NMR quantum gate factorization through canonical cosets

TL;DR

This paper introduces a universal algorithmic method using block canonical coset decomposition to synthesize multi-qubit quantum gates with NMR elements, demonstrated on Fourier transforms.

Contribution

It develops a novel decomposition technique that connects numerical analysis with practical NMR quantum gate synthesis for multiple qubits.

Findings

Successfully synthesized 2-, 3-, and 4-qubit Fourier transforms

Bridged numerical analysis with experimental NMR gate synthesis

Provided a universal algorithmic framework for quantum gate construction

Abstract

The block canonical coset decomposition is developed as a universal algorithmic tool to synthesize n-qubit quantum gates out of experimentally realizable NMR elements. The two-, three-, and four-qubit quantum Fourier transformations are worked out as examples. The proposed decomposition bridges the state of the art numerical analysis with NMR quantum gate synthesis.