**Speaker Talks**

**Marin Bukov,** University of California, Berkeley

*Glassy and Correlated Phases of Optimal Quantum Control*

Modern Machine Learning (ML) relies on cost function optimization to train model parameters. The non-convexity of cost function landscapes results in the emergence of local minima in which state-of-the-art gradient descent optimizers get stuck. Similarly, in modern Quantum Control (QC), a key to understanding the difficulty of multiqubit state preparation holds the control landscape -- the mapping assigning to every control protocol its cost function value. Reinforcement Learning (RL) and QC strive to find a better local minimum of the control landscape; the global minimum corresponds to the optimal protocol. Analyzing a decrease in the learning capability of our RL agent as we vary the protocol duration, we found rapid changes in the search for optimal protocols, reminiscent of phase transitions. These "control phase transitions" can be interpreted within Statistical Mechanics by viewing the cost function as "energy" and control protocols – as "spin configurations". I will show that optimal qubit control exhibits continuous and discontinuous phase transitions familiar from macroscopic systems: correlated/glassy phases and spontaneous symmetry breaking. I will then present numerical evidence for a universal spin-glass-like transition controlled by the protocol time duration. The glassy critical point is marked by a proliferation of protocols with close-to-optimal fidelity and with a true optimum that appears exponentially difficult to locate. Using a ML inspired framework based on the manifold learning algorithm t-SNE, we visualize the geometry of the high-dimensional control landscape in an effective low-dimensional representation. Across the transition, the control landscape features an exponential number of clusters separated by extensive barriers, which bears a strong resemblance with random satisfiability problems.

**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.

**Michele Ceriotti**, École polytechnique fédérale de Lausanne

*Simulating Thermal and Quantum Fluctuations in Materials and Molecules*

Both electrons and nuclei follow the laws of quantum mechanics, and even though classical approximations and/or empirical models can be quite successful in many cases, a full quantum description is needed to achieve predictive simulations of matter. Traditionally, simulations that treat both electrons and nuclei as quantum particles have been prohibitively demanding. I will present several recent algorithmic advances that have increased dramatically the range of systems that are amenable to quantum modeling: on one hand, by using accelerated path integral schemes to treat the nuclear degrees of freedom, and on the other by using machine-learning potentials to reproduce inexpensively high-end electronic-structure calculations. I will give examples of both approaches, and discuss how the two can be used in synergy to make fully quantum modeling affordable.

**Paul Ginsparg,** Cornell University

*Attention is all you get*

For the past decade, there has been a new major architectural fad in deep learning every year or two.

One such fad for the past two years has been the transformer model, an implementation of the attention method which has superseded RNNs in most sequence learning applications. I'll give an overview of the model, with some discussion of non-physics applications, and intimate some possibilities for physics.

**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)

**Stefan Leichenauer**, Google

*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.

**Isaac Tamblyn**, National Research Council Canada

*Deep learning and density functional theory*

Density functional theory is a widely used electronic structure method for simulating and designing nanoscale systems based on first principles. I will outline our recent efforts to improve density functionals using deep learning. Improvement would mean achieving higher accuracy, better scaling (with respect to system size), improved computational parallelizability, and achieving reliable performance transferability across different electronic environments.

To this end, we have generated a large and diverse dataset of 2d simulations of electrons (http://clean.energyscience.ca/datasets) with a varying number of electrons in confining potentials for several (approximate) density functionals. As a proof-of-principal, we have used extensive deep neural networks to reproduce the results of these simulations to high accuracy at significantly reduced computational cost. By learning the screening length-scale of the electrons directly from the data, we are able to train on small-scale calculations, yet perform inference at effectively arbitrary length-scales at only O(N) cost. This overcomes a key-scaling limitation of Kohn-Sham DFT (which scales as O(N^3)), paving the way for accurate, large scale ab initio enabled design of nanoscale components and devices.

**Kristan Temme**, IBM Research

*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.

**Evert van Nieuwenburg**, California Institute of Technology

*Integrating Neural Networks with a Quantum Simulator for State Reconstruction*

In this talk I will discuss how (unsupervised) machine learning methods can be useful for quantum experiments. Specifically, we will consider the use of a generative model to perform quantum many-body (pure) state reconstruction directly from experimental data. The power of this machine learning approach enables us to trade few experimentally complex measurements for many simpler ones, allowing for the extraction of sophisticated observables such as the Rényi mutual information. These results open the door to integration of machine learning architectures with intermediate-scale quantum hardware.

**Lei Wang**, 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.

**Peter Wittek**, University of Toronto

*Vulnerability of quantum systems to adversarial perturbations*

High-dimensional quantum systems are vital for quantum technologies and are essential in demonstrating practical quantum advantage in quantum computing, simulation and sensing. Since dimensionality grows exponentially with the number of qubits, the potential power of noisy intermediate-scale quantum (NISQ) devices over classical resources also stems from entangled states in high dimensions. An important family of quantum protocols that can take advantage of high-dimensional Hilbert space are classification tasks. These include quantum machine learning algorithms, witnesses in quantum information processing and certain decision problems. However, due to counter-intuitive geometrical properties emergent in high dimensions, classification problems are vulnerable to adversarial attacks. We demonstrate that the amount of perturbation needed for an adversary to induce a misclassification scales inversely with dimensionality. This is shown to be a fundamental feature independent of the details of the classification protocol. Furthermore, this leads to a trade-off between the security of the classification algorithm against adversarial attacks and quantum advantages we expect for high-dimensional problems. In fact, protection against these adversarial attacks require extra resources that scale at least polynomially with the Hilbert space dimension of the system, which can erase any significant quantum advantage that we might expect from a quantum protocol. This has wide-ranging implications in the use of both near-term and future quantum technologies for classification.

**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.

**Andrea Zen**, University College London

*The challenge to deliver high accuracy on large computer simulations*

Computer simulations are extremely useful in providing insight on the physical and chemical processes taking places in nature. Very often simulations are complementary to experimental investigations, providing the interpretations and the molecular level understanding that experiments struggle to deliver. Yet, simulations are useful only when their results may be relied upon, that is, when they can accurately model the physical system and the forces therein.

Thriving nanotechnologies and exciting experiments pose a big challenge to computational approaches, especially when dealing with solid-liquid interfaces. On the one hand, the systems to be simulated are large and often long molecular dynamics simulations are needed. On the other hand, extremely high accuracy is required.

We discuss here an approach to deliver high accuracy at low computational cost using quantum Monte Carlo and Machine Learning.

**Contributed Talks**

**Emily Davis,** Stanford University

*Engineering Programmable Spin Interactions in a Near-Concentric Cavity*

Photon-mediated interactions among atoms coupled to an optical cavity are a powerful tool for engineering quantum many-body Hamiltonians. We present observations of dynamics of spins evolving under continuously tunable Heisenberg models, where the relative strength and sign of spin-exchange and Ising couplings are controllable parameters. The interaction dynamics manifest as rotations of large effective spins in a mean-field picture, as well as a spin-mixing process seeded by quantum fluctuations, which in principle generates a highly entangled twin Fock state. Whereas the single-mode cavity most naturally mediates all-to-all couplings, I will discuss progress in generalizing to control the distance-dependence of the interactions. The optical access afforded by the near-concentric cavity geometry enables spatially-dependent addressing and imaging with micron-scale resolution, providing opportunities to perform both state and Hamiltonian tomography on the experimental data.

**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

**Timothy Hsieh**, Perimeter Institute

*Shortcuts in Real and Imaginary Time*

In the first half, I will demonstrate an efficient and general approach for realizing non-trivial quantum states, such as quantum critical and topologically ordered states, in quantum simulators. In the second half, I will present a related variational ansatz for many-body quantum systems that is remarkably efficient. In particular, representing the critical point of the one-dimensional transverse field Ising model only requires a number of variational parameters scaling logarithmically with system size. Though optimizing the ansatz generally requires Monte Carlo sampling, our ansatz potentially enables a partial mitigation of the sign problem at the expense of having to optimize a few parameters.

**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.

**Giacomo Torlai,** Flatiron Institute

*Alleviating the sign structure of quantum states*

The sign structure of quantum states - the appearance of “probability” amplitudes with negative sign - is one of the most striking contrasts between the classical and the quantum world, with far-reaching implications in condensed matter physics and quantum information science. Because it is a basis-dependent property, one may wonder: is a given sign structure truly intrinsic, or can it be removed by a local change of basis? In this talk, I will present an algorithm based on automatic differentiation of tensor networks for discovering non-negative representations of many-body wavefunctions. I will show some numerical results for ground states of a two-leg triangular Heisenberg ladder, including an exotic Bose-metal phase.