Arbitrary phases in quantum amplitude amplification

By Peter Høyer. 2000

161 citations recorded by the source corpus.

We consider the use of arbitrary phases in quantum amplitude amplification which is a generalization of quantum searching. We prove that the phase condition in amplitude amplification is given by $\tan(\varphi/2) = \tan(\phi/2)(1-2a)$, where $\phi$ and $\phi$ are the phases used and where $a$ is the success probability of the given algorithm. Thus the choice of phases depends nontrivially and nonlinearly on the success probability. Utilizing this condition, we give methods for constructing quantum algorithms that succeed with certainty and for implementing arbitrary rotations. We also conclude that phase errors of order up to $\frac{1}{\sqrt{a}}$ can be tolerated in amplitude amplification.

Subfields: Artificial Intelligence, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/65895679205594f74d81bb4a84d0fe1f094073c3

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In Artificial Intelligence

In Electrical and Electronic Engineering

Citations in the corpus

Quantum Models of Cognition and Decision (2012, methodology): “The amplitude amplification algorithm is an extension by Brassard and Hoyer of Grover’s (1997) search algorithm (Hoyer, 2000).”
Methodology of Resonant Equiangular Composite Quantum Gates (2016, background): “[56] Peter Høyer, “Arbitrary phases in quantum amplitude amplification,” Phys.”
Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity (2018, unknown): “A circuit that uses amplitude amplification [69, 70] to conditionally and reversibly prepare the uniform superposition (1/ √ 2kL) ∑2kL−1 `=0 |`〉, where L is odd, starting from the |0〉 state.”