Limits of Clifford Disentangling in Tensor Network States

TL;DR

This paper investigates the effectiveness and fundamental limits of Clifford transformations in disentangling tensor network states, revealing their capabilities and constraints in simulating complex quantum systems.

Contribution

It provides a detailed analysis of Clifford disentanglers, identifying regimes of effectiveness and proving their limitations beyond stabilizer states.

Findings

Clifford disentanglers are effective in certain regimes for tensor networks.

The breakdown of Clifford disentangling correlates with non-Clifford resource accumulation.

No Clifford operation can universally disentangle a qubit from arbitrary non-Clifford rotations.

Abstract

Tensor network methods leverage the limited entanglement of quantum states to efficiently simulate many-body systems. Alternatively, Clifford circuits provide a framework for handling highly entangled stabilizer states, which have low magic and are thus also classically tractable. Clifford tensor networks combine the benefits of both approaches, exploiting Clifford circuits to reduce the classical complexity of the tensor network description of states, with promising effects on simulation approaches. We study the disentangling power of Clifford transformations acting on tensor networks, with a particular emphasis on entanglement cooling strategies. We identify regimes where exact or heuristic Clifford disentanglers are effective, explain the link between the two approaches, and characterize their breakdown as non-Clifford resources accumulate. Additionally, we prove that, beyond stabilizer settings, no Clifford operation can universally disentangle even a single qubit from an arbitrary non-Clifford rotation. Our results clarify both the capabilities and fundamental limitations of Clifford-based simulation methods.