Preparation of 3-qubit states

TL;DR

This paper introduces efficient methods for preparing real 3-qubit states using a limited set of quantum gates, improving upon previous algorithms by reducing the number of controlled-Z gates needed.

Contribution

It presents a new algorithm for preparing any 3-qubit state with fewer controlled-Z gates and discusses the optimality of gate counts for real states.

Findings

Any real 3-qubit state can be prepared with at most four controlled-Z gates.

A new algorithm prepares any 3-qubit state with at most three controlled-Z gates.

The proposed methods are demonstrated through illustrative videos.

Abstract

We will call a pure qubit state real if all its amplitudes are real numbers. We show that any real 3-qubit state can be prepared using $R_y(\theta)$ gates and at most four controlled-$Z$ gates, and we conjecture that four is optimal. We also present an algorithm -- different from the 2008 algorithm given by Znidaric, Giraud and Georgeot -- that prepares any 3-qubit state using local gates and at most three controlled-$Z$ gates. Videos showing how our method works for two- and three-qubit states can be found at https://youtu.be/LIdYSs-rE-o and https://youtu.be/Kne0Vq7gyzQ