Doped stabilizer states in many-body physics and where to find them

TL;DR

This paper establishes a connection between doped stabilizer states and eigenstates of perturbed many-body quantum systems, enabling new classical algorithms for simulating complex quantum phenomena.

Contribution

It proves that eigenstates of certain perturbed stabilizer Hamiltonians can be represented as doped stabilizer states, facilitating classical simulation techniques.

Findings

Eigenstates can be represented as doped stabilizer states with small nullity

Efficient algorithms for low-energy states, dynamics, and entanglement entropy

Broad applicability to highly entangled many-body systems

Abstract

This work uncovers a fundamental connection between doped stabilizer states, a concept from quantum information theory, and the structure of eigenstates in perturbed many-body quantum systems. We prove that for Hamiltonians consisting of a sum of commuting Pauli operators (i.e., stabilizer Hamiltonians) and a perturbation composed of a limited number of arbitrary Pauli terms, the eigenstates can be represented as doped stabilizer states with small stabilizer nullity. This result enables the application of stabilizer techniques to a broad class of many-body systems, even in highly entangled regimes. Building on this, we develop efficient classical algorithms for tasks such as finding low-energy eigenstates, simulating quench dynamics, preparing Gibbs states, and computing entanglement entropies in these systems. Our work opens up new possibilities for understanding the robustness of topological order and the dynamics of many-body systems under perturbations, paving the way for novel insights into the interplay of quantum information, entanglement, and many-body systems.