# Machine Learning for Quantum Design

Conference Date:
Monday, July 8, 2019 (All day) to Friday, July 12, 2019 (All day)
Scientific Areas:
Condensed Matter
Quantum Information

Machine learning techniques are rapidly being adopted into the field of quantum many-body physics, including condensed matter theory, experiment, and quantum information science.  The steady increase in data being produced by highly-controlled quantum experiments brings the potential of machine learning algorithms to the forefront of scientific advancement.  Particularly exciting is the prospect of using machine learning for the discovery and design of quantum materials, devices, and computers.  In order to make progress, the field must address a number of fundamental questions related to the challenges of studying many-body quantum mechanics using classical computing algorithms and hardware.

The goal of this conference is to bring together experts in computational physics, machine learning, and quantum information, to make headway on a number of related topics, including:

• Data-drive quantum state reconstruction
• Machine learning strategies for quantum error correction
• Neural-network based wavefunctions
• Near-term prospects for data from quantum devices
• Machine learning for quantum algorithm discovery

To register for this event, please fill out this form.

Sponsorship for this event has been provided by:

• Marin Bukov, University of California, Berkeley
• Giuseppe Carleo, Flatiron Institute
• Michele Ceriotti, École polytechnique fédérale de Lausanne
• Eun-Ah Kim, Cornell University
• Sebastiano Pilati, University of Camerino
• Pooya Ronagh, University of Waterloo
• Maria Schuld, University of KwaZulu-Natal
• Kristan Temme, California Institute of Technology
• Evert van Nieuwenburg, California Institute of Technology
• Lei Wang, Chinese Academy of Sciences
• Peter Wittek, University of Toronto
• Yi-Zhuang You, University of California, San Diego
• Riccardo Zecchina, Bocconi University
• Andrea Zen, Thomas Young Centre and London Centre for Nanotechnology
• Nour Abura'ed, University of Dubai
• Michael Albergo, Perimeter Institute
• Juan Atalaya, University of California, Berkeley
• Tanisha Bassan, The Knowledge Society
• Matthew Beach, Perimeter Institute
• Aleksandr Berezutskii, Skolkovo Institute of Science and Technology
• Yael Birenbaum, National Research Council Canada
• Kristine Boone, University of Waterloo
• Peter Cha, Cornell University
• Wissam Chemissany, California Institute of Technology
• Ian Convy, University of California, Berkeley
• Emily Davis, Stanford University
• Isaac De Vlugt, University of Waterloo
• Nicolo Defenu, Heidelberg University
• Dong-Ling Deng, Tsinghua University
• Olivia Di Matteo, TRIUMF
• Nicholas Duchene, Polytechnique Montréal
• Marcus Edwards, University of Waterloo
• Timo Felser, University of Padova & Univerity of Saarland
• Martin Ganahl, Perimeter Institute
• Chloe-Aminata Gauvin-Ndiaye, University of Sherbrooke
• Anna Golubeva, Perimeter Institute
• Eliska Greplova, ETH Zurich
• Jan Friedrich Haase, Institute for Quantum Computing
• Lauren Hayward Sierens, Perimeter Institute
• Florian Hopfmueller, Perimeter Institute
• Timothy Hsieh, Perimeter Institute
• Hong-Ye Hu, University of California, San Diego
• Emilie Huffman, Perimeter Institute
• Shih-Chun (Jimmy) Hung, Institute for Quantum Computing
• Katharine Hyatt, Flatiron Institute
• Pavithran Iyer, University of Waterloo
• Aditya Jain, Institute for Quantum Computing
• Angus Kan, Institute for Quantum Computing
• Achim Kempf, Perimeter Institute & University of Waterloo
• Faisal Khan, Khalifa University
• Ehsan Khatami, San Jose State University
• Mohammad Kohandel, University of Waterloo
• Xiangzhou Kong, University of Waterloo
• Emine Kucukbenli, SISSA
• Bohdan Kulchytskyy, Perimeter Institute & University of Waterloo
• Samuel Lederer, Cornell University
• Marco Letizia, University of Waterloo and Perimeter Institute
• Haoran Liao, University of California, Berkeley
• JinGuo Liu, Chinese Academy of Sciences
• Junwei Liu, Hong Kong Univversity
• Yehua Liu, University of Sherbrooke
• Irene Lopez Gutierrez, Dresden University of Technology
• Ilia Luchnikov, Moscow Institute of Physics and Technology
• Xiuzhe Luo, University of Waterloo
• Hao Ma, 1QB Information Technologies
• Benjamin MacLellan, INRS
• Glen Bigan Mbeng, SISSA
• Kai Meinerz, University of Cologne
• Andre Melo, Delft University of Technology
• Ejaaz Merali, University of Waterloo
• Friederike Metz, Okinawa Institute of Science and Technology
• Christine Muschik, Perimeter Institute & University of Waterloo
• Reza Nourafkan, University of Sherbrooke
• Etude O'Neel-Judy, University of Waterloo
• Jonathon Riddell, McMaster University
• Shengru Ren, 1QB Information Technologies
• Piotr Roztocki, INRS-EMT
• Kevin Ryczko, University of Ottawa
• Hossein Sadeghi, D-Wave Systems Inc.
• Artur Scherer, 1QB Information Technologies
• Dan Sehayek, University of Waterloo
• Miles Stoudenmire, Flatiron Institute
• Isaac Tamblyn, National Research Council Canada
• Alain Tchagang, National Research Council Canada
• Hugo Theveniaut, CNRS
• Evan Thomas, University of Ottawa
• Brian Timar, California Institute of Technology
• Giacomo Torlai, Flatiron Institute
• Simon Verret, University of Montreal
• Stephen Vintskevich, Moscow Institute of Physics and Technology
• Yan Wang, University of Sherbrooke
• Yi Zhang, Peking University

Speaker Talks

Giuseppe Carleo, Flatiron Institute

Deep learning for quantum many-body physics or: Toolmaking beyond the papyrus complexity

In this talk I will discuss some of the long-term challenges emerging with the effort of making deep learning a relevant tool for controlled scientific discovery in many-body quantum physics.   The current state of the art of deep neural quantum states and learning tools will be discussed in connection with open challenging problems in condensed matter physics, including frustrated magnetism and quantum dynamics.

Optimizing Quantum Optimization

Variational algorithms for a gate-based quantum computer, like the QAOA, prescribe a fixed circuit ansatz --- up to a set of continuous parameters --- that is designed to find a low-energy state of a given target Hamiltonian. After reviewing the relevant aspects of the QAOA, I will describe attempts to make the algorithm more efficient. The strategies I will explore are 1) tuning the variational objective function away from the energy expectation value, 2) analytical estimates that allow elimination of some of the gates in the QAOA circuit, and 3) using methods of machine learning to search the design space of nearby circuits for improvements to the original ansatz. While there is evidence of room for improvement in the circuit ansatz, finding an ML algorithm to effect that improvement remains an outstanding challenge.

Sebastiano Pilati, University of Camerino

Machine learning ground-state energies and many-body wave functions

In the first part of this presentation, I will present supervised machine-learning studies of the low-lying energy levels of disordered quantum systems. We address single-particle continuous-space models that describe cold-atoms in speckle disorder, and also 1D quantum Ising glasses. Our results show that a sufficiently deep feed-forward neural network (NN) can be trained to accurately predict low-lying energy levels. Considering the long-term prospect of using cold-atoms quantum simulator to train neural networks to solve computationally intractable problems, we consider the effect of random noise in the training data, finding that the NN model is remarkably resilient. We explore the use of convolutional NN to build scalable models and to accelerate the training process via transfer learning.

In the second part, I will discuss how generative stochastic NN, specifically, restricted and unrestricted Boltzmann machines, can be used as variational Ansatz for the ground-state many-body wave functions. In particular, we show how to employ them to boost the efficiency of projective quantum Monte Carlo (QMC) simulations, and how to automatically train them within the projective QMC simulation itself.

SP, P. Pieri, Scientific Reports 9, 5613 (2019)
E. M. Inack, G. Santoro, L. Dell’Anna, SP, Physical Review B 98, 235145 (2018)

Maria Schuld, University of KwaZulu-Natal

How to use a Gaussian Boson Sampler to learn from graph-structured data

A device called a ‘Gaussian Boson Sampler’ has initially been proposed as a near-term demonstration of classically intractable quantum computation. But these devices can also be used to decide whether two graphs are similar to each other. In this talk, I will show how to construct a feature map and graph similarity measure (or ‘graph kernel’) using samples from an optical Gaussian Boson Sampler, and how to combine this with a support vector machine to do machine learning on graph-structured datasets. I will present promising benchmarking results and try to motivate why such a continuous-variable quantum computer can actually extract interesting properties from graphs.

Kristan Temme, California Institute of Technology

Quantum machine learning and the prospect of near-term applications on noisy devices.

Prospective near-term applications of early quantum devices rely on accurate estimates of expectation values to become relevant. Decoherence and gate errors lead to wrong estimates. This problem was, at least in theory, remedied with the advent of quantum error correction. However, the overhead that is needed to implement a fully fault-tolerant gate set with current codes and current devices seems prohibitively large. In turn, steady progress is made in improving the quality of the quantum hardware, which leads to the believe that in the foreseeable future machines could be build that cannot be emulated by a conventional computer. In light of recent progress mitigating the effect of decoherence on expectation values, it becomes interesting to ask what these noisy devices can be used for. In this talk we will present our advances in finding quantum machine learning applications for noisy quantum computers.

Peter Wittek, University of Toronto

Vulnerability of quantum systems to adversarial perturbations

Yi-Zhuang You, University of California, San Diego

Machine Learning Physics: From Quantum Mechanics to Holographic Geometry

Inspired by the "third wave" of artificial intelligence (AI), machine learning has found rapid applications in various topics of physics research. Perhaps one of the most ambitious goals of machine learning physics is to develop novel approaches that ultimately allows AI to discover new concepts and governing equations of physics from experimental observations. In this talk, I will present our progress in applying machine learning technique to reveal the quantum wave function of Bose-Einstein condensate (BEC) and the holographic geometry of conformal field theories. In the first part, we apply machine translation to learn the mapping between potential and density profiles of BEC and show how the concept of quantum wave function can emerge in the latent space of the translator and how the Schrodinger equation is formulated as a recurrent neural network. In the second part, we design a generative model to learn the field theory configuration of the XY model and show how the machine can identify the holographic bulk degrees of freedom and use them to probe the emergent holographic geometry.

Contributed Talks

Nicolo Defenu, Heidelberg University

Quantum scale anomaly and spatial coherence in a 2D Fermi superfluid

Quantum anomalies are violations of classical scaling symmetries caused by quantum fluctuations. Although they appear prominently in quantum field theory to regularize divergent physical quanti- ties, their influence on experimental observables is difficult to discern. Here, we discovered a striking manifestation of a quantum anomaly in the momentum-space dynamics of a 2D Fermi superfluid of ultracold atoms. We measured the position and pair momentum distribution of the superfluid during a breathing mode cycle for different interaction strengths across the BEC-BCS crossover. Whereas the system exhibits self-similar evolution in the weakly interacting BEC and BCS limits, we found a violation in the strongly interacting regime. The signature of scale-invariance breaking is enhanced in the first-order coherence function. In particular, the power-law exponents that char- acterize long-range phase correlations in the system are modified due to this effect, indicating that the quantum anomaly has a significant influence on the critical properties of 2D superfluids.

Dong-Ling Deng, Tsinghua University

Machine learning meets quantum physics

Recently, machine learning has attracted tremendous interest across different communities. In this talk, I will briefly introduce some new progresses in the emergent field of quantum machine learning ---an interdisciplinary field that explores the interactions between quantum physics and machine learning. On the one hand, I will talk about a couple of quantum algorithms that promise an exponential speed-up for machine learning tasks. On the other hand, I will show how ideas and techniques from machine learning can help solve challenging problems in the quantum domain.

Olivia Di Matteo, TRIUMF

Operational quantum tomography

As quantum processors become increasingly refined, benchmarking them in useful ways becomes a critical topic. Traditional approaches to quantum tomography, such as state tomography, suffer from self-consistency problems, requiring either perfectly pre-calibrated operations or measurements. This problem has recently been tackled by explicitly self-consistent protocols such as randomized benchmarking, robust phase estimation, and gate set tomography (GST). An undesired side-effect of self-consistency is the presence of gauge degrees of freedom, arising from the lack fiducial reference frames, and leading to large families of gauge-equivalent descriptions of a quantum gate set which are difficult to interpret.

We solve this problem through introducing a gauge-free representation of a quantum gate set inspired by linear inversion GST. This allows for the efficient computation of any experimental frequency without a gauge fixing procedure. We use this approach to implement a Bayesian version of GST using the particle filter approach, which was previously not possible due to the gauge.

Within Bayesian GST, the prior information allows for inference on tomographically incomplete data sets, such as Ramsey experiments, without giving up self-consistency. We demonstrate the stability and generality of both our gauge-free representation and Bayesian GST by simulating a number of common characterization protocols, such as randomized benchmarking, as well characterizing a trapped-ion qubit using experimental data.

Sandia National Labs is managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a subsidiary of Honeywell International, Inc., for the U.S. Dept. of Energy’s National Nuclear Security Administration under contract DE-NA0003525.
The views expressed in this presentation do not necessarily represent the views of the DOE, the ODNI, or the U.S. Government. This material was funded in part by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research Quantum Testbed Program.

Olivia Di Matteo, TRIUMF, Vancouver, BC, Canada and Microsoft Research, Redmond, WA, USA
John Gamble, Microsoft Research, Redmond, WA, USA
Chris Granada, Microsoft Research, Redmond, WA, USA
Kenneth Ruddinger, Quantum Performance Laboratory, Sandia National Laboratories, Albuquerque, NM, USA
Nathan Wiebe, Microsoft Research, Redmond, WA, USA

Eliska Greplova, ETH Zurich

Quantum Error Correction via Hamiltonian Learning

Successful implementation of error correction is imperative for fault-tolerant quantum computing. At present, the toric code, surface code and related stabilizer codes are state of the art techniques in error correction.
Standard decoders for these codes usually assume uncorrelated single qubit noise, which can prove problematic in a general setting.
In this work, we use the knowledge of topological phases of modified toric codes to identify the underlying Hamiltonians for certain types of imperfections. The Hamiltonian learning is employed to adiabatically remove the underlying noise and approach the ideal toric code Hamiltonian. This approach can be used regardless of correlations. Our method relies on a neural network reconstructing the Hamiltonian given as input a linear amount of expectation values. The knowledge of the Hamiltonian offers significant improvement of standard decoding techniques
Eliska Greplova, Agnes Valenti, Evert van Nieuwenburg, Sebastian Huber

Ehsan Khatami, San Jose State University

Machine learning phase discovery in quantum gas microscope images

Site resolution in quantum gas microscopes for ultracold atoms in optical lattices have transformed quantum simulations of many-body Hamiltonians. Statistical analysis of atomic snapshots can produce expectation values for various charge and spin correlation functions and have led to new discoveries for the Hubbard model in two dimensions. Conventional approaches, however, fail in general when the order parameter is not known or when an expected phase has no clear signatures in the density basis. In this talk, I will introduce our efforts in using machine learning techniques to overcome this challenge with snapshots of fermionic atoms. Collaborators: Richard Scalettar (UC Davis), Waseem Bakr (Princeton), and Juan Carrasquilla (Vector Institute)

Emine Kucukbenli, SISSA

Machine learning inter-atomic potentials

Describing the relationship between atomic positions and total energy, E({R}), is a fundamental aim for many modern physics, chemistry and material science simulations. This relationship, due to its quantum mechanical foundation, is tractable only in a small domain of systems, and even relatively low cost first principles methods such as Density Functional Theory are limited in addressing systems of realistic size and complexity. To overcome those limits, inter-atomic potentials have been parametrized to approximate the function that maps atomic positions to energy in the domain of a target material. In this talk, we will report our efforts in performing this functional approximation via neural network methods on a range of materials. We will examine the dependence of network performance on the data, representation, activation functions and training dynamics; and explore the strategies of obtaining the best results with the least computational effort. We will conclude with a brief overview of current developments and challenges in the field.

JinGuo Liu, Chinese Academy of Sciences

Differentiable Programming Tensor Networks and Quantum Circuits

Differentiable programming makes the optimization of a tensor network much cheaper (in unit of brain energy consumption) than before [e.g. arXiv: 1903.09650]. This talk mainly focuses on the technical aspects of differentiable programming tensor networks and quantum circuits with Yao.jl (https://github.com/QuantumBFS/Yao.jl). I will also show how quantum circuits can help with contracting and differentiating tensor networks.

Yehua Liu, University of Sherbrooke

Neural Belief-Propagation Decoders for Quantum Error-Correcting Codes

Belief-propagation (BP) decoders are responsible for the success of many modern coding schemes. While many classical coding schemes have been generalized to the quantum setting, the corresponding BP decoders are flawed by design in this setting. Inspired by an exact mapping between BP and deep neural networks, we train neural BP decoders for quantum low-density parity-check codes, with a loss function tailored for the quantum setting. Training substantially improves the performance of the original BP decoders. The flexibility and adaptability of the neural BP decoders make them suitable for low-overhead error correction in near-term quantum devices.
Reference: arXiv:1811.07835 (to appear in PRL)

Glen Bigan Mbeng, SISSA

The Quantum Approximate Optimization Algorithm and spin chains

Various optimization problems that arise naturally in science are frequently solved by heuristic algorithms. Recently, multiple quantum enhanced algorithms have been proposed to speed up the optimization process, however a quantum speed up on practical problems has yet to be observed. One of the most promising candidates is the Quantum Approximate Optimization Algorithm (QAOA), introduced by Farhi et al. I will then discuss numerical and exact results we have obtained for the quantum Ising chain problem and compare the performance of the QAOA and the Quantum Annealing algorithm. I will also briefly describe the landscape that emerges from the optimization problem and how techniques borrowed from machine learning can be used to improve the optimization process.

Kevin Ryczko, University of Ottawa

Designing a Quantum Transducer With Genetic Algorithms and Electron Transport Calculations

The fields of quantum information and quantum computation are reliant on creating and maintaining low-dimensional quantum states. In two-dimensional hexagonal materials, one can describe a two-dimensional quantum state with electron quasi-momentum. This description, often referred to as valleytronics allows one to define a two-state vector labelled by k and k', which correspond to symmetric valleys in the conduction band. In this work, we present an algorithm that allows one to construct a nanoscale device that topologically separates k and k' current. Our algorithm incorporates electron transport calculations, artificial neural networks, and genetic algorithms to find structures that optimize a custom objective function. Our first result is that when modifying the on-site energies via doping with simple shapes the genetic algorithm is able to find structures that are able to topologically separate the valley currents with approximately 90% purity. We then introduce an arbitrary shape generator via a policy defined by an artificial neural network to modify the on-site energies of the nanoribbons. We study the dynamics of the genetic algorithms for both cases. Lastly, we then attempt to physically motivate the solutions by mapping the high dimensional search space to a lower dimensional one that can be better understood.

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• Juan Carrasquilla, Vector Institute
• Estelle Inack Perimeter Institute
• Roger Melko, Perimeter Institute & University of Waterloo
• Sandro Sorella, SISSA