Journal
PHYSICAL REVIEW LETTERS
Volume 113, Issue 21, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.113.210501
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Funding
- NSF RQCC Project [1111337]
- ARO Quantum Algorithms Program
- NSF iQuISE IGERT program
- Direct For Computer & Info Scie & Enginr
- Division of Computing and Communication Foundations [1111337] Funding Source: National Science Foundation
- Division Of Physics
- Direct For Mathematical & Physical Scien [1125846] Funding Source: National Science Foundation
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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 lambda 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 lambda.
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