Stabilizer Tensor Networks: universal quantum simulator on a basis of stabilizer states

TL;DR

This paper introduces a unified framework combining tensor networks and stabilizer formalism to enable efficient, universal simulation of quantum circuits, including non-Clifford gates and measurements, expanding the capabilities of quantum state simulation.

Contribution

It generalizes the stabilizer tableau formalism to incorporate non-Clifford gates and measurements, allowing for universal quantum circuit simulation within a tensor network approach.

Findings

Framework enables efficient simulation of universal quantum circuits.

Simulation results support the framework's effectiveness.

Raises questions on the representation power of tensor networks.

Abstract

Efficient simulation of quantum computers relies on understanding and exploiting the properties of quantum states. This is the case for methods such as tensor networks, based on entanglement, and the tableau formalism, which represents stabilizer states. In this work, we integrate these two approaches to present a generalization of the tableau formalism used for Clifford circuit simulation. We explicitly prove how to update our formalism with Clifford gates, non-Clifford gates, and measurements, enabling universal circuit simulation. We also discuss how the framework allows for efficient simulation of more states, raising some interesting questions on the representation power of tensor networks and the quantum properties of resources such as entanglement and magic, and support our claims with simulations.