Deep Learning Quantum States for Hamiltonian Estimation

Human experts cannot efficiently access physical information of a quantum many-body states by simply "reading"its coefficients, but have to reply on the previous knowledge such as order parameters and quantum measurements.We demonstrate that convolutional neural network(CNN) can learn from coefficients of many-body states or reduced density matrices to estimate the physical parameters of the interacting Hamiltonians, such as coupling strengths and magnetic fields, provided the states as the ground states. We propose QubismNet that consists of two main parts: the Qubism map that visualizes the ground states(or the purified reduced density matrices) as images, and a CNN that maps the images to the target physical parameters. By assuming certain constraints on the training set for the sake of balance, QubismNet exhibits impressive powers of learning and generalization on several quantum spin models. While the training samples are restricted to the states from certain ranges of the parameters, QubismNet can accurately estimate the parameters of the states beyond such training regions. For instance, our results show that QubismNet can estimate the magnetic fields near the critical point by learning from the states away from the critical vicinity. Our work provides a data-driven way to infer the Hamiltonians that give the designed ground states, and therefore would benefit the existing and future generations of quantum technologies such as Hamiltonian-based quantum simulations and state tomography.

Unsupervised Recognition of Informative Features via Tensor Network Machine Learning and Quantum Entanglement Variations

Given an image of a white shoe drawn on a blackboard,how are the white pixels deemed(say by human minds)to be informative for recognizing the shoe without any labeling information on the pixels?Here we investigate such a“white shoe”recognition problem from the perspective of tensor network(TN)machine learning and quantum entanglement.Utilizing a generative TN that captures the probability distribution of the features as quantum amplitudes,we propose an unsupervised recognition scheme of informative features with variations of entanglement entropy(EE)caused by designed measurements.In this way,a given sample,where the values of its features are statistically meaningless,is mapped to the variations of EE that statistically characterize the gain of information.We show that the EE variations identify the features that are critical to recognize this specific sample,and the EE itself reveals the information distribution of the probabilities represented by the TN model.The signs of the variations further reveal the entanglement structures among the features.We test the validity of our scheme on a toy dataset of strip images,the MNIST dataset of hand-drawn digits,the fashion-MNIST dataset of the pictures of fashion articles,and the images of nerve cord.Our scheme opens the avenue to the quantum-inspired and interpreted unsupervised learning,which can be applied to,e.g.,image segmentation and object detection.

Experimental realization of a quantum image classifier via tensor-network-based machine learning

Quantum machine learning aspires to overcome intractability that currently limits its applicability to practical applications.However,quantum machine learning itself is limited by low effective dimensions achievable in stateof-the-art experiments.Here,we demonstrate highly successful classifications of real-life images using photonic qubits,combining a quantum tensor-network representation of hand-written digits and entanglement-based optimization.Specifically,we focus on binary classification for hand-written zeroes and ones,whose features are cast into the tensor-network representation,further reduced by optimization based on entanglement entropy and encoded into two-qubit photonic states.We then demonstrate image classification with a high success rate exceeding 98%,through successive gate operations and projective measurements.Although we work with photons,our approach is amenable to other physical realizations such as nitrogen-vacancy centers,nuclear spins,and trapped ions,and our scheme can be scaled to efficient multi-qubit encodings of features in the tensor-product representation,thereby setting the stage for quantum-enhanced multi-class classification.

Thermodynamics of spin-1/2 Kagomé Heisenberg antiferromagnet:algebraic paramagnetic liquid and finite-temperature phase diagram

Quantum fluctuations from frustration can trigger quantum spin liquids(QSLs) at zero temperature.However, it is unclear how thermal fluctuations affect a QSL. We employ state-of-the-art tensor network-based methods to explore the ground state and thermodynamic properties of the spin-1=2 kagomé Heisenberg antiferromagnet(KHA). Its ground state is shown to be consistent with a gapless QSL by observing the absence of zero-magnetization plateau as well as the algebraic behaviors of susceptibility and specific heat at low temperatures, respectively. We show that there exists an algebraic paramagnetic liquid(APL) that possesses both the paramagnetic properties and the algebraic behaviors inherited from the QSL. The APL is induced under the interplay between quantum fluctuations from geometrical frustration and thermal fluctuations. By studying the temperature-dependent behaviors of specific heat and magnetic susceptibility, a finite-temperature phase diagram in a magnetic field is suggested, where various phases are identified. This present study gains useful insight into the thermodynamic properties of the spin-1/2 KHA with or without a magnetic field and is helpful for relevant experimental studies.