Session W17: Quantum Machine Learning II

Advances in Quantum Reinforcement Learning

Vedran Dunjko has made key advances in understanding how reinforcement learning can assist in quatnum computing and quantum error correction.   

Artificial Spiking Quantum Neural Networks

Within the realm of classical computing, the paradigm of artificial spiking neural networks has found a wide range of applications in settings where the temporal aspects of such networks are advantageous, such as in time-series prediction and signal analysis. In this talk, we will present a class of simple quantum spin-network models inspired by this classical paradigm, combining both an explicit neural network structure and explicit temporality through quantum evolution, and with the inherent ability to operate on quantum data as input. A set of neuron-like building blocks for such networks will be presented, and a network combining these objects into a structure capable of comparing pairs of Bell states will be proposed, a task with applications in quantum certification. Finally, a few comments on inherent properties related to the generation of entanglement and measurement back-action through these networks will be given.

The content of this talk is based on the arXiv-preprint 1907.06269   

A Path Towards Obtaining Quantum Advantage in Training Classical Deep Generative Models with Quantum Priors

A class of quantum-classical hybrid machine-learning algorithms can be obtained by integrating classical deep generative models with quantum probability distributions as 'priors' over their latent variables. We introduce a hybrid implementation of variational autoencoders (QVAE) and also present a technique to hybridize flow-based invertible generative models. We demonstrate the use of D-Wave quantum annealers as pysical simulators of quantum Boltzmann machines (QBM) to perform quantum-assisted training of QVAE. Latent-space QBM develop slowly mixing modes, opening a path to obtain quantum advantage in generative modeling with available quantum devices.   

Experimental demonstration of quantum-enhanced machine learning in NV center system

We demonstrate the quantum-enhanced supervised classication of vectors in an NV center system
using the algorithm of Lloyd, Mohseni and Rebentrost [arXiv:1307.0411 (2013)]. A ¹³C nuclear spin
is employed to encode the vectors with the spin-triplet state of the NV center as an ancilla. We design
efficient methods to prepare the initial electron-nuclear entangled state within the coherence time T_2^*
of the electron spin, and then compute the distance between the test vector and the center of each
class by measuring the level population through maximum likelihood estimation. Our experiment
allows more than one reference vectors in each class, thus forms an important enabling step toward
quantum-enhanced machine learning.   

Cost function embedding and dataset encoding for machine learning with parameterized quantum circuits

Machine learning is seen as a promising application of quantum computation. For near-term noisy intermediate-scale quantum (NISQ) devices, parametrized quantum circuits (PQCs) have been proposed as machine learning models due to their robustness and ease of implementation. However, the cost function is normally calculated classically from repeated measurement outcomes, such that it is no longer encoded in a quantum state. This prevents the value from being directly manipulated by a quantum computer for algorithms such as gradient estimation using the Hadamard Test. In this talk, we introduce a routine to embed a cost function for machine learning into a quantum circuit, which accepts a training dataset encoded in superposition or an easily preparable mixed state. We characterize the utility of such a routine using numerical simulations and introduce proof-of-principle experiments in an optimized superconducting qubit device.   

Physical-Layer Supervised Learning Assisted by an Entangled Sensor Network

Many existing quantum supervised learning (SL) schemes consider data given in a classical description. There, however, also exist a multitude of SL tasks whose data are acquired by sensors, e.g., pattern classification based on data produced by imaging sensors. Solving such SL tasks naturally requires an integrated approach harnessing tools from both quantum sensing and quantum computing. We introduce supervised learning assisted by an entangled sensor network (SLAEN) as a means to carry out SL tasks at the physical layer. The entanglement shared by the sensors in SLAEN boosts the performance of extracting global features of the object under investigation. We leverage SLAEN to construct an entanglement-assisted support-vector machine for data classification and entanglement-assisted principal component analyzer for data compression. In both schemes, variational circuits are employed to seek the optimum entangled probe states and measurement settings to maximize the entanglement-enabled enhancement. We observe that SLAEN enjoys an appreciable entanglement-enabled performance gain, even in the presence of loss, over conventional strategies in which classical data are acquired by separable sensors and subsequently processed by classical SL algorithms.   

Quantum-inspired nonlocal parallel tempering with approximate tensor network contractions

We use tensor networks to represent probability distribution of spin-glass models that are encoding combinatorial optimization problems. We then develop greedy approximation tensor contraction for efficient Gibbs sampling of the low energy states for structured quasi-2D spin-glass models. Our deterministic approach can reveal certain geometrical properties of such hard optimization problems known as “droplet excitations”. The knowledge of such droplets can be used to enhance traditional probabilistic Monte Carlo techniques. Specifically we provide two new cluster Monte Carlo techniques in which we combine tensor network contractions with “parallel tempering” (PT). In the first method the tensor networks provide certain high-quality initial states for PT instead of traditional random restarts. In the second method, the tensor network contraction provide droplet information that can be used for dynamical cluster updates unfreezing low-temperature replicas near a computational phase transition. We demonstrate several orders of magnitude improvement in time-to-solutions in comparison to local Monte Carlo techniques such as PT. We also observe significant improvement over commercial solvers, such as Gurobi, or other heuristic cluster PT approaches powered by iso-energetic moves.   

Generative quantum models over tensor network architectures

Generative models are able to produce new data according to an underlying probability distribution that they learn from a given data set. Inspired by the probabilistic nature of quantum mechanics, we employ a generative model, known as the "Born machine". which uses quantum state representation and learns the joint probabilities over such quantum degrees of freedom. To represent the quantum states we train tensor network architectures that could provide efficient expressivity, training, and sampling when the quantum probability distribution has some local structure. Specifically, we train two types of tensor networks known as matrix product states (MPS) and tree tensor network (TTN) over both classical and quantum data. We first show that our TTN model can generate the MNIST handwritten digits efficiently. In the next step, we variationally train tensor network models to generate desired quantum entanglement produced by shallow quantum circuits given iterative input-output information from actual quantum hardware with typically unknown systematic and random errors.   

RNN-VQE: a machine learning approach to generating variational ansatze

The variational quantum eigensolver (VQE) is a leading near-term hybrid classical/quantum algorithm for calculating spectra of molecular Hamiltonians. As with any variational approach, its performance depends sensitively on the selection of an appropriate variational form. Recent work has detailed the effectiveness of ADAPT-VQE, an adaptive approach to VQE in which the variational form is grown iteratively, resulting in ansatze which yield high performance with minimal numbers of variational parameters. This approach, however, is quantum resource intensive, requiring many quantum circuit executions and state measurements to grow the ansatze. Here we present RNN-VQE, a machine learning model which uses recurrent neural networks to learn and quickly generate effective variational ansatze for VQE.   

Measuring Correlation Scaling in Images via Logistic Regression

It is well known in quantum many-body physics that local Hamiltonians often have ground states whose entanglement entropies scale with the boundary of the bipartition (known as an "area law"), allowing them to be characterized efficiently using tensor networks. Given recent interest in using tensor network models for machine learning, we explore whether correlations in classical image data may possess analogous scaling behavior in the mutual information (MI) between bipartitions of the pixels. Building on techniques developed in the context of generative machine learning, we recast the MI estimation problem as logistic regression on samples drawn from the joint and marginal distributions of the image partitions. We test the accuracy of our model using Gaussian Markov random fields designed to have analytic boundary law and volume law scaling patterns, and perform regression on the well-known MNIST and CIFAR image datasets to evaluate the MI scaling in real-world images. We find that our model can capture the scaling behavior of the Markov random fields even with hundreds of pixels, while the large MI values found in CIFAR and MNIST remain challenging to reproduce.   

Quantum neural network for generating quantum states

Quantum machine learning has become a research focus in quantum computation nowadays. One direction of quantum machine learning is developing quantum neural network based on parametrized quantum circuits. However, previous works of quantum neural network based on parameterized quantum circuits provide few systemic and general ways to introduce non-linear activation function. In the meantime, non-linear activation function is one of the most important parts in classical neural network as it makes the multi-layer neural network not work as a single layer. In this work, we give a new contruction of quantum neural network to introduce non-linear activation functions. To demonstrate the new approach, we present results of using the quantum neural network to generate ground states as well as excited states for different quantum chemistry systems. The generated states approximate exact states closely, which not only show the potential of the new construction of quantum neural network, but also may be a new approach to solve quantum chemistry problems.   

Gauge Enhanced Quantum Criticality and Time Reversal Domain Wall: SU(2) Yang-Mills Dynamics with Topological Terms

We study the low energy dynamics of the four siblings of Lorentz symmetry enriched SU(2) Yang-Mills theory with a theta term at θ = π. Since there exists a mixed anomaly between time reversal symmetry and the center symmetry, the low energy dynamics must be nontrivial. We focus on two possible scenarios: 1) time reversal symmetry is spontaneously broken by the two confining vacua, and 2) the low energy theory describes a U(1) spin liquid which is deconfined and gapless while preserving time reversal symmetry. In the first scenario, we first identify the global symmetry on the time reversal domain wall, where time reversal symmetry in the bulk induces a Z2 unitary symmetry on the domain wall. We explore how the Lorentz symmetry and the unitary Z2 symmetry enriches the domain wall theory. In the second scenario, we relate the symmetry enrichments of the SU(2) Yang-Mills to that of the U(1) spin liquids. This further opens up the possibility that SU(2) QCD with large and odd flavors of fermions could be a second order phase transition between two phases of U(1) spin liquids as well as between a U(1) spin liquid and the a trivial paramagnet, where the gauge symmetry is enhanced to be non-Abelian at and only at the transition. We name them as Gauge Enhanced Quantum Critical Points.   

Robust Decomposition of Quantum States

We show that quantum states over multiple subsystems can be recursively decomposed into states on one fewer subsystem and quantum operations that extend the state onto the omitted subsystem. This decomposition is robust in the sense that dephasing errors on subsystems between operations do not alter the marginal state on error-free subsystems. By restricting the form of these operations to a truncated cluster expansion, their classical simulation cost is reduced to the cost of simulating the maximal clusters. Such simulations provide direct access to independent statistical samples of observables and systematically improvable lower bounds on the von Neumann entropy, which together enable variational free energy minimization.