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...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.展开更多
基金National Key R&D Program of China(Grant Nos.2017YFA0303302 and 2018YFA0305602)National Natural Science Foundation of China(Grant No.11921005)+3 种基金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.SDepartment of Energy(Contract No.de-sc0012567)European Research Council(Grant No.742104)。
文摘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.
