Download **symposium’s schedule**

### Sunday, 18 March

Location: IWH, Haupstrasse 242, 69117 Heidelberg

### Monday, 19 March

Welcome remarks from Prof. Peter Comba, Director of IWH, Prof. Karlheinz Meier, the Structures initiative, Prof. Carlo Ewerz, Scientific Coordinator of EMMI, and the organizers.

The brain is a complex network of 10^11 nodes and 10^15 synaptic connections. It evolves in continuous interaction with the environment on timescales from milliseconds to years. Numerical simulations of this system provide some insights but are severely constrained by energy consumption and simulation times.

In 1982 Feynman postulated a method, in which the number of computer elements required to simulate a large physical system is proportional to the space-time volume of the physical system. Similar to todays quantum emulators neuromorphic systems follow this path by building physical models of brain circuits under user control rather than solving differential equations numerically.

Like the biological archetype physical model neuromorphic systems exhibit attractive features like energy efficiency, fault tolerance and the ability to learn.

The talk will introduce this approach and present some recent results.

A key step in the roadmap to build a useful quantum computer will be to demonstrate its exponentially growing computing power. I will explain how a 7 by 7 array of superconducting xmon qubits with nearest-neighbor coupling, and with programmable single- and two-qubit gate with errors of about 0.2%, can execute a modest depth quantum computation that fully entangles the 49 qubits. Sampling of the resulting output can be checked against a classical simulation to demonstrate proper operation of the quantum computer and compare its system error rate with predictions. With a computation space of 2^49 = 5 x 10^14 states, the quantum computation can only be checked using the biggest supercomputers. I will show experimental data towards this demonstration from a 9 qubit adjustable-coupler “gmon” device, which implements the basic sampling algorithm of quantum supremacy for a computational (Hilbert) space of about 500. We have begun testing of the quantum supremacy chip.

In this talk I will present recent applications of machine-learning-based approaches to quantum physics. First, I will discuss how a systematic machine learning of the many-body wave-function can be realized. This goal has been achieved in [1], introducing a variational representation of quantum states based on artificial neural networks. In conjunction with Monte Carlo schemes, this representation can be used to study both ground-state and unitary dynamics, with controlled accuracy. Moreover, I will show how a similar representation can be used to perform efficient Quantum State Tomography on highly-entangled states [2], previously inaccessible to state-of-the art tomographic approaches.

[1] Carleo, and Troyer – Science 355, 602 (2017).

[2] Torlai, Mazzola, Carrasquilla, Troyer, Melko, and Carleo – Nature Physics (in press, 2018) arXiv:1703.05334.

The ability to perform probabilistic (Bayesian) inference is a hallmark of mammalian cognition and a coveted feature for embedded AI. Recent developments in machine learning have tried to capture this kind of computation with so-called “deep” architectures, but the analogy to biology remains superficial. I will discuss a framework for cognitive computation with spiking neurons that narrows the gap between biological and artificial deep networks, while employing well-documented aspects of cortical dynamics such as spike-based communication, operation in a high-conductance state, short-term plasticity and background-driven stochasticity. By design, these models lend themselves to neuromorphic implementation, which allows them to profit from the advantages offered by these new technologies.

A new method to describe the unitary evolution of interacting quantum many-body systems has been introduced recently which is based on the representation of quantum states in terms of an artificial neural network (ANN). Focusing on the spin 1/2 quantum Ising model with transverse and longitudinal field after a quench near criticality, we study the prospects and limitations of this method. We compare our results to those obtained with exact analytical results, with a semi-classical discrete Truncated-Wigner approach, and with tDMRG simulations. We find that the dTWA gives good results only at short times or near zero transverse field. The ANN approach works well in a much wider range of parameters. Only in regimes where long-range spin correlations build up the long-time dynamics becomes unstable and deviates from the exact results. The ANN approach yields qualitatively correct results in regimes where the entanglement entropy in the long-time limit is extensive.

Artificial neural networks play a prominent role in the rapidly growing field of machine learning and are recently introduced to quantum many-body systems. This talk will focus on using a machine-learning model, the restricted Boltzmann machine (RBM) to describe entangled quantum states. Both short- and long-range coupled RBM will be discussed. For a short-range RBM, the associated quantum state satisfies an entanglement area law, regardless of spatial dimensions. I will present our recently constructed exact RBM models for nontrivial topological phases, including a 1d cluster state and a 2d toric code. For a long-range RBM, the captured entanglement entropy scales linearly with the number of variational parameters in the RBM model, in sharp contrast to the log-scaling in matrix product state representation.

Machine learning techniques have become ubiquitous, but often hidden helpmates in our daily life. This includes pattern recognition technologies that have long filtered data in electronic mailboxes and have more recently become powerful enough to identify users by the touch of a button or the scan of a face.

In my talk, I will briefly review the algorithmic foundations of machine learning approaches and then turn to their application in the context of statistical physics problems. I will demonstrate that machine learning techniques are capable to discriminate phases of matter by extracting essential features in the many-body wavefunction or the ensemble of correlators sampled for instance in Monte Carlo simulations. Of particular interest are quantum many-fermion problems that have long resisted a thorough numerical understanding — will we be able to guide our understanding of the emergence of superconductivity or topological order in such systems using machine learning?

We report a proof-of-principle experimental demonstration of the quantum speed-up for learning agents utilizing a small-scale quantum information processor based on radiofrequency-driven trapped ions [1]. The decision-making process of a quantum learning agent within the projective simulation paradigm for machine learning is implemented in a system of two qubits. The latter are realized using hyperfine states of two frequency-addressed atomic ions exposed to a static magnetic field gradient. We show that the deliberation time of this quantum learning agent is quadratically improved with respect to comparable classical learning agents. The performance of this quantum-enhanced learning agent highlights the potential of scalable quantum processors taking advantage of machine learning.

[1] Th. Sriarunothai et al., arXiv: 1709.01366 (2017).

### Tuesday, 20 March

The SpiNNaker (Spiking Neural Network Architecture) project aims to produce a massively-parallel computer capable of modelling large-scale neural networks in biological real time. The machine has been 18 years in conception and ten years in construction, and has so far delivered a 500,000-core machine in six 19-inch racks, and now being expanded towards the million-core full system. Although primarily intended as a platform to support research into information processing in the brain, SpiNNaker has also proved useful for Deep Networks and similar applied Big Data applications. In this talk I will present an overview of the machine and the design principles that went into its development, and I will indicate the sort of applications for which it is proving useful.

The quantum toolbox of the Innsbruck ion-trap quantum computer is applied to simulate the dynamics and to investigate the propagation of entanglement in a quantum many-body system represented by long chains of trapped-ion qubits [1]. With strings of up to 10 ions, a dynamical phase transition was recently observed [2] and an efficient procedure for the characterization of a quantum many-body system of up to 14 entangled ions has been implemented [3].

Moreover, using the quantum toolbox operations, universal (digital) quantum simulation was realized with a string of trapped ions [4]. Here we report the experimental demonstration of a digital quantum simulation of a lattice gauge theory, by realizing (1 + 1)-dimensional quantum electrodynamics (the Schwinger model) on a few-qubit trapped-ion quantum computer [3]. We are interested in the real-time evolution of the Schwinger mechanism, describing the instability of the bare vacuum due to quantum fluctuations, which manifests itself in the spontaneous creation of electron–positron pairs. To make efficient use of our quantum resources, we map the original problem to a spin model by eliminating the gauge fields in favor of exotic long-range

interactions, which can be directly and efficiently implemented on an ion trap architecture.

[1] P. Jurcevic et al., Nature 511, 202 (2014)

[2] P. Jurcevic et al., Phys. Rev. Lett. 111, 080501 (2017)

[3] B. P. Lanyon et al., Nature Physics 13, 1158 (2017)

[4] E. A. Martinez et al., Nature 534, 516 (2016)

Quantum correlations are fundamental for quantum information protocols and for our understanding of many-body quantum physics. The detection of these correlations in these systems is challenging because it requires the estimation and processing of an exponentially growing amount of parameters. We present methods to alleviate these problem and discuss their application to physically relevant quantum states.

Classifying phases of matter is key to our understanding of many problems in physics. For quantum-mechanical systems in particular, the task can be daunting due to the exponentially large Hilbert space. With modern computing power and access to ever-larger data sets, classification problems are now routinely solved using machine-learning techniques. Here, we propose a neural-network approach to finding phase transitions, based on the performance of a neural network after it is trained with data that are deliberately labelled incorrectly. We demonstrate the success of this method on the topological phase transition in the Kitaev chain, the thermal phase transition in the classical Ising model, and the many-body-localization transition in a disordered quantum spin chain. Our method does not depend on order parameters, knowledge of the topological content of the phases, or any other specifics of the transition at hand.

In this talk I will present some ideas for quantum simualators that may be operated at room temperature.

Presentation slides: BDC2018_Martin_Plenio

Quantum simulation is a tool to investigate problems, e.g., in chemistry or condensed matter physics, that are not solvable analytically or on classical computers. However, the inevitability of perturbations constitutes a major roadblock to useful quantum simulations. Since we cannot predict the result of the simulation, it is difficult to estimate the effect of perturbations.

We show that in specific systems a measurement of additional correlators can be used to verify the reliability of the quantum simulation. The procedure only requires additional measurements on the quantum simulator itself. Besides, we present a method which, in certain circumstances, allows for the reconstruction of the ideal result from measurements on a perturbed quantum simulator.

To exploit near term applications for quantum simulation we have founded a company to develop quantum algorithms to predict material properties for chemical and pharmaceutical companies. We will discuss the various steps that are necessary to implement quantum chemical problems on a quantum computer and the challenges involved in solving concrete consumer problems. We intend for our software to be hardware agnostic and to work on conventional and state of the art quantum computers.

Starting from ideas developed in the realm of strongly interacting cold atoms, I will show how to realize quantum spin transistors in small spin networks. Then I will outline how these could be realized in current superconducting platforms using transmons or flux qubits. Other neat applications of these principles for modular quantum computation includes small quantum routers and quantum spin diodes.

Ultracold atoms are a versatile system to study the fascinating phenomena of gauge fields and topological band structures. By Floquet driving of optical lattices, the topology of the Bloch bands can be engineered. This poster presents experimental schemes for momentum-resolved Bloch state tomography, which allow mapping out the Berry curvature and obtaining the Chern number. Furthermore, it discusses the dynamics of the wave function after a quench into the Floquet system. We observe the appearance of dynamical vortices, which trace out a closed contour, the topology of which can be directly mapped to the Chern number. Our measurements provide a new perspective on topology and dynamics and a unique starting point for studying interacting topological phases.

Location: Physics Institute, Neuenheim Feld Campus

Location: Physics Institute, Neuenheim Feld Campus

Location: Physics Institute, Neuenheim Feld Campus

### Wednesday, 21 March

Complex networks defined on quantum states via quantum mutual information turn out to give a surprising level of new insight on physical problems ranging from quantum critical phenomena to far-from-equilibrium quantum dynamics. Measures on such networks serve to rapidly and efficiently identify quantum critical points for workhorse many-body models studied in present quantum simulator experiments. A small modification of such models allows one to produce entangled quantum cellular automata. Complex network-based averages and dynamics serve as key quantifiers for emergent complexity along with localized robust dynamical structures and entropy fluctuations. They show that a new class of highly entangled yet also highly structured quantum states arise out of dynamics just a short step away from present experimental protocols. They also identify a set of simple criteria, called Goldilocks Rules, which consistently produce complexity independent of the details of the protocol.

We present some recent and ongoing results related optimal solutions to the alternating operator ansatz (QAOA). This is the backbone behind gate-model based quantum deep learning networks based on generative Boltzmann machine models. Time permitting, we will present results about those as well.

Quantum machine learning is an exciting new field emerging at the intersection between quantum computing and machine learning (ML). On one hand, advances in quantum algorithms provide new approaches for widely used classical routines that could improve both training of and sampling from ML models by increasing accuracy and/or efficiency, or allowing for richer model classes. On the other hand quantum computers are a natural fit for applying machines learning techniques to study quantum systems, where the ability to more easily process and model quantum states could give a significant edge over classical approximations.

The development of quantum computing devices with an increasingly large number of qubits encourages to investigate the practicality of these algorithms and what progress one could hope for as quantum technology matures. In my talk I will give an overview over existing quantum machine learning algorithms, their potential, and their caveats.

Lattice gauge theories describe fundamental phenomena in nature, but calculating their real-time dynamics on classical computers is notoriously difficult. In a recent publication [Nature 534, 516 (2016)], we proposed and experimentally demonstrated a digital quantum simulation of 1+1-dimensional quantum electrodynamics (Schwinger model) on a few-qubit trapped-ion quantum computer. We are interested in the real-time evolution of the Schwinger mechanism, describing the instability of the bare vacuum due to quantum fluctuations, which manifests itself in the spontaneous creation of electron-positron pairs. To make efficient use of our quantum resources, we map the original problem to a spin model by eliminating the gauge fields in favour of exotic long-range interactions, which have a direct and efficient implementation on an ion trap architecture. Our work represents a first step towards quantum simulating high-energy theories with atomic physics experiments.

The rich physics of the Fermi-Hubbard model arises due to the interplay of the charge and spin degrees of freedom. Here we highlight novel detection methods for these degrees of freedom using spin and charge resolved single atom detection in ultracold lattice systems. The detection of the full local and global counting statistics allows us to analyze non-local correlation functions and perform data-postselection, which reveal hidden spin correlations and incommensurate magnetism in 1D chains.

Despite enabling impressive advances, the big-data driven deep learning paradigm has been challenged by AI scholars for not holding the potential to reach human scale intelligence. Instead, they propose studies of human psychology as a basis for hybrid human-machine intelligence. An open question for the future of research is therefore how to design interfaces that allow for an optimal interaction between human intuition, complex machinery, and increasingly powerful ML.

In the www.scienceathome.org project, we have developed gamified interfaces allowing so far 250,000 players to contribute to research by providing insightful seeds for quantum optimization algorithms and remote access to our ultra-cold atoms experiment for amateur scientists, students, and researchers. Finally, I will discuss our effort to provide efficient, game-based heuristics for NP-hard computational problems related to spin glasses and ongoing efforts to demonstrate quantum supremacy using quantum annealing.

### Posters

We propose mathematical formulations for localizing source acitivity in EEG data sets for PTSD victims using quantum machine learning. We explore several techniques in source localization for global optimization and select the Ising annealing model to localize source activity instantaneously. Calculations are performed on a DWAVE 2000 for quantum computation and are rapid and efficient with high accuracy. We also adopt the use of restricted boltzmann machines based on adaptive filtering and parametric fitting to obtain optimal solutions. The data used for this exercise and proposal are eeg wave trains for 4D datasets in a spatio-temporal sense. We compare source quantization with conventional classical techniques and find that adaptive speed improvements lend itslef to clinical success and validity as concerns to diagnosing the PTSD problem. Several iterations of continuous calculation allow for expedited results and neural recovery.

The Human Brain Project (HBP) aims to understand by means of Synthesis Biology how the inconceivably efficient system of the Human Brain works. The BrainScaleS system at the Kirchhoff-Institute for Physics in Heidelberg is part of the HBP and pursues this goal by developing a neuromorphic analog hardware system in combination with a conventional computing cluster. This poster summarizes the development of a new network interface for the FPGAs controlling the data communication between the neuromorphic hardware chips and the conventional digital system. The new interface will enable the BrainScaleS system to use the benefits of the Extoll network, a high-performance interconnection network, optimized for low latency and high message rates.

Cavity/circuit QED is a promising system for realizing quantum information processing, because the deterministic atom-photon interaction can efficiently make single photon sources, and atom-photon quantum gates. One of the difficulty of realizing scalable quantum computing is the trade-off between the high-fidelity operation and the integration of many qubits. Cavity/circuit QED systems may solve the problem by deterministically connecting remote atomic systems through flying photons/microwave photons and by efficiently reproducing lossy photonic qubits. Here, I present two physical systems from my collaborative works. One is the nanofiber cavity QED systems, which is a promising candidate for obtaining the high cooperativity and cavity array systems. The other is a circuit QED system that can make entanglement between remote superconducting atoms by using a quantum gate between a superconducting atom and a propagating microwave photon [Phys. Rev. Applied, 7, 064006 (2017)].

The Data Vortex (DV) network is used to communicate large amounts of data between different nodes of a parallel computer. We present benchmarks illustrating how DV excels at communicating random packets in situations where aggregation is difficult and for algorithms involving the fast Fourier transform. Next, we briefly describe a programming model for DV and draw comparisons with MPI. Finally, we summarize ongoing research projects: (i) inviscid incompressible fluid flow, (ii) the Schrödinger equation for few-body systems, and (iii) the simulation of ideal quantum computers capable of running general quantum circuits.