Bulletin of the American Physical Society
APS March Meeting 2021
Volume 66, Number 1
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session S32: Quantum Machine Learning IFocus Live
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Sponsoring Units: DQI GDS Chair: Pierre-Luc Dallaire-Demers, Zapata Computing Inc |
Thursday, March 18, 2021 11:30AM - 11:42AM Live |
S32.00001: The power of quantum neural networks Amira Abbas, David Sutter, Christa Zoufal, Aurelien Lucchi, Alessio Figalli, Stefan Woerner Fault-tolerant quantum computers offer the promise of dramatically improving machine learning. In the near-term, however, the benefits of quantum machine learning are not so clear. Expressibility and trainability of quantum models–and quantum neural networks in particular–require further investigation. In this work, we use tools from information geometry to define a notion of expressibility for quantum and classical models. The effective dimension, which depends on the Fisher information, is used to prove a novel generalisation bound and establish a robust measure of expressibility. We show that quantum neural networks achieve a better effective dimension than classical neural networks. To understand the trainability of quantum models, we connect the Fisher information to barren plateaus, the problem of vanishing gradients. Importantly, quantum neural networks can show resilience to this phenomenon and train faster than classical models due to their favourable optimisation landscapes, captured by a more evenly spread Fisher information spectrum. Our work is the first to demonstrate that well-designed quantum neural networks offer an advantage over classical neural networks through a higher effective dimension and faster training ability, which we verify on real quantum hardware. |
Thursday, March 18, 2021 11:42AM - 11:54AM Live |
S32.00002: Variational Quantum Boltzmann Machines Christa Zoufal, Aurélien Lucchi, Stefan Woerner
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Thursday, March 18, 2021 11:54AM - 12:06PM Live |
S32.00003: Data re-uploading for a universal quantum classifier Adrián Pérez-Salinas, Alba Cervera-Lierta, Elies Gil-Fuster, José I. Latorre A single qubit provides sufficient computational capabilities to construct a universal quantum classifier when assisted with a classical subroutine. This fact may be surprising since a single qubit only offers a simple superposition of two states and single-qubit gates only make a rotation in the Bloch sphere. The key ingredient to circumvent these limitations is to allow for multiple data re-uploading. A quantum circuit can then be organized as a series of data re-uploading and single-qubit processing units. Furthermore, both data re-uploading and measurements can accommodate multiple dimensions in the input and several categories in the output, to conform to a universal quantum classifier. The extension of this idea to several qubits enhances the efficiency of the strategy as entanglement expands the superpositions carried along with the classification. Extensive benchmarking on different examples of the single- and multi-qubit quantum classifier validates its ability to describe and classify complex data. |
Thursday, March 18, 2021 12:06PM - 12:18PM Live |
S32.00004: Learnability and Complexity of Quantum Sample Murphy Yuezhen Niu, Andrew Dai, Li Li, Vadim Smelyanskiy, Hartmut Neven, Sergio Boixo Given a quantum circuit, a quantum computer can sample the output distribution exponentially faster in the number of bits than classical computers. A similar exponential separation has yet to be established in generative models through quantum sample learning: given samples from an n-qubit computation, can we learn the underlying quantum distribution using models with training parameters that scale polynomial in n under a fixed training time? We study four kinds of generative models: Deep Boltzmann machine, Generative Adversarial Networks (GANs), Long Short-Term Memory (LSTM) and Autoregressive GAN, on learning quantum data set generated by deep random circuits. We demonstrate the autoregressive structure present in the underlying quantum distribution from random quantum circuits. Both numerical experiments and a theoretical proof in the case of the DBM show exponentially growing complexity of learning-agent parameters required for achieving a fixed accuracy as n increases. Finally, we establish a connection between learnability and the complexity of generative models by benchmarking learnability against different sets of samples drawn from probability distributions of variable degrees of complexities in their quantum and classical representations. |
Thursday, March 18, 2021 12:18PM - 12:30PM Not Participating |
S32.00005: Operational Natural Gradients For Variational Quantum Algorithms Nathan McMahon One of the obvious uses for a quantum computer is as a co-processor for a quantum machine learning problems. Combining this with traditional optimisation and machine learning techniques would give an efficient process to approximate the ground state of a given Hamiltonian. |
Thursday, March 18, 2021 12:30PM - 12:42PM Live |
S32.00006: Generation of High Resolution Handwritten Digits with Samples from a Quantum Device Manuel S. Rudolph, Ntwali Toussaint Bashige, Amara Katabarwa, Borja Peropadre, Alejandro Perdomo-Ortiz We present the first practical and experimental implementation of a quantum-classical generative algorithm capable of generating high-resolution images of handwritten digits with quantum samples from an ion-trap quantum device. In our scheme, we take advantage of a recently proposed quantum generative framework known as the Quantum Circuit Born Machine (QCBM) to model and sample the prior distribution of an Associative Adversarial Network; the latter being an extension of the widely-used Generative Adversarial Networks (GANs). To maximize the potential of this algorithm on NISQ devices, we propose a novel technique that leverages on the unique quantum possibilities of measuring in bases other than the computational basis, enhancing the expressibility of the prior distribution of our quantum-classical approach. A fully-connected classical neural network layer is trained to extract maximal information of the measurements unlocked by the basis-enhanced QCBM model. We present experimental realization of a full training on an ion-trap device and use the algorithm to generate high-quality images and quantitatively outperform comparable classical GANs trained on the MNIST data set for handwritten digits. |
Thursday, March 18, 2021 12:42PM - 1:18PM Live |
S32.00007: Tensor-Flow Quantum: An open source software framework for hybrid quantum-classical machine learning Invited Speaker: Masoud Mohseni We provide an overview of our progress on quantum-assisted and quantum-inspired algorithms for machine learning at Quantum AI Lab at Google. We present several new techniques for quantum circuit learning on Noisy Intermediate-Scale Quantum (NISQ) processors. In particular, we introduce TensorFlow Quantum (TFQ), an open source library for the rapid prototyping of hybrid quantum-classical models for classical or quantum data. This framework offers high-level abstractions for the design and training of both discriminative and generative quantum models under TensorFlow and Cirq, and supports high-performance quantum circuit simulators such as qsim. We provide an overview of the software architecture and building blocks through several examples. We illustrate TFQ functionalities via several basic applications including supervised learning for quantum state classification, quantum control, and quantum approximate optimization. Moreover, we demonstrate how one can apply TFQ to tackle advanced quantum learning tasks including meta-learning and layerwise learning. Specifically, we show how to train varying subsets of the quantum circuit's parameters iteratively while increasing the circuit depth to have sufficient representation of classical or quantum data. |
Thursday, March 18, 2021 1:18PM - 1:30PM Live |
S32.00008: Barren Plateaus in Quantum Neural Networks Marco Cerezo de la Roca, Akira Sone, Kunal Sharma, Tyler Volkoff, Lukasz Cincio, Patrick Coles Variational quantum-classical algorithms (VQCAs), and more generally Quantum Neural Networks (QNNs), optimize the parameters of a gate sequence, V, to minimize a cost function, C. It is believed that VQCAs and QNNs will enable the first practical applications of noisy quantum computers. Recently it has been shown that the cost training landscape can exhibit the so-called barren-plateau phenomena, where the gradients of C vanish exponentially with the system size and makes the architectures non-scalable. In this talk we first discuss the importance of performing rigorous scaling analysis on the trainability of VQAs and QNNs, and we argue that such study should be a stable for the community. We then review recent results where we analyze the trainability of two types of QNNs, the first is a parametrized quantum circuit commonly known as a layered hardware efficient ansatz, and the second is a dissipative perceptron-based QNN. For both of these we provide conditions under which the parameter trainability can be guaranteed, and we connect the notion of locality of the cost with its trainability. |
Thursday, March 18, 2021 1:30PM - 1:42PM Live |
S32.00009: Power of data in quantum machine learning Hsin-Yuan Huang, Michael Broughton, Masoud Mohseni, Ryan Babbush, Jarrod McClean The use of quantum computing in machine learning has been an exciting prospect. At the crux of excitement is the potential for quantum computers to perform some computations exponentially faster than their classical counterparts. However, a machine learning task, where some data is provided, is different from a computational task. In this work, we show that some problems that are classically hard to compute can, in fact, be predicted easily with classical machines that learn from data. Using rigorous prediction error bounds as a foundation, we develop a methodology for assessing the potential for quantum advantage in learning tasks. We show rigorously how existing quantum models can result in significantly inferior prediction performance compared to classical models, even for datasets generated by quantum evolution. To circumvent the setbacks, we propose an improvement by projecting quantum states to classical space. The projected quantum model provides a simple and rigorous quantum speed-up in the fault-tolerant regime. For more near-term quantum models, the projected versions demonstrate large prediction advantages over standard classical models on engineered data sets in one of the largest numerical tests for gate-based quantum machine learning to date, up to 30 qubits. |
Thursday, March 18, 2021 1:42PM - 1:54PM Live |
S32.00010: Quantum Machine Learning with Quantum-Probabilistic Generative Models Antonio Javier Martinez, Geoffrey Roeder, Guillaume Verdon-Akzam In this work we explore the task of generatively modelling mixed quantum states using hybridizations of classical probabilistic machine learning models and quantum neural networks (QNNs). More specifically, we explore applications of these models to the tasks of either learning to replicate a mixed quantum state from a collection of measurements outcomes for a set of local observables or direct coherent quantum-access to copies of the quantum state. We focus on a particular class of quantum-probabilistic models called quantum Hamiltonian-based models, which are a composition of a classical energy-based model (EBM) with a parameterized unitary QNN. We show how one can tractably sample from this class of hybrid model via classical MCMC sampling and conditional sampling through a QNN running on a quantum computer. Furthermore, we derive analytic expressions for unbiased estimators of both the gradients of the quantum relative entropy and the Quantum Fisher information metric for the full hybrid model. We demonstrate how this enables scalable training of such models via global natural gradient descent. Finally, we discuss implementation of sampling and training algorithms for such models via a combination of TensorFlow Probability and TensorFlow Quantum. |
Thursday, March 18, 2021 1:54PM - 2:06PM Live |
S32.00011: A divide-and-conquer algorithm for quantum state preparation Israel F. Araujo, Kyungdeock Daniel Park, Francesco Petruccione, Adenilton J. da Silva Advantages in several fields of research and industry are expected with the rise of quantum computers. However, the computational cost to load classical data in quantum computers can impose restrictions on possible quantum speedups. Known algorithms to create arbitrary quantum states require quantum circuits with depth O(N) to load an N-dimensional vector. Here, we show that it is possible to load an N-dimensional vector with exponential time advantage using a quantum circuit with polylogarithmic depth and entangled information in ancillary qubits. Results show that we can efficiently load data in quantum devices using a divide-and-conquer strategy to exchange computational time for space. We demonstrate a proof of concept on a quantum device and present two applications for quantum machine learning. We expect that this loading strategy allows the quantum speedup of tasks that require to load a significant volume of information to quantum devices. |
Thursday, March 18, 2021 2:06PM - 2:18PM Live |
S32.00012: Enhancing Combinatorial Optimization with Quantum Generative Models Francisco Fernandez Alcazar, Alejandro Perdomo Combinatorial optimization is one of the key candidates in the race for practical quantum advantage. In this work we introduce a new family of quantum-enhanced optimizers and demonstrate how quantum machine learning models, knows as quantum generative models, can enhance the performance over results based only on state-of-the-art classical solvers. We present two new quantum-enhanced optimization strategies. The first scheme works as a stand-alone solver and we show here its superior performance when the goal is to find the best minimum within the least number of cost function evaluations. We compare our results with Bayesian optimizers which are known to be one of the best competing solvers in such tasks. The second optimization strategy corresponds to a quantum-classical scheme which leverages on data points evaluated during the optimization search from any quantum or classical optimizer. We show how our quantum-assisted generative model boosts the performance of a classical solver in hard-to-solve instances where the classical solver is not capable of making progress as a stand-alone solution. To illustrate our findings, we benchmark our quantum-enhanced optimization strategies in portfolio optimization problems by constructing instances from the S&P 500 stock market index. |
Thursday, March 18, 2021 2:18PM - 2:30PM Live |
S32.00013: Adversarial Robustness of Quantum Machine Learning Models Haoran Liao, Ian Convy, William Huggins, Birgitta K Whaley State-of-the-art classical neural networks are observed to be vulnerable to small crafted adversarial perturbations. A more severe vulnerability has been noted for QML models classifying Haar-random pure states. This stems from the concentration of measure phenomenon, a property of the metric space when sampled probabilistically, and is independent of the classification protocol. In this paper, we focus on the adversarial robustness in classifying a subset of encoded states that are smoothly generated from a Gaussian latent space. We show that the vulnerability of this task is considerably weaker than that of classifying Haar-random pure states. Our analysis provides insights into the adversarial robustness of any quantum classifier in real-world classification tasks. In particular, we find only mildly polynomially decreasing potential robustness in the number of qubits, in contrast to the exponentially decreasing robustness when classifying Haar-random pure states. |
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