Unsupervised Interpretable Learning of Phases From Many-Qubit Systems

Abstract

Experimental progress in qubit manufacturing calls for the development of new theoretical tools to analyze quantum data. We show how an unsupervised machine-learning technique can be used to understand short-range entangled many-qubit systems using data of local measurements. The method successfully constructs the phase diagram of a cluster-state model and detects the respective order parameters of its phases, including string order parameters. For the toric code subject to external magnetic fields, the machine identifies the explicit forms of its two stabilizers. Prior information of the underlying Hamiltonian or the quantum states is not needed; instead, the machine outputs their characteristic observables. Our work opens the door for a first-principles application of hybrid algorithms that aim at strong interpretability without supervision.

arXiv comment9 pages, 7 figures

References in corpus (34)

• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• The density-matrix renormalization group in the age of matrix product states
• Quantum Convolutional Neural Networks
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Predicting Many Properties of a Quantum System from Very Few Measurements
• Many-body quantum state tomography with neural networks
• Efficient quantum state tomography
• Optical quantum computation using cluster states
• Probing entanglement entropy via randomized measurements
• Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
• 10-qubit entanglement and parallel logic operations with a superconducting circuit
• Cluster-state quantum computation
• Valence Bond Solids for Quantum Computation
• Reconstructing quantum states with generative models
• Identifying topological order through unsupervised machine learning
• Efficient tomography of a quantum many-body system
• Provably efficient machine learning for quantum many-body problems
• Efficient estimation of Pauli observables by derandomization
• Unsupervised machine learning and band topology
• Crossing a topological phase transition with a quantum computer
• Machine Learning ${\mathbb{Z}}_2$ Quantum Spin Liquids with Quasi-particle Statistics
• Classifying Snapshots of the Doped Hubbard Model with Machine Learning
• Unsupervised phase discovery with deep anomaly detection
• A classification of 3+1D bosonic topological orders (I): the case when point-like excitations are all bosons
• Probing scrambling using statistical correlations between randomized measurements
• Many-body topological invariants from randomized measurements
• Phase diagram of the toric code model in a parallel magnetic field
• Probing hidden spin order with interpretable machine learning
• A classification of 3+1D bosonic topological orders (II): the case when some point-like excitations are fermions
• Learning multiple order parameters with interpretable machines
• Finding hidden order in spin models with persistent homology
• Identification of hidden order and emergent constraints in frustrated magnets using tensorial kernel methods
• Persistent Homology of ${\mathbb{Z}}_2$ Gauge Theories

Cited by in corpus (6)

• Model-Independent Learning of Quantum Phases of Matter with Quantum Convolutional Neural Networks
• Mapping out phase diagrams with generative classifiers
• Human-machine collaboration: ordering mechanism of rank-2 spin liquid on breathing pyrochlore lattice
• Classifying topological neural network quantum states via diffusion maps
• Artificial intelligence for representing and characterizing quantum systems
• A Unsupervised Framework for Identifying Diverse Quantum Phase Transitions Using Classical Shadow Tomography