Monitor Qubits
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 O(N/k) 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 O(N), similar to the best quantum approximate counting algorithm, or better, given appropriate physical resources.
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