Universal Quantum Algorithm

TL;DR

This paper introduces a universal quantum algorithm that encompasses quantum amplitude amplification and phase estimation, eliminating the need for quantum Fourier transform in phase estimation.

Contribution

The paper proposes a unified quantum algorithm framework that explains key algorithms as special cases, simplifying quantum phase estimation.

Findings

Quantum phase estimation can be performed without quantum Fourier transform.

The universal algorithm explains all known quantum algorithms derived from amplitude amplification and phase estimation.

Adiabatic quantum algorithms can be simulated using this universal approach.

Abstract

Quantum amplitude amplification and quantum phase estimation are two fundamental quantum algorithms. All known quantum algorithms are derived from these two algorithms. Even the adiabatic quantum algorithms can also be efficiently simulated using quantum phase estimation. We present a universal quantum algorithm which explains these two algorithms as special cases. An interesting result is that we do not need quantum fourier transform to do quantum phase estimation.