Search

Abstract Driven by human ingenuity and creativity, the discovery of super-resolution techniques, which circumvent the classical diffraction limit of light, represent a leap in optical microscopy. However, the vast space encompassing all possible experimental configurations suggests that some powerful concepts and techniques might have not been discovered yet, and might never be with a human-driven direct design approach. Thus, AI-based exploration techniques could provide enormous benefit, by exploring this space in a fast, unbiased way. We introduce XLuminA, an open-source computational framework developed using JAX, a high-performance computing library in Python. XLuminA offers enhanced computational speed enabled by JAX’s accelerated linear algebra compiler (XLA), just-in-time compilation, and its seamlessly integrated automatic vectorization, automatic differentiation capabilities and GPU compatibility. XLuminA demonstrates a speed-up of 4 orders of magnitude compared to well-established numerical optimization methods. We showcase XLuminA’s potential by re-discovering three foundational experiments in advanced microscopy, and identifying an unseen experimental blueprint featuring sub-diffraction imaging capabilities. This work constitutes an important step in AI-driven scientific discovery of new concepts in optics and advanced microscopy.

As the field of quantum physics evolves, researchers naturally form subgroups focusing on specialized problems. While this encourages in-depth exploration, it can limit the exchange of ideas across structurally similar problems in different subfields. To encourage cross-talk among these different specialized areas, data-driven approaches using machine learning have recently shown promise to uncover meaningful connections between research concepts, promoting cross-disciplinary innovation. Current state-of-the-art approaches represent concepts using knowledge graphs and frame the task as a link prediction problem, where connections between concepts are explicitly modeled. In this work, we introduce a novel approach based on dynamic word embeddings for concept combination prediction. Unlike knowledge graphs, our method captures implicit relationships between concepts, can be learned in a fully unsupervised manner, and encodes a broader spectrum of information. We demonstrate that this representation enables accurate predictions about the co-occurrence of concepts within research abstracts over time. To validate the effectiveness of our approach, we provide a comprehensive benchmark against existing methods and offer insights into the interpretability of these embeddings, particularly in the context of quantum physics research. Our findings suggest that this representation offers a more flexible and informative way of modeling conceptual relationships in scientific literature.

Usually, observation of quantum interference in a non-local scenario (that is, when Alice’s measurement settings and Bob’s outcomes are space-like separated) relies on entanglement. Here, the authors experimentally show four-photon frustrated interference originating from the sources’ indistinguishability, without the need for entanglement.

The search for macroscopic quantum phenomena is a fundamental pursuit in quantum mechanics. It allows us to test the limits of quantum physics and provides new avenues for exploring the interplay between quantum mechanics and relativity. In this work, we introduce a novel approach to generate macroscopic quantum systems by demonstrating that the creation process of a quantum system can span a macroscopic distance. Specifically, we generate photon pairs in a coherent superposition of two origins separated by up to 70 meters. This new approach not only provides an exciting opportunity for foundational experiments in quantum physics, but also has practical applications for high-precision measurements of distributed properties such as pressure and humidity of air or gases.

Despite their promise to facilitate new scientific discoveries, the opaqueness of neural networks presents a challenge in interpreting the logic behind their findings. Here, we use a eXplainable-AI technique called inception or deep dreaming , which has been invented in machine learning for computer vision. We use this technique to explore what neural networks learn about quantum optics experiments. Our story begins by training deep neural networks on the properties of quantum systems. Once trained, we ‘invert’ the neural network—effectively asking how it imagines a quantum system with a specific property, and how it would continuously modify the quantum system to change a property. We find that the network can shift the initial distribution of properties of the quantum system, and we can conceptualize the learned strategies of the neural network. Interestingly, we find that, in the first layers, the neural network identifies simple properties, while in the deeper ones, it can identify complex quantum structures and even quantum entanglement. This is in reminiscence of long-understood properties known in computer vision, which we now identify in a complex natural science task. Our approach could be useful in a more interpretable way to develop new advanced AI-based scientific discovery techniques in quantum physics.

Generative Artificial Intelligence (AI) models can propose solutions to scientific problems beyond human capability. To truly make conceptual contributions, researchers need to be capable of understanding the AI-generated structures and extracting the underlying concepts and ideas. When algorithms provide little explanatory reasoning alongside the output, scientists have to reverse-engineer the fundamental insights behind proposals based solely on examples. This task can be challenging as the output is often highly complex and thus not immediately accessible to humans. In this work we show how transferring part of the analysis process into an immersive virtual reality (VR) environment can assist researchers in developing an understanding of AI-generated solutions. We demonstrate the usefulness of VR in finding interpretable configurations of abstract graphs, representing Quantum Optics experiments. Thereby, we can manually discover new generalizations of AI-discoveries as well as new understanding in experimental quantum optics. Furthermore, it allows us to customize the search space in an informed way—as a human-in-the-loop—to achieve significantly faster subsequent discovery iterations. As concrete examples, with this technology, we discover a new resource-efficient 3-dimensional entanglement swapping scheme, as well as a 3-dimensional 4-particle Greenberger–Horne–Zeilinger-state analyzer. Our results show the potential of VR to enhance a researcher’s ability to derive knowledge from graph-based generative AI. This type of AI is a widely used abstract data representation in various scientific fields.

Photons are the physical system of choice for performing experimental tests of the foundations of quantum mechanics. Furthermore, photonic quantum technology is a main player in the second quantum revolution, promising the development of better sensors, secure communications, and quantum-enhanced computation. These endeavors require generating specific quantum states or efficiently performing quantum tasks. The design of the corresponding optical experiments was historically powered by human creativity but is recently being automated with advanced computer algorithms and artificial intelligence. While several computer-designed experiments have been experimentally realized, this approach has not yet been widely adopted by the broader photonic quantum optics community. The main roadblocks consist of most systems being closed-source, inefficient, or targeted to very specific use-cases that are difficult to generalize. Here, we overcome these problems with a highly-efficient, open-source digital discovery framework PyTheus, which can employ a wide range of experimental devices from modern quantum labs to solve various tasks. This includes the discovery of highly entangled quantum states, quantum measurement schemes, quantum communication protocols, multi-particle quantum gates, as well as the optimization of continuous and discrete properties of quantum experiments or quantum states. PyTheus produces interpretable designs for complex experimental problems which human researchers can often readily conceptualize. PyTheus is an example of a powerful framework that can lead to scientific discoveries – one of the core goals of artificial intelligence in science. We hope it will help accelerate the development of quantum optics and provide new ideas in quantum hardware and technology.

Logic Artificial Intelligence (AI) is a subfield of AI where variables can take two defined arguments, True or False, and are arranged in clauses that follow the rules of formal logic. Several problems that span from physical systems to mathematical conjectures can be encoded into these clauses and solved by checking their satisfiability (SAT). In contrast to machine learning approaches where the results can be approximations or local minima, Logic AI delivers formal and mathematically exact solutions to those problems. In this work, we propose the use of logic AI for the design of optical quantum experiments. We show how to map into a SAT problem the experimental preparation of an arbitrary quantum state and propose a logic-based algorithm, called Klaus, to find an interpretable representation of the photonic setup that generates it. We compare the performance of Klaus with the state-of-the-art algorithm for this purpose based on continuous optimization. We also combine both logic and numeric strategies to find that the use of logic AI significantly improves the resolution of this problem, paving the path to developing more formal-based approaches in the context of quantum physics experiments.

We demonstrate how machine learning is able to model experiments in quantum physics. Quantum entanglement is a cornerstone for upcoming quantum technologies, such as quantum computation and quantum cryptography. Of particular interest are complex quantum states with more than two particles and a large number of entangled quantum levels. Given such a multiparticle high-dimensional quantum state, it is usually impossible to reconstruct an experimental setup that produces it. To search for interesting experiments, one thus has to randomly create millions of setups on a computer and calculate the respective output states. In this work, we show that machine learning models can provide significant improvement over random search. We demonstrate that a long short-term memory (LSTM) neural network can successfully learn to model quantum experiments by correctly predicting output state characteristics for given setups without the necessity of computing the states themselves. This approach not only allows for faster search, but is also an essential step towards the automated design of multiparticle high-dimensional quantum experiments using generative machine learning models.

Artificial intelligence (AI) is a potentially disruptive tool for physics and science in general. One crucial question is how this technology can contribute at a conceptual level to help acquire new scientific understanding. Scientists have used AI techniques to rediscover previously known concepts. So far, no examples of that kind have been reported that are applied to open problems for getting new scientific concepts and ideas. Here, we present Theseus, an algorithm that can provide new conceptual understanding, and we demonstrate its applications in the field of experimental quantum optics. To do so, we make four crucial contributions. (i) We introduce a graph-based representation of quantum optical experiments that can be interpreted and used algorithmically. (ii) We develop an automated design approach for new quantum experiments, which is orders of magnitude faster than the best previous algorithms at concrete design tasks for experimental configuration. (iii) We solve several crucial open questions in experimental quantum optics which involve practical blueprints of resource states in photonic quantum technology and quantum states and transformations that allow for new foundational quantum experiments. Finally, and most importantly, (iv) the interpretable representation and enormous speed-up allow us to produce solutions that a human scientist can interpret and gain new scientific concepts from outright. We anticipate that Theseus will become an essential tool in quantum optics for developing new experiments and photonic hardware. It can further be generalized to answer open questions and provide new concepts in a large number of other quantum physical questions beyond quantum optical experiments. Theseus is a demonstration of explainable AI (XAI) in physics that shows how AI algorithms can contribute to science on a conceptual level.

The discovery of novel materials and functional molecules can help to solve some of society’s most urgent challenges, ranging from efficient energy harvesting and storage to uncovering novel pharmaceutical drug candidates. Traditionally matter engineering–generally denoted as inverse design–was based massively on human intuition and high-throughput virtual screening. The last few years have seen the emergence of significant interest in computer-inspired designs based on evolutionary or deep learning methods. The major challenge here is that the standard strings molecular representation SMILES shows substantial weaknesses in that task because large fractions of strings do not correspond to valid molecules. Here, we solve this problem at a fundamental level and introduce S ELFIES (SELF-referencIng Embedded Strings), a string-based representation of molecules which is 100% robust. Every S ELFIES string corresponds to a valid molecule, and S ELFIES can represent every molecule. S ELFIES can be directly applied in arbitrary machine learning models without the adaptation of the models; each of the generated molecule candidates is valid. In our experiments, the model’s internal memory stores two orders of magnitude more diverse molecules than a similar test with SMILES. Furthermore, as all molecules are valid, it allows for explanation and interpretation of the internal working of the generative models.

Beams of light with a large topological charge significantly change their spatial structure when they are focused strongly. Physically, it can be explained by an emerging electromagnetic field component in the direction of propagation, which is neglected in the simplified scalar wave picture in optics. Here we ask: is this a specific photonic behavior, or can similar phenomena also be predicted for other species of particles? We show that the same modification of the spatial structure exists for relativistic electrons as well as for focused gravitational waves. However, this is for different physical reasons: for electrons, which are described by the Dirac equation, the spatial structure changes due to a spin–orbit coupling in the relativistic regime. In gravitational waves described with linearized general relativity, the curvature of space–time between the transverse and propagation direction leads to the modification of the spatial structure. Thus, this universal phenomenon exists for both massive and massless elementary particles with spin 1/2, 1 and 2. It would be very interesting whether other types of particles such as composite systems (neutrons or C _60 ) or neutrinos show a similar behavior and how this phenomenon can be explained in a unified physical way.

We derive a framework for quantifying entanglement in multipartite and high dimensional systems using only correlations in two unbiased bases. We furthermore develop such bounds in cases where the second basis is not characterized beyond being unbiased, thus enabling entanglement quantification with minimal assumptions. Furthermore, we show that it is feasible to experimentally implement our method with readily available equipment and even conservative estimates of physical parameters.

Light beams can carry a discrete, in principle unbounded amount of angular momentum. Examples of such beams, the Laguerre–Gauss modes, are frequently expressed as solutions of the paraxial wave equation. The paraxial wave equation is a small-angle approximation of the Helmholtz equation, and is commonly used in beam optics. There, the Laguerre–Gauss modes have well-defined orbital angular momentum (OAM). The paraxial solutions predict that beams with large OAM could be used to resolve arbitrarily small distances—a dubious situation. Here we show how to solve that situation by calculating the properties of beams free from the paraxial approximation. We find the surprising result that indeed one can resolve smaller distances with larger OAM, although with decreased visibility. If the visibility is kept constant (for instance at the Rayleigh criterion, the limit where two points are reasonably distinguishable), larger OAM does not provide an advantage. The drop in visibility is due to a field in the direction of propagation, which is neglected within the paraxial limit. Our findings have implications for imaging techniques and raise questions on the difference between photonic and matter waves, which we briefly discuss in the conclusion.

The spatial modes of photons are one realization of a QuDit, a quantum system that is described in a D -dimensional Hilbert space. In order to perform quantum information tasks with QuDits, a general class of D -dimensional unitary transformations is needed. Among these, cyclic transformations are an important special case required in many high-dimensional quantum communication protocols. In this paper, we experimentally demonstrate a cyclic transformation in the high-dimensional space of photonic orbital angular momentum (OAM). Using simple linear optical components, we show a successful four-fold cyclic transformation of OAM modes. Interestingly, our experimental setup was found by a computer algorithm. In addition to the four-cyclic transformation, the algorithm also found extensions to higher-dimensional cycles in a hybrid space of OAM and polarization. Besides being useful for quantum cryptography with QuDits, cyclic transformations are key for the experimental production of high-dimensional maximally entangled Bell-states.

Transverse spatial modes of light offer a large state-space with interesting physical properties. For exploiting these special modes in future long-distance experiments, the modes will have to be transmitted over turbulent free-space links. Numerous recent lab-scale experiments have found significant degradation in the mode quality after transmission through simulated turbulence and consecutive coherent detection. Here, we experimentally analyze the transmission of one prominent class of spatial modes—orbital-angular momentum (OAM) modes—through 3 km of strong turbulence over the city of Vienna. Instead of performing a coherent phase-dependent measurement, we employ an incoherent detection scheme, which relies on the unambiguous intensity patterns of the different spatial modes. We use a pattern recognition algorithm (an artificial neural network) to identify the characteristic mode patterns displayed on a screen at the receiver. We were able to distinguish between 16 different OAM mode superpositions with only a ∼1.7% error rate and to use them to encode and transmit small grayscale images. Moreover, we found that the relative phase of the superposition modes is not affected by the atmosphere, establishing the feasibility for performing long-distance quantum experiments with the OAM of photons. Our detection method works for other classes of spatial modes with unambiguous intensity patterns as well, and can be further improved by modern techniques of pattern recognition.