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Revision #1 to TR14-151 | 26th April 2016 11:06

#### Applications of Quantum Amplitude Amplification

Revision #1
Authors: Debajyoti Bera
Accepted on: 26th April 2016 11:06
Keywords:

Abstract:

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 input is accessed in the form of initial states of quantum circuits and where arbitrary projective measurements may be used to ascertain success or failure. This generalization allows us to derive interesting applications of amplitude amplification for distinguishing between two given distributions based on their samples, detection of faults in quantum circuits and eliminating error of one and two-sided quantum algorithms with exact errors.

Changes to previous version:

1. Generalized technique.

### Paper:

TR14-151 | 13th November 2014 19:48

#### Quantum One-Sided Exact Error Algorithms

TR14-151
Authors: Debajyoti Bera
Publication: 13th November 2014 20:10
We define a complexity class for randomized algorithms with one-sided error that is exactly equal to a constant (unlike the usual definitions, in which the error is only bounded above or below by a constant). We show that the corresponding quantum classes (one each for a different error probability) are in fact all equivalent to each other and to $\mathbf{EQP}$, the quantum analogue of $\mathbf{P}$. The technique used is a form of quantum amplitude amplification.