Session E27: Quantum Machine Learning I

Improved Training of Quantum Boltzmann Machines

Quantum Boltzmann machines (QBMs) are a natural quantum generalization of restricted Boltzmann machines (RBMs) that, at least under numerical simulation, perform better than their classical counterparts in learning generic data distributions. However, training QBMs using gradient-based methods requires sampling observables in quantum thermal distributions, a problem that generically is NP-hard. In this work, we find that the locality of the gradient observables that must be sampled gives rise to an efficient sampling method based on the Eigenstate Thermalization Hypothesis (ETH), and thus an efficient method for training QBMs on quantum devices. Furthermore, we demonstrate a hybrid gradient-based/black box optimization procedure that outperforms strictly gradient-based training methods.   

Measurement-based adaptation protocol with quantum reinforcement learning

Machine learning employs dynamical algorithms that mimic the human capacity to learn, where the reinforcement learning ones are among the most similar to humans in this respect. On the other hand, adaptability is an essential aspect to perform any task efficiently in a changing environment, and it is fundamental for many purposes, such as natural selection. Here, we propose an algorithm based on successive measurements to adapt one quantum state to a reference unknown state, in the sense of achieving maximum overlap. The protocol naturally provides many identical copies of the reference state, such that in each measurement iteration more information about it is obtained. In our protocol, we consider a system composed of three parts, the "environment" system, which provides the reference state copies; the register, which is an auxiliary subsystem that interacts with the environment to acquire information from it; and the agent, which corresponds to the quantum state that is adapted by digital feedback with input corresponding to the outcome of the measurements on the register. F. Albarrán-Arriagada, J. C. Retamal, E. Solano, and L. Lamata, Phys. Rev. A 98, 042315 (2018).   

Improving training of Boltzmann machines with error corrected quantum annealing

Boltzmann machines, a class of machine learning models, are the basis of several deep learning methods that have been successfully applied to both supervised and unsupervised machine learning tasks. Quantum annealing may help lead to future advances in the development of these learning algorithms, but its usefulness is determined in part by the effective temperature. We have applied nested quantum annealing correction (NQAC) to do unsupervised learning with a small bars and stripes (BAS) dataset, and to a coarse-grained MNIST dataset, which consists of black-and-white images of hand-written integers, to do supervised learning. For both datasets, we demonstrate an effective temperature reduction with NQAC that leads to an increase in learning performance. We also find better performance overall with longer annealing times and offer some interpretation of the results based on comparison to simulated quantum annealing (SQA) simulations.   

Opportunities and Challenges in Quantum-Assisted Machine Learning

With quantum computing technologies nearing the era of commercialization and quantum advantage, machine learning (ML) has been proposed as one of the promising ``killer" applications. Despite significant effort, there has been a disconnect between most quantum ML proposals, the needs of ML practitioners, and the capabilities of near-term quantum devices towards a conclusive demonstration of a meaningful quantum advantage in the near future. In this talk, we provide concrete examples of intractable ML tasks that could be enhanced with near-term devices. We argue that to reach this target, the focus should be on areas where ML researchers are struggling, such as generative models in unsupervised and semi-supervised learning, instead of the popular and more tractable supervised learning tasks. We focus on hybrid quantum-classical approaches and illustrate some of the key challenges we foresee for near-term implementations.   

Quantum generative adversarial learning in a superconducting quantum circuit

Generative adversarial learning is one of the most exciting recent breakthroughs in machine learning---a subfield of artificial intelligence that is currently driving a revolution in many aspects of modern society. It has shown splendid performance in a variety of challenging tasks such as image and video generations. More recently, a quantum version of generative adversarial learning has been theoretically proposed and shown to possess the potential of exhibiting an exponential advantage over its classical counterpart. Here, we report the first proof-of-principle experimental demonstration of quantum generative adversarial learning in a superconducting quantum circuit. We demonstrate that, after several rounds of adversarial learning, a quantum state generator can be trained to replicate the statistics of the quantum data output from a digital qubit channel simulator, with a high fidelity (98.8% on average) that the discriminator cannot distinguish between the true and the generated data. Our results pave the way for experimentally exploring the intriguing long-sought-after quantum advantages in machine learning tasks with noisy intermediate-scale quantum devices.   

Noncommutative Boltzmann Machines

Building on the 2018 paper on quantum Boltzmann Machines (qBM) by Amin et al [1], the concept of noncommutative Boltzmann Machines (ncBM) is introduced. ncBM contain qBM as a subset, but can be viewed, for example, as machine learning with superoperators. In particular, we study ncBM with the Liouvillian superoperator, and show the negative phase of machine learning becomes easy to calculate in a particular limit. Both Bernoulli data sets [1] and quantum dragon datasets [2] are utilized for both generative and discriminative learning. Possibilities of using near-term adiabatic quantum annealing machines for ncBM will be discussed.

[1] M.H. Amin, E. Andriyash, J. Rolfe, B. Kulchytskyy, and R. Melko, Quantum Boltzmann Machine, Phys. Rev. X 8, 021050 (2018).
[2] M.A. Novotny, Energy-Independent Total Quantum Transmission of Electrons through Nanodevices with Correlated Disorder, Phys. Rev. B 90, 165103 (2014).   

Hybrid quantum-classical schemes for generative adversarial learning: HQGANs

Quantum computing and machine learning are two fast-growing research areas. Recently, these two areas have been merged into the field of quantum machine learning (QML), seeking to find ways in which quantum computers can offer advantages at solving machine learning problems over classical computers. Here, we propose to use quantum computers to learn models that mimic observed data distributions, a type of task known as generative learning, by substituting neural networks with variational quantum circuits in the generative adversarial networks (GANs) framework. GANs are statistical models that learn to sample from an observed data distribution by looking at individual samples. They consist of two neural networks, known as the discriminator and the generator, competing against each other in a minimax game. We propose a hybrid-quantum classical scheme that trains two variational quantum circuits, playing the role of discriminator and generator, to perform the same task on classical data. The proposed hybrid quantum GANs (HQGANs) might benefit machine learning by improving the ability to model more complex data distributions and could offer a new niche of applications for near-term quantum computers.   

Variational circuits for machine learning with near-term devices

Variational circuits are parameter-dependent quantum algorithms that can be optimized for a certain task. One approach in quantum machine learning is to interpret these circuits as machine learning models that can be trained to generalise from data. Such models are often refered to as variational quantum classifiers. This talk will focus on various issues around this approach, for example how to think about the power of variational quantum classifiers, how we can train them and what they might be good for.   

Quantum Manifold Learning Algorithms for Dimensionality Reduction

Manifold learning is a kind of method which discusses the machine learning problems under the manifold hypothesis. It assumes that the sampled high-dimensional data actually comes from the embedding of some low-dimensional manifold structure. Manifold learning has wide range of applications in dimensionality reduction and data visualization. In the field of manifold learning, two most representative and commonly used algorithms are isometric mapping and locally linear embedding. Using techniques of quantum computing, we research out two quantum algorithms in correspondence to them. Compared with corresponding classical algorithms, the two quantum algorithms proposed in this paper can be implemented on a quantum computer with quantum speed-up. Quantum isometric mapping provides at least quadratic acceleration and quantum locally linear embedding takes logarithmic resources. In addition, we attempt to find out a common process to deal with quantization of manifold learning algorithms.   

Differentiable Quantum Circuits and Generative Modeling

We present a fresh approach to quantum machine learning by using quantum circuits as probabilistic generative models. The proposed QCBM overcomes the challenging problem in training implicit density models with discrete outputs in deep learning. The key component of our gradient-based learning algorithm is to measure the gradient of the two sample test loss function on a quantum computer unbiasedly and efficiently. With the inspiration of matrix product state, we are able to train a Born machine to generate intermediate-scale images with number of qubits much less than pixel numbers.
We demostrate the generative power of these learning schemes with our new Julia quantum circuit simulator Yao.jl [1]. With Yao.jl, one can simulate quantum machine learning models, quantum optimization algorithms and quantum chemistry problems efficiently and easily. We combined our framework with state of art machine learning framework like Zygote.jl, aimming for quantum software 2.0: "Automatic Differentiable Quantum Circuits".
[1] https://github.com/QuantumBFS/Yao.jl   

Machine-learned QCVV for distinguishing single-qubit noise

We investigate the use of machine learning (ML) algorithms for developing new QCVV protocols. ML algorithms learn approximations to functions that relate experimental data to some property of interest. As an example, we show ML algorithms can successfully learn separating surfaces for distinguishing coherent and stochastic noise affecting a single qubit. The performance of various ML algorithms depends strongly on the geometry of experimental data (in this case, data from gate set tomography experiments). We show performance can be boosted by hyperparameter tuning and feature engineering.   

Quantum optical neural networks for next generation quantum information processing

Physically motivated quantum algorithms for specific near-term quantum hardware will likely be the next frontier in quantum information science. Here, we show how many of the features of neural networks for machine learning can naturally be mapped into the quantum optical domain by introducing the quantum optical neural network (QONN). Through numerical simulation and analysis we train the QONN to perform a range of quantum information processing tasks, including protocols for quantum optical state compression, reinforcement learning, and black-box quantum simulation. Our results indicate QONNs are a powerful design tool for quantum optical systems and a promising architecture for next generation quantum processors.