Extended quantum circuit diagrams

TL;DR

This paper introduces a novel formulation of quantum circuit diagrams using the exponential map, enabling graphical calculations with a new set of rewrite rules and demonstrating their application through various examples.

Contribution

It presents a new exponential map-based formulation for quantum circuit diagrams along with a consistent set of rewrite rules and illustrative examples.

Findings

The formulation allows for graphical calculations of quantum circuits.

Rewrite rules are sound and facilitate circuit transformations.

Examples demonstrate the practical utility of the approach.

Abstract

We present a formulation of quantum circuit diagrams based on the exponential map which provides a new way to calculate graphically with circuits. We present a sound list of rewrite rules for this formulation and demonstrate a variety of example calculations.