# Research

## Computer-Inspired Quantum Experiments

Some years ago, we wanted to investigate experimentally a completelely new type of entanglement - namely high-dimensional multipartite entangled photons. Unfortunately, even after several weeks of investigating the experimental configurations, we did not find any feasible way to do it. At that point I thought we need a very different way to solve that question and I wrote a computer program which helps us designing quantum experiments. The program has found the solution within a few hours, which we human scientists have not found for several weeks. Interestingly, the solutions from the program are very different than what a human scientist usually would come up with. Numerous experimental setups have been build experimentally, and the approach has even led to new scientific ideas and concepts. This multi-year story has been prominently featured in an **Scientific American** article in July 2021 and we described it in **Nature Review Physics** in September 2020.

With this algorithm, we were able to successfully implement many experiments in our labs that we otherwise might not have found a solution to. Among them, Melvin's solutions has led to

- Multi-photon entanglement in high dimensions
- Experimental GHZ Entanglement beyond Qubits
- Cyclic transformation of orbital angular momentum modes
- High-Dimensional Single-Photon Quantum Gates
- Generation of the complete four-dimensional Bell basis
- Gouy Phase Radial Mode Sorter for Light
- First high-dimensional GHZ state in a superconducting quantum computer

Other experiments based computer-inspired proposals are being built right now.

For me, the **most surprising and notable result** was that the solutions of the computer gave us completely **new ideas** for quantum technologies and quantum experiments:

- Entanglement by Path Identity

This is a concept for the controlled generation of entanglement for multi-photonic and high-dimensional systems. After dozens of hours investigating one surprisingly odd solution from my program, I discovered that the program uses a*trick*that I have never seen before, and that we can immediately generalize to many cases. This article describes the generalizations: - Quantum Experiments and Graphs and Quantum Experiments and Graphs II

In a certain solution from the computer program, very odd number sequences appeared. After investigating them for some time, we put them into the Online Encyclopedia for Integer Sequences (OEIS) and indeed found exactly one entry that pointed directly to graph theory. That link is quite fruitful so far, and we are still in an early stage of investigating the consequences. One consequence of the link is a new, never described form of multi-photonic quantum interference. This has very recently (March 2021) been experimentally observed for the first time in a photonic chip. - New type of creating heralded photonic entanglement by destructively quantum interfering the vacuum contribution.

Algorithmically we have investigated numerous approaches:

**Melvin**[GitHub] (2016) - an algorithm which found most of the experimental designs and concepts mentioned above. Uses a toolbox of all optical elements in a lab. A machine learning routine can extend the toolbox to speed-up computation significantly, and automatic simplification of setups.- Reinforcement learning (2018) - in collaboration with Hans Briegel's group. While not faster than Melvin, it can learn to automatically simplify (as a consequence, more complex to apply).
- LSTM deep neural nets (2019) - in collaboration with Sepp Hochreiter's team. Can predict entanglement structure directly from setup (precursor to generative model)
**Theseus**[GitHub] (2021) - graph based representation, orders of magnitude faster than previous approaches. Can*extract the conceptual cores of solutions*.- Deep Generative Model (2021) - an unsupervised variational autoencoder, we can 100% interpret its internal latent space representation.
- Klaus [GitHub] (2021) - the first logical Artificial Intelligence design method for quantum physics. Translates design-task to boolean equation which is solved with highly efficient SAT solvers.

Because of these new insights inspired by a computer program, I am convinced that one can find many more scientific ideas using computer programs. While a pure, fully automated artificial scientist may still be a long way off, these results show that computer-inspired creative ideas in science are already possible at this moment. I find that incredibly exciting.

# Computer-Inspired Science via Semantic Networks

What can computer algorithms do with access to a huge body of scientific knowledge?

I build a semantic network of Quantum Physics, using Wikipedia, 13 quantum physics books and 750.000 papers (from arXiv and APS), in order to predict and suggest interesting future research developments. For suggesting surprising, out-of-the-box seeds of ideas, I use network theoretical tools to identify outliers. These concepts have unique locations in the semantic network, which make them unusual. In conjunction with personalisation of suggestions (by identifying a scientists research agends from their past publications), this method hopefully allows for suggesting research directions, which a human researcher might not have thought about.

In the very far future, one could imagine that clever computer algorithm with access to structured scientific knowledge could potentially point out new links between different fields or discover contradictions within the body of knowledge. See the corresponding GitHub codes.

To advance this project, we created a very similar semantic network for the field of Machine Learning and Artificial Intelligence. There, the** number of papers grow exponentially**, making research in those fields highly challenging. To confront this challenge, and learn in general how to deal with predictions in semantic networks, we initialized the **ML competition Science4Cast**, with the goal to predict future states in these exponentially growing networks.

# Computer-designed Structures using Deep Learning with Interpretability

Inverse design algorithms for the discovery and design of novel, functional molecules has progressed enormously in the last few years. My goal in these research projects is to learn various technologies developed by ML for chemistry, and bring them back to the world of (quantum) physics.

In the lab of Alan Aspuru-Guzik, we developed new ways for discovering potential useful molecules. I am mainly interested in the following: Let's say we were able to train a neural network to predict properties or suggest candidate molecules - better than a human could do it. Then - What did this algorithm learn? Can we extract scientific knowledge? An interesting result in a different field has been shown by Raban Iten and Tony Metger in the group of Renato Renner (see my APS Viewpoint or a Nature News story with a short statement of myself). They were able to extract the heliocentric world view as an internal representation of a deep neural network. Can we do this for molecules (or quantum experiments)? As a first step, we developed a robust representation of molecules (SELFIES), which might simplify the interpretation of the latent space. We made the first steps towards this direction by exploiting an idea from computer vision, and generated a Deep Molecular Dreaming algorithms that leads to interpretable results.

Furthermore, Science is not necessarily goal-driven. How would an algorithm explore the universe of molecules, if it was not goal driven, but maybe curiosity-driven? We made the first steps towards curious artificial agents in the chemical universe.

# Experimental High-Dimensional Quantum Entanglement

Spatial Modes of Photons (such as Laguerre-Gaussian modes which carry orbital-angular momentum (OAM)) can be very high-dimensional entanglement. One important question is how such entanglement can be certified. Together with our collaborator and entanglement expert Marcus Huber, we were able to certify that the two-photonic state was entangled at least in 100x100 dimensions. This was possible by applying a novel type of entanglement witness, and performing roughly 200.000 measurements which resulted in 750 million detected photon pairs.

High-dimensional quantum entanglement can also be observed in other spatial modes such as Ince-Gaussian modes. One particularly nice set of modes are Ince-Gauss modes, because they are continuous transition between Laguerre-Gaussian and Hermit-Gaussian modes, and very interesting vortex behavior (such as splitting of vortices and generation of new vortex pairs). In my first experiment during the Master thesis, I investigated these structures and their entanglement experimentally.

Recently we extended this research towards supercondicting quantum computers. See our Review of high-dimensional entanglement in **Nature Review Physics**.

# Contact

**Marquardt Division**

**Krenn Junior Research Group**

MPI for the Science of Light

Staudtstr. 2

D-91058 Erlangen, Germany

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