Two-sided Quantum Amplitude Amplification and Exact-Error Algorithms

TL;DR

This paper generalizes quantum amplitude amplification to two-sided error algorithms, enabling improved decision-making, distribution distinction, fault detection, and exact error elimination in quantum computing.

Contribution

It introduces a two-sided error amplitude amplification framework, expanding the applicability of amplitude amplification in quantum algorithms and error correction.

Findings

Enhanced algorithms for distribution distinction

Fault detection in quantum circuits

Exact error elimination in quantum algorithms

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 two-sided error quantum algorithm 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.