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Dr. Clara Wanjura

Group leader

  • Head of research group Topology and neuromorphic computing
  • Theory Division
  • Room A.2.110
  • Phone +49 9131 7133 420
  • Email

Since December 2024, Clara Wanjura is leading her own research group (more details can be found below or on the group website).

2025

Unifying framework for non-Hermitian and Hermitian topology in driven-dissipative systems

Unifying framework for non-Hermitian and Hermitian topology in driven-dissipative systems

Clara C. Wanjura, Andreas Nunnenkamp

arXiv 2509.19433 (2025) | Preprint | PDF

Recently, a one-to-one correspondence between non-trivial non-Hermitian topology and directional amplification has been demonstrated, theoretically and experimentally, for the case of one complex band. Here, we extend our framework to multiple bands and higher spatial dimension. This proves to be far from trivial. Building on the singular value decomposition, we introduce a new quantity that we dub generalised singular spectrum (GSS). The GSS allows us to define physically meaningful bands related to the system's scattering behaviour and to define invariants for novel notions of point gaps (non-Hermitian topology) and line gaps (Hermitian-like topology), respectively. For both invariants, we prove a bulk-boundary correspondence and show that they give rise to two different kinds of topological edge modes. We illustrate our results with a 1D non-Hermitian Su-Schrieffer-Heeger (SSH) model and a 2D non-Hermitian model that features corner-to-corner amplification. Our work is relevant for many state-of-the-art experimental platforms and it sets the stage for applications such as novel directional amplifiers and non-reciprocal sensors.

Training of physical neural networks

Training of physical neural networks

Ali Momeni, Babak Rahmani, Benjamin Scellier, Logan G. Wright, Peter L. McMahon, Clara C. Wanjura, Yuhang Li, Anas Skalli, Natalia G. Berloff, et al.

Nature 645 53-61 (2025) | Journal

Physical neural networks (PNNs) are a class of neural-like networks that make use of analogue physical systems to perform computations. Although at present confined to small-scale laboratory demonstrations, PNNs could one day transform how artificial intelligence (AI) calculations are performed. Could we train AI models many orders of magnitude larger than present ones? Could we perform model inference locally and privately on edge devices? Research over the past few years has shown that the answer to these questions is probably “yes, with enough research”. Because PNNs can make use of analogue physical computations more directly, flexibly and opportunistically than traditional computing hardware, they could change what is possible and practical for AI systems. To do this, however, will require notable progress, rethinking both how AI models work and how they are trained—primarily by considering the problems through the constraints of the underlying hardware physics. To train PNNs, backpropagation-based and backpropagation-free approaches are now being explored. These methods have various trade-offs and, so far, no method has been shown to scale to large models with the same performance as the backpropagation algorithm widely used in deep learning today. However, this challenge has been rapidly changing and a diverse ecosystem of training techniques provides clues for how PNNs may one day be used to create both more efficient and larger-scale realizations of present-scale AI models.

Artificial discovery of lattice models for wave transport

Artificial discovery of lattice models for wave transport

Jonas Landgraf, Clara C. Wanjura, Vittorio Peano, Florian Marquardt

arXiv 2508.10693 (2025) | Preprint | PDF

Wave transport devices, such as amplifiers, frequency converters, and nonreciprocal devices, are essential for modern communication, signal processing, and sensing applications. Of particular interest are traveling wave setups, which offer excellent gain and bandwidth properties. So far, the conceptual design of those devices has relied on human ingenuity. This makes it difficult and time-consuming to explore the full design space under a variety of constraints and target functionalities. In our work, we present a method which automates this challenge. By optimizing the discrete and continuous parameters of periodic coupled-mode lattices, our approach identifies the simplest lattices that achieve the target transport functionality, and we apply it to discover new schemes for directional amplifiers, isolators, and frequency demultiplexers. Leveraging automated symbolic regression tools, we find closed analytical expressions that facilitate the discovery of generalizable construction rules. Moreover, we utilize important conceptual connections between the device transport properties and non-Hermitian topology. The resulting structures can be implemented on a variety of platforms, including microwave, optical, and optomechanical systems. Our approach opens the door to extensions like the artificial discovery of lattice models with desired properties in higher dimensions or with nonlinear interactions.

Training nonlinear optical neural networks with Scattering Backpropagation

Training nonlinear optical neural networks with Scattering Backpropagation

Nicola Dal Cin, Florian Marquardt, Clara C. Wanjura

arXiv 2508.11750 (2025) | Preprint | PDF

As deep learning applications continue to deploy increasingly large artificial neural networks, the associated high energy demands are creating a need for alternative neuromorphic approaches. Optics and photonics are particularly compelling platforms as they offer high speeds and energy efficiency. Neuromorphic systems based on nonlinear optics promise high expressivity with a minimal number of parameters. However, so far, there is no efficient and generic physics-based training method allowing us to extract gradients for the most general class of nonlinear optical systems. In this work, we present Scattering Backpropagation, an efficient method for experimentally measuring approximated gradients for nonlinear optical neural networks. Remarkably, our approach does not require a mathematical model of the physical nonlinearity, and only involves two scattering experiments to extract all gradient approximations. The estimation precision depends on the deviation from reciprocity. We successfully apply our method to well-known benchmarks such as XOR and MNIST. Scattering Backpropagation is widely applicable to existing state-of-the-art, scalable platforms, such as optics, microwave, and also extends to other physical platforms such as electrical circuits.

Magnetic tunnel junctions driven by hybrid optical-electrical signals as a flexible neuromorphic computing platform

Magnetic tunnel junctions driven by hybrid optical-electrical signals as a flexible neuromorphic computing platform

Felix Oberbauer, Tristan Joachim Winkel, Tim Böhnert, Clara C. Wanjura, Marcel S. Claro, Luana Benetti, Ihsan Çaha, Francis Leonard Deepak, Farshad Moradi, et al.

Communications Physics 8 329 (2025) | Journal | PDF

Magnetic tunnel junctions (MTJs) offer a promising pathway toward energy-efficient neuromorphic computing due to their nanoscale footprint, nonvolatile switching, and intrinsic nonlinear dynamics that emulate synaptic behavior. However, generating large thermoelectric voltages with bias-tunable nonlinearities for neuromorphic use remains largely unexplored. Here, we introduce a hybrid opto-electrical excitation scheme—combining pulsed laser heating with DC bias—to drive MTJs into the nonlinear bias-enhanced tunnel magneto-Seebeck regime. This regime yields thermoelectric voltages in the tens of millivolts with a strong contrast between magnetic states, while also revealing spiking and double-switching behavior linked to vortex dynamics and fixed-layer depinning. The thermovoltage exhibits cubic dependence on bias current, enabling tunable synaptic weights. We simulate a single-layer neuromorphic network using optically encoded inputs and achieve 93.7% classification accuracy on handwritten digits. These results establish hybrid-driven MTJs as a compact, CMOS-compatible platform for neuromorphic computing, integrating optical input with spintronic functionality.

Quantum equilibrium propagation for efficient training of quantum systems based on Onsager reciprocity

Quantum equilibrium propagation for efficient training of quantum systems based on Onsager reciprocity

Clara C. Wanjura, Florian Marquardt

Nature Communications 16 6595 (2025) | Journal | PDF

The widespread adoption of machine learning and artificial intelligence in all branches of science and technology creates a need for energy-efficient, alternative hardware. While such neuromorphic systems have been demonstrated in a wide range of platforms, it remains an open challenge to find efficient and general physics-based training approaches. Equilibrium propagation (EP), the most widely studied approach, has been introduced for classical energy-based models relaxing to an equilibrium. Here, we show a direct connection between EP and Onsager reciprocity and exploit this to derive a quantum version of EP. For an arbitrary quantum system, this can now be used to extract training gradients with respect to all tuneable parameters via a single linear response experiment. We illustrate this new concept in examples in which the input or the task is of quantum-mechanical nature, e.g., the recognition of many-body ground states, phase discovery, sensing, and phase boundary exploration. Quantum EP may be used to solve challenges such as quantum phase discovery for Hamiltonians which are classically hard to simulate or even partially unknown. Our scheme is relevant for a variety of quantum simulation platforms such as ion chains, superconducting circuits, Rydberg atom tweezer arrays and ultracold atoms in optical lattices.

Massive quantum systems as interfaces of quantum mechanics and gravity

Massive quantum systems as interfaces of quantum mechanics and gravity

Sougato Bose, Ivette Fuentes, Andrew A. Geraci, Saba Mehsar Khan, Sofia Qvarfort, Markus Rademacher, Muddassar Rashid, Marko Toroš, Hendrik Ulbricht, et al.

Reviews of Modern Physics 97 015003 (2025) | Journal

The traditional view from particle physics is that quantum-gravity effects should become detectable only at extremely high energies and small length scales. Owing to the significant technological challenges involved, there has been limited progress in identifying experimentally detectable effects that can be accessed in the foreseeable future. However, in recent decades, the size and mass of quantum systems that can be controlled in the laboratory have reached unprecedented scales, enabled by advances in ground-state cooling and quantum-control techniques. Preparations of massive systems in quantum states pave the way for the exploration of a low-energy regime in which gravity can be both sourced and probed by quantum systems. Such approaches constitute an increasingly viable alternative to accelerator-based, laser-interferometric, torsion-balance, and cosmological tests of gravity. This review provides an overview of proposals where massive quantum systems act as interfaces between quantum mechanics and gravity. Conceptual difficulties in the theoretical description of quantum systems in the presence of gravity are discussed, tools for modeling massive quantum systems in the laboratory are reviewed, and an overview of the current state-of-the-art experimental landscape is provided. Proposals covered in this review include precision tests of gravity, tests of gravitationally induced wave-function collapse and decoherence, and gravity-mediated entanglement. The review concludes with an outlook and a summary of the key questions raised.

A central theme of my research is the exploration of coupled mode systems such as optical, optomechanical and photonic systems, and how to harness them for science and quantum technologies. Specifically, I am working along two main lines of research: scattering phenomena associated with non-Hermitian topology enabling devices such as topological, directional amplifiers and sensors; and neuromorphic computing.

Academic Background:

  • 12/2025 – present:  Max Planck Research Group Leader, Max Planck Institute for the Science of Light
  • 12/2024 – 11/2025: Minerva Fast Track Research Group Leader, Max Planck Institute for the Science of Light
  • 11/2022 – 12/2024: Postdoctoral fellow, Max Planck Institute for the Science of Light
  • 10/2018 – 07/2022: PhD Student, Cavendish Laboratory, University of Cambridge
  • 10/2017 – 03/2018: Visiting Student, Cavendish Laboratory, University of Cambridge
  • 10/2016 – 07/2018: Master’s Studies in Physics, Ulm University
  • 10/2013 – 10/2016: Bachelor’s Studies in Physics, Ulm University

 

Selected Prizes and Awards:

Please find my detailed CV here.

 

About the Max Planck Research Group

Advances in engineering optical and hybrid systems allow us to realise more and more complex physical systems. It is therefore an exciting time for theoretical physicists to devise coupled multimode systems that can be harnessed for quantum science and technological applications. In this new Max Planck Research Group, we are exploring two directions fuelled by these advances.

 

Topology in driven-dissipative quantum systems

Topology is a powerful principle for understanding many physically very different complex systems and has been a major research theme in condensed matter physics. More recently, a notion of topology in systems experiencing gain and loss has been investigated, sparking the field of non-Hermitian topology. Non-Hermitian topology can lead to a variety of phenomena that have no Hermitian counterpart. In particular, we have previously shown that non-trivial non-Hermitian topology is in one-to-one correspondence with the phenomenon of directional amplification, i.e, signals are amplified in one direction but blocked or attenuated in reverse. Such unidirectionality is highly sought-after for quantum information processing applications. We recently collaborated with Ewold Verhagen's group at AMOLF, Amsterdam, and demonstrated topological amplification in an optomechanical experiment. Furthermore, non-Hermitian topology is a resource for sensing. In the group, we are continuing to explore how the unique properties of non-Hermitian, topological systems can be harnessed for technological applications such as signal routing, non-reciprocity and directional amplification, sensing, as well as multi-partite entanglement generation.

Non-trivial, non-Hermitian topology is in one-to-one correspondence with directional amplification

Further reading:

C. C. Wanjura, M. Brunelli, A. Nunnenkamp. Topological framework for directional amplification in driven-dissipative cavity arrays. Nature Communications 11, 3149 (2020).

C. C. Wanjura, M. Brunelli, A. Nunnenkamp. Correspondence between non-Hermitian topology and directional amplification in the presence of disorder. Phys. Rev. Lett. 127, 213601 (2021).

M. Brunelli, C. C. Wanjura, A. Nunnenkamp. Restoration of the non-Hermitian bulk-boundary correspondence via topological amplification. SciPost Phys. 15, 173 (2023). 

C. C. Wanjura, J. J. Slim, J. del Pino, M. Brunelli, E. Verhagen, A. Nunnenkamp. Quadrature nonreciprocity in bosonic networks without breaking time-reversal symmetry. Nature Physics 19, 1429–1436 (2023).

J. J. Slim, C. C. Wanjura, M. Brunelli, J. del Pino, A. Nunnenkamp, E. Verhagen. Optomechanical realization of the bosonic Kitaev chain. Nature 627, 767–771 (2024).

 

You can learn more on non-Hermitian physics in this online seminar series.

 

Neuromorphic Computing

With the exponentially growing trend in digital neural network sizes and the associated energy consumption of machine learning applications, there is a need for alternative hardware approaches. In response to this demand, neuromorphic computing aims to replace our digital neural networks with physical systems. Indeed, optical or photonic systems can be engineered to perform the desired machine learning tasks and are a promising platform for neuromorphic computing as they offer high computation speeds at a low energy consumption. However, realising the necessary non-linear computation had previously been challenging. We made an important step to solving this challenge by developing a new framework for performing non-linear computation with purely linear scattering (check out our video below). This approach can be implemented in essentially any linear system with access to a sufficient number of tunable parameters, in particular, in existing scalable state-of-the-art platforms such as optics, microwave and electrical circuits and integrated photonics. Another very important aspect is physical training, i.e., physical access to gradients. It has been shown that in-silico training, i.e. training in simulation, does generally not transfer well to the experiment since even small discrepancies between model and reality can lead to a disastrous accumulation of errors during training. Therefore, we are looking into new training approaches for neuromorphic systems.

Fully non-linear neuromorphic system based on linear wave propagation

Learn more on non-linear computation with linear wave scattering in this video:

Further reading:

C. C. Wanjura, F. Marquardt. Fully non-linear neuromorphic computing with linear wave scattering. Nature Physics (2024).

Q. Wang, C. C. Wanjura, F. Marquardt. Training coupled phase oscillators as a neuromorphic platform using equilibrium propagation. arXiv:2402.08579 (2024).

A. Momeni, B. Rahmani et al. Training of physical neural networks. arxiv:2406.03372 (2024).

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