Fixed-Point Quantum Search with an Optimal Number of Queries
Author(s)Low, Guang Hao; Yoder, Theodore James; Chuang, Isaac L.
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Grover’s quantum search and its generalization, quantum amplitude amplification, provide a quadratic advantage over classical algorithms for a diverse set of tasks but are tricky to use without knowing beforehand what fraction λ of the initial state is comprised of the target states. In contrast, fixed-point search algorithms need only a reliable lower bound on this fraction but, as a consequence, lose the very quadratic advantage that makes Grover’s algorithm so appealing. Here we provide the first version of amplitude amplification that achieves fixed-point behavior without sacrificing the quantum speedup. Our result incorporates an adjustable bound on the failure probability and, for a given number of oracle queries, guarantees that this bound is satisfied over the broadest possible range of λ.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Department of Physics
Physical Review Letters
American Physical Society
Yoder, Theodore J., Guang Hao Low, Isaac L. Chuang. "Fixed-point quantum search with an optimal number of queries." Phys. Rev. Lett. 113, 210501 (November 2014). © 2014 American Physical Society
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