ZX-Rules for 2-qubit Clifford+T Quantum Circuits

TL;DR

This paper introduces a concise set of ZX-calculus rules for deriving all equations in 2-qubit Clifford+T circuits, simplifying quantum circuit rewriting and highlighting ZX-calculus's flexibility over fixed gate sets.

Contribution

It presents a minimal, novel ZX-rule set for 2-qubit Clifford+T circuits, extending stabilizer ZX-calculus and surpassing previous rule complexity.

Findings

The rule set derives all 2-qubit Clifford+T circuit equations.

The new rule is potentially useful beyond circuit equations.

ZX-calculus offers a more convenient framework for quantum circuit rewriting.

Abstract

ZX-calculus is a high-level graphical formalism for qubit computation. In this paper we give the ZX-rules that enable one to derive all equations between 2-qubit Clifford+T quantum circuits. Our rule set is only a small extension of the rules of stabilizer ZX-calculus, and substantially less than those needed for the recently achieved universal completeness. One of our rules is new, and we expect it to also have other utilities. These ZX-rules are much simpler than the complete of set Clifford+T circuit equations due to Selinger and Bian, which indicates that ZX-calculus provides a more convenient arena for quantum circuit rewriting than restricting oneself to circuit equations. The reason for this is that ZX-calculus is not constrained by a fixed unitary gate set for performing intermediate computations.