Unsupervised detection of decoupled subspaces: many-body scars and beyond

Abstract

Highly excited eigenstates of quantum many-body systems are typically featureless thermal states. Some systems, however, possess a small number of special, low-entanglement eigenstates known as quantum scars. We introduce a quantum-inspired machine learning platform based on a Quantum Variational Autoencoder (QVAE) that detects families of scar states in spectra of many-body systems. Unlike a classical autoencoder, QVAE performs a parametrized unitary operation, allowing us to compress a single eigenstate into a smaller number of qubits. We demonstrate that the autoencoder trained on a scar state is able to detect the whole family of scar states sharing common features with the input state. We identify families of quantum many-body scars in the PXP model beyond the ${\mathbb{Z}}_2$ and ${\mathbb{Z}}_3$ families and find dynamically decoupled subspaces in the Hilbert space of disordered, interacting spin ladder model. The possibility of an automatic detection of subspaces of scar states opens new pathways in studies of models with a weak breakdown of ergodicity and fragmented Hilbert spaces.

Author accepted manuscript to be published in PRB

References in corpus (12)

• Probing many-body dynamics on a 51-atom quantum simulator
• Many body localization and thermalization in quantum statistical mechanics
• Strong quantum computational advantage using a superconducting quantum processor
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• Phase-Programmable Gaussian Boson Sampling Using Stimulated Squeezed Light
• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains
• Emergent SU(2) dynamics and perfect quantum many-body scars
• Quantum Many-Body Scar States with Emergent Kinetic Constraints and Finite-Entanglement Revivals
• A proposal for realising quantum scars in the tilted 1D Fermi-Hubbard model
• Exact many-body scars and their stability in constrained quantum chains
• Variational Quantum Anomaly Detection: Unsupervised mapping of phase diagrams on a physical quantum computer
• Extreme many-body scarring in a quantum spin chain via weak dynamical constraints