Machine Learning for Quantum Design

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.

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.

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.

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.

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.

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.

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.

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