Optimal Ancilla-free Pauli+V Circuits for Axial Rotations

TL;DR

This paper adapts a deterministic-search technique from Clifford+T circuits to Pauli+V circuits, enabling more efficient approximation of z-rotations with simpler geometric methods.

Contribution

It introduces a new approach for approximating z-rotations using Pauli+V circuits, simplifying the process with geometric techniques.

Findings

Achieved shallower Pauli+V circuits for z-rotation approximation

Demonstrated the effectiveness of geometric methods in this context

Extended the deterministic-search technique to a new circuit framework

Abstract

Recently Neil Ross and Peter Selinger analyzed the problem of approximating z- rotations by means of single-qubit Clifford+T circuits. Their main contribution is a deterministic-search technique which allowed them to make approximating circuits shallower. We adapt the deterministic-search technique to the case of Pauli+V circuits and prove similar results. Because of the relative simplicity of the Pauli+V framework, we use much simpler geometric methods.