摘要
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.
作者
Frank Wilczek
Hong-Ye Hu
Biao Wu
Frank Wilczek;扈鸿业;吴飙(Center for Theoretical Physics,MIT,Cambridge,MA 02139,USA;D.Lee Institute,Shanghai Jiao Tong University,Shanghai 200240,China;Wilczek Quantum Center,School of Physics and Astronomy,Shanghai Jiao Tong University,Shanghai 200240,China;Department of Physics,Stockholm University,Stockholm,SE-10691,Sweden;Department of Physics,Arizona State University,Tempe,AZ 25287,USA;Department of Physics,University of Californian,San Diego,CA 92093,USA;International Center for Quantum Materials,School of Physics,Peking University,Beijing 100871,China;Collaborative Innovation Center of Quantum Matter,Beijing 100871,China)
基金
National Key R&D Program of China(Grant Nos.2017YFA0303302 and 2018YFA0305602)
National Natural Science Foundation of China(Grant No.11921005)
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)
European Research Council(Grant No.742104)。
