Quantum Feedback Amplification

Controlled Quantum Amplification

We propose a new framework for turning quantum search algorithms that decide into quantum algorithms for finding a solution. Consider we are given an abstract quantum search algorithm A that can determine whether a target g exists or not. We give a general construction of another operator U that both determines and finds the target, whenever one exists. Our amplification method at most doubles ...

Quantum Amplitude Amplification and Estimation

Consider a Boolean function χ : X → {0, 1} that partitions set X between its good and bad elements, where x is good if χ(x) = 1 and bad otherwise. Consider also a quantum algorithm A such that A|0〉 = ∑ x∈X αx|x〉 is a quantum superposition of the elements of X, and let a denote the probability that a good element is produced if A|0〉 is measured. If we repeat the process of running A, measuring t...

Quantum key distribution & Privacy Amplification

Applications of Quantum Amplitude Amplification

Amplitude amplification is a central tool used in Grover’s quantum search algorithm and has been used in various forms in numerous quantum algorithms since then. It has been shown to completely eliminate one-sided error of quantum search algorithms where input is accessed in the form of black-box queries. We generalize amplitude amplification for decision problems in the familiar form where inp...

Feedback in Quantum Communication

Communication is primarily the generation of correlations between two parties. The transmission of information is undertaken to correlate the received message with an possible set of transmitted messages. In the classical theory of information the maximum rate of information transmission through a memoryless channel is given by a measure of the maximum correlation that may be generated through ...