# Clifford Gates in the Holant Framework

## TL;DR

This paper demonstrates that Clifford gates and stabilizer circuits, which are efficiently simulatable classically, correspond to affine signatures within the Holant framework under a unitary condition.

## Contribution

It establishes a novel equivalence between quantum Clifford gates and affine signatures in the Holant framework, linking quantum computing and computational complexity.

## Key findings

- Clifford gates are equivalent to affine signatures under a unitary condition.
- Stabilizer circuits correspond to tractable functions in the Holant framework.
- Provides a new perspective on classical simulation of quantum circuits.

## Abstract

We show that the Clifford gates and stabilizer circuits in the quantum computing literature, which admit efficient classical simulation, are equivalent to affine signatures under a unitary condition. The latter is a known class of tractable functions under the Holant framework.