Uncovering Quantum Many-body Scars with Quantum Machine Learning

TL;DR

This paper demonstrates that quantum convolutional neural networks can effectively identify and characterize non-thermal eigenstates, known as quantum many-body scars, in complex chaotic quantum systems, with high accuracy even on noisy quantum hardware.

Contribution

The study introduces the use of quantum convolutional neural networks to detect quantum many-body scars and non-thermal states, achieving high accuracy and validating on real quantum devices.

Findings

QCNNs achieve over 99% accuracy in simulations

Successfully identify new non-thermal states in multiple models

Achieve over 63% accuracy on IBM quantum devices with error mitigation

Abstract

Quantum many-body scars are rare eigenstates hidden within the chaotic spectra of many-body systems, representing a weak violation of the eigenstate thermalization hypothesis (ETH). Identifying these scars, as well as other non-thermal states in complex quantum systems, remains a significant challenge. Besides exact scar states, the nature of other non-thermal states lacking simple analytical characterization remains an open question. In this study, we employ tools from quantum machine learning -- specifically, (enhanced) quantum convolutional neural networks (QCNNs), to explore hidden non-thermal states in chaotic many-body systems. Our simulations demonstrate that QCNNs achieve over 99% single-shot measurement accuracy in identifying all known scars. Furthermore, we successfully identify new non-thermal states in models such as the xorX model, the PXP model, and the far-coupling Su-Schrieffer-Heeger model. In the xorX model, some of these non-thermal states can be approximately described as spin-wave modes of specific quasiparticles. We further develop effective tight-binding Hamiltonians within the quasiparticle subspace to capture key features of these many-body eigenstates. Finally, we validate the performance of QCNNs on IBM quantum devices, achieving single-shot measurement accuracy exceeding 63% under real-world noise and errors, with the aid of error mitigation techniques. Our results underscore the potential of QCNNs to uncover hidden non-thermal states in quantum many-body systems.