Machine Learning Initiative

The past decade has witnessed tremendous advancements in the size, coherence and control accuracy of qubits across various material platforms. In the case of superconducting qubits fabricated from Josephson junctions, quantum systems with over 50 qubits and >99% gate fidelities can now be reliably fabricated. In this talk, I will introduce the basics of superconducting qubits, with a particular focus on the implementation and calibration of two-qubit gates. I will then describe an experiment demonstrating quantum computational advantage on a specific task, namely sampling from random quantum circuits comprising 53 qubits [1]. The success of this experiment hinges on the chaotic dynamics underlying the random circuits, which generates sufficiently large entanglement to challenge classical simulation within the coherence times of the qubits. To systematically study the physics of quantum chaos, we perform a second experiment which investigates the “fingerprints” of chaos on local quantum observables [2]. We demonstrate how the two fundamental mechanisms of quantum chaos, operator spreading and operator entanglement, may be diagnosed by reversing the flow of time and measuring the so-called out-of-time-order correlators (OTOCs). Additionally, we find that with proper error-mitigation strategies, even local quantum observables such as OTOCs may be measured up to accuracies requiring non-trivial classical computational resources to simulate. These works pave a critical path toward using quantum computers for scientific discovery in the NISQ era.

[1] Google Quantum AI, Nature 574, 505 (2019).

[2] X. Mi et al., Science 374, 1479 (2021).

Zoom Link: https://pitp.zoom.us/j/93446337538?pwd=UXpsUFZ4M0tDSDd6bnA0VFBsazNPQT09

Recent advances in quantum simulation experiments have paved the way for a new perspective on strongly correlated quantum many-body systems. Digital as well as analog quantum simulation platforms are capable of preparing desired quantum states, and various experiments are starting to explore non-equilibrium many-body dynamics in previously inaccessible regimes in terms of system sizes and time scales. State-of-the art quantum simulators provide single-site resolved quantum projective measurements of the state. Depending on the platform, measurements in different local bases are possible. The question emerges which observables are best suited to study such quantum many-body systems.

In this talk, I will cover two different approaches to make the most use of these possibilities. In the first part, I will discuss the use of machine learning techniques to study the thermalization behavior of an interacting quantum system. A neural network is trained to distinguish non-equilibrium from thermal equilibrium data, and the network performance serves as a probe for the thermalization behavior of the system. We apply this method to numerically simulated data, as well experimental snapshots of ultracold atoms taken with a quantum gas microscope. 

In the second part of this talk, I will present a scheme to perform adaptive quantum state tomography using active learning. Based on an initial, small set of measurements, the active learning algorithm iteratively proposes the basis configurations which will yield the maximum information gain. We apply this scheme to GHZ states of a few qubits as well as ground states of one-dimensional lattice gauge theories and show an improvement in accuracy over random basis configurations.

The vast and growing number of publications in all disciplines of science cannot be comprehended by a single human researcher. As a consequence, researchers have to specialize in narrow subdisciplines, which makes it challenging to uncover scientific connections beyond the own field of research.

In my talk, I will present a possible solution: I demonstrate the development of a semantic network for quantum physics (SemNet), using 750,000 scientific papers and knowledge from books and Wikipedia. I use it in conjunction with an artificial neural network for predicting future research directions. Finally, I show first indications how individual scientists can use SemNet for suggesting and inspiring personalized, out-of-the-box ideas.

I believe that computer-inspired scientific ideas will play a significant role in accelerating scientific progress, and am looking forward hearing your thoughts and ideas about this crucial question.

References
[1] Mario Krenn, Anton Zeilinger, Predicting research trends with semantic and neural networks with an application in quantum physics, PNAS 117(4) 1910-1916 (2020).
[2] IEEE BigData 2021 competition: Science4Cast: https://github.com/iarai/science4cast

Zoom Link: https://pitp.zoom.us/j/92240839439?pwd=LytUTHlMWE9ycjlsUXJkdHRta2c1UT09

In the last two decades the field of nonequilibrium quantum many-body physics
has seen a rapid development driven, in particular, by the remarkable progress
in quantum simulators, which today provide access to dynamics in quantum
matter with an unprecedented control. However, the efficient numerical
simulation of nonequilibrium real-time evolution in isolated quantum matter
still remains a key challenge for current computational methods especially
beyond one spatial dimension. In this talk I will present a versatile and
efficient machine learning inspired approach. I will first introduce the
general idea of encoding quantum many-body wave functions into artificial
neural networks. I will then identify and resolve key challenges for the
simulation of real-time evolution, which previously imposed significant
limitations on the accurate description of large systems and long-time
dynamics. As a concrete example, I will consider the dynamics of the
paradigmatic two-dimensional transverse field Ising model, where we observe
collapse and revival oscillations of ferromagnetic order and demonstrate that
the reached time scales are comparable to or exceed the capabilities of state-
of-the-art tensor network methods.

Majorana zero modes have attracted much interest in recent years because of their promising properties for topological quantum computation. A key question in this regard is how fast two Majoranas can be exchanged giving rise to a unitary gate operation. In this presentation I will first explain that the transport of Majoranas in one-dimensional topological superconductors can be formulated as a “simple” optimal control optimization problem for which we propose several different control regimes. Next I will discuss the optimization methods, Differential Programming and Natural Evolution Strategies, that were applied to the Majorana control problem and came up with a counter-intuitive transport strategy. This strategy, which we dubbed jump-move-jump, will form the focus of the last part of the presentation in which I explain the key underlying mechanisms behind the strategy by reformulating the motion of Majoranas in a moving frame. I will conclude by arguing that these results demonstrate that machine learning for quantum control can be applied efficiently to quantum many-body dynamical systems with performance levels that make it relevant to the realization of large-scale quantum technology.

The sign problem is a widespread numerical hurdle preventing us from simulating the equilibrium behaviour of many interesting models, most notably the Hubbard model. Research aimed at solving the sign problem, via various clever manipulations, has been thriving for a long time with various recent exciting results. The complementary question, of whether some phases of matter forbid the existence of any sign-free microscopic model, has received attention only recently. In this talk, I’ll review recent progress and discuss a novel and quite general criteria we obtained for when a topological quantum field theory has no sign-free microscopic model. I’ll also point out relations to sign problems in frustrated magnets and to the notion of quantum supremacy.

Neural networks (NNs) normally do not allow any insight into the reasoning behind their predictions. We demonstrate how influence functions can unravel the black box of NN when trained to predict the phases of the one-dimensional extended spinless Fermi-Hubbard model at half-filling. Results provide strong evidence that the NN correctly learns an order parameter describing the quantum transition. Moreover, we demonstrate that influence functions not only allow to check that the network, trained to recognize known quantum phases, can predict new unknown ones but even guide physicists in understanding patterns responsible for the phase transition. This method requires no a priori knowledge on the order parameter, the system itself, or even the architecture of the ML model.

We propose a reinforcement learning (RL) scheme for feedback quantum control within the quantum approximate optimization algorithm (QAOA). QAOA requires a variational minimization for states constructed by applying a sequence of unitary operators, depending on parameters living in a highly dimensional space. We reformulate such a minimum search as a learning task, where a RL agent chooses the control parameters for the unitaries, given partial information on the system. We show that our RL scheme learns a policy converging to the optimal adiabatic solution for QAOA found by Mbeng et al. arXiv:1906.08948 for the translationally invariant quantum Ising chain. In presence of disorder, we show that our RL scheme allows the training part to be performed on small samples, and transferred successfully on larger systems. Finally, we discuss QAOA on the p-spsin model and how its robustness is enhanced by reinforce learning. Despite the possibility of finding the ground state with polynomial resources even in the presence of a first order phase transition, local optimizations in the p-spsin model suffer from the presence of many minima in the energy landscape. RL helps to find regular solutions that can be generalized to larger systems and make the optimization less sensitive to noise.

References

https://arxiv.org/abs/2003.07419

https://arxiv.org/abs/2004.12323

I’ll talk about two independent works on classical and quantum neural networks connected by information theory. In the first part of the talk, I’ll treat sequence models as one-dimensional classical statistical mechanical systems and analyze the scaling behavior of mutual information. I'll provide a new perspective on why recurrent neural networks are not good at natural language processing. In the second part of the talk, I’ll study information scrambling dynamics when quantum neural networks are trained by classical gradient descent algorithm. For many problems, this hybrid quantum-classical training process consists of two stages where information scrambles very differently in the network. 

Meta-learning involves learning mathematical devices using problem instances as training data. In this talk, we first describe recent meta-learning approaches involving the learning of objects such as: initial weights, parameterized losses, hyper-parameter search strategies, and samplers. We then discuss learned optimizers in further detail and their applications towards optimizing variational circuits. This talk also covers some lessons learned starting a spin-off from academia.

Solving classical and quantum physics many-body systems are amongst the hardest problems in the natural sciences, but also of fundamental importance for applications such as material and drug design. In this talk, I will give a an overview of fundamental physics problems at multiple time- and lengthscales and describe deep learning methods to address them: 1) solving the quantum-chemical electronic Schrödinger equation with deep variational Monte Carlo, 2) learning to coarse-grain many-body systems, and 3) sampling equilibrium states of classical many-body systems with generative learning.

So far artificial neural networks have been applied to discover phase diagrams in many different physical models. However, none of these studies have revealed any fundamentally new physics. A major problem is that these neural networks are mainly considered as black box algorithms. On the journey to detect new physics it is important to interpret what artificial neural networks learn. On the one hand this allows us to judge whether to trust the results, and on the other hand this can give us insight to possible new physics. In this talk I will 
discuss applications to different models where we successfully interpreted what was learned by the neural networks.