Reinforcement learning (RL) has proven itself as a powerful tool for the discovery of quantum circuits and quantum protocols. We have recently shown that including composite quantum gates -- referred to as ``gadgets'' -- in the action space of RL agents substantially enhances the RL performance in the context of quantum error correction. However, up to now the gadgets themselves had to be constructed manually. In this paper, we suggest an algorithm for the automated discovery of new gadgets and families of related gadgets. The algorithm is based on the representation of quantum circuits as directed graphs and an automated search for repeated subgraphs. The latter are identified as gadgets. We demonstrate the efficiency of the algorithm, which allows us to find two new gadget families suitable for RL. We compare the performance of 4-qubit gadgets taken from a previously known and a newly discovered family and discuss their advantages and disadvantages.
The process of scientific discovery relies on an interplay of observations, analysis, and hypothesis generation. Machine learning is increasingly being adopted to address individual aspects of this process. However, it remains an open challenge to fully automate the open-ended, heuristic, iterative loop required to discover the laws of an unknown system by exploring it through experiments and analysis, without tailoring the approach to the specifics of a given task. Here, we introduce SciExplorer, an agent that leverages large language model tool-use capabilities to enable free-form exploration of systems without any domain-specific blueprints, and apply it to the exploration of physical systems that are initially unknown to the agent. We test SciExplorer on a broad set of models spanning mechanical dynamical systems, wave evolution, and quantum many-body physics. Despite using a minimal set of tools, primarily based on code execution, we observe impressive performance on tasks such as recovering equations of motion from observed dynamics and inferring Hamiltonians from expectation values. The demonstrated effectiveness of this setup opens the door towards similar scientific exploration in other domains, without the need for finetuning or task-specific instructions.
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.
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.
Training nonlinear optical neural networks with Scattering Backpropagation
Nicola Dal Cin,
Florian Marquardt,
Clara C. Wanjura
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.
Artificial discovery of lattice models for wave transport
Jonas Landgraf,
Clara C. Wanjura,
Vittorio Peano,
Florian Marquardt
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.
Quantum equilibrium propagation for efficient training of quantum systems based on Onsager reciprocity
Clara C. Wanjura,
Florian Marquardt
Nature Communications
16
6595
(2025)
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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.
A neural-network-based Python package for performing large-scale atomic CI using pCI and other high-performance atomic codes
Pavlo Bilous,
Charles Cheung,
Marianna Safronova
Computer Physics Communications
315
109731
(2025)
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| PDF
Modern atomic physics applications in science and technology pose ever higher demands on the precision of compu- tations of properties of atoms and ions. Especially challenging is the modeling of electronic correlations within the configuration interaction (CI) framework, which often requires expansions of the atomic state in huge bases of Slater determinants or configuration state functions. This can easily render the problem intractable even for highly efficient atomic codes running on distributed supercomputer systems. Recently, we have successfully addressed this problem using a neural-network (NN) approach [1]. In this work, we present our Python code for performing NN-supported large-scale atomic CI using pCI [2] and other high-performance atomic codes.
Many-Body Neural Network Wavefunction for a Non-Hermitian Ising Chain
Lavoisier Wah,
Remmy Augusta Menzata Zen,
Flore K. Kunst
Non-Hermitian (NH) quantum systems have emerged as a powerful framework for describing open quantum systems, non-equilibrium dynamics, and engineered quantum optical materials. However, solving the ground-state properties of NH systems is challenging due to the exponential scaling of the Hilbert space, and exotic phenomena such as the emergence of exceptional points. Another challenge arises from the limitations of traditional methods like exact diagonalization (ED). For the past decade, neural networks (NN) have shown promise in approximating many-body wavefunctions, yet their application to NH systems remains largely unexplored. In this paper, we explore different NN architectures to investigate the ground-state properties of a parity-time-symmetric, one-dimensional NH, transverse field Ising model with a complex spectrum by employing a recurrent neural network (RNN), a restricted Boltzmann machine (RBM), and a multilayer perceptron (MLP). We construct the NN-based many-body wavefunctions and validate our approach by recovering the ground-state properties of the model for small system sizes, finding excellent agreement with ED. Furthermore, for larger system sizes, we demonstrate that the RNN outperforms both the RBM and MLP. However, we show that the accuracy of the RBM and MLP can be significantly improved through transfer learning, allowing them to perform comparably to the RNN for larger system sizes. These results highlight the potential of neural network-based approaches--particularly for accurately capturing the low-energy physics of NH quantum systems.
Quantum computing and artificial intelligence: status and perspectives
Giovanni Acampora,
Andris Ambainis,
Natalia Ares,
Leonardo Banchi,
Pallavi Bhardwaj,
Daniele Binosi,
G. Andrew D. Briggs,
Tommaso Calarco,
Vedran Dunjko, et al.
This white paper discusses and explores the various points of intersection between quantum computing and artificial intelligence (AI). It describes how quantum computing could support the development of innovative AI solutions. It also examines use cases of classical AI that can empower research and development in quantum technologies, with a focus on quantum computing and quantum sensing. The purpose of this white paper is to provide a long-term research agenda aimed at addressing foundational questions about how AI and quantum computing interact and benefit one another. It concludes with a set of recommendations and challenges, including how to orchestrate the proposed theoretical work, align quantum AI developments with quantum hardware roadmaps, estimate both classical and quantum resources - especially with the goal of mitigating and optimizing energy consumption - advance this emerging hybrid software engineering discipline, and enhance European industrial competitiveness while considering societal implications.
Tackling Decision Processes with Non-Cumulative Objectives using Reinforcement Learning
Maximilian Nägele,
Jan Olle,
Thomas Fösel,
Remmy Zen,
Florian Marquardt
Markov decision processes (MDPs) are used to model a wide variety of applications ranging from game playing over robotics to finance. Their optimal policy typically maximizes the expected sum of rewards given at each step of the decision process. However, a large class of problems does not fit straightforwardly into this framework: Non-cumulative Markov decision processes (NCMDPs), where instead of the expected sum of rewards, the expected value of an arbitrary function of the rewards is maximized. Example functions include the maximum of the rewards or their mean divided by their standard deviation. In this work, we introduce a general mapping of NCMDPs to standard MDPs. This allows all techniques developed to find optimal policies for MDPs, such as reinforcement learning or dynamic programming, to be directly applied to the larger class of NCMDPs. Focusing on reinforcement learning, we show applications in a diverse set of tasks, including classical control, portfolio optimization in finance, and discrete optimization problems. Given our approach, we can improve both final performance and training time compared to relying on standard MDPs.
Automated Discovery of Coupled Mode Setups
Jonas Landgraf,
Vittorio Peano,
Florian Marquardt
Physical Review X
15
021038
(2025)
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In optics and photonics, a small number of building blocks, like resonators, waveguides, arbitrary couplings, and parametric interactions, allow the design of a broad variety of devices and func- tionalities, distinguished by their scattering properties. These include transducers, amplifiers, and nonreciprocal devices, like isolators or circulators. Usually, the design of such a system is hand- crafted by an experienced scientist in a time-consuming process where it remains uncertain whether the simplest possibility has indeed been found. In our work, we develop a discovery algorithm that automates this challenge. By optimizing the continuous and discrete system properties our auto- mated search identifies the minimal resources required to realize the requested scattering behavior. In the spirit of artificial scientific discovery, it produces a complete list of interpretable solutions and leads to generalizable insights, as we illustrate in several examples. This now opens the door to rapid design in areas like photonic and microwave architectures or optomechanics.
Discovering Local Hidden-Variable Models for Arbitrary Multipartite Entangled States and Arbitrary Measurements
Measurement correlations in quantum systems can exhibit non-local behavior, a fundamental aspect of quantum mechanics with applications such as device-independent quantum information processing. However, the explicit construction of local hidden-variable (LHV) models remains an outstanding challenge in the general setting. To address this, we develop an approach that employs gradient-descent algorithms from machine learning to find LHV models which reproduce the statis- tics of arbitrary measurements for quantum many-body states. In contrast to previous approaches, our method employs a general ansatz, enabling it to discover an LHV model in all cases where the state is local. Therefore, it provides actual estimates for the critical noise levels at which two-qubit Werner states and three-qubit GHZ and W states become non-local. Furthermore, we find evidence suggesting that two-spin subsystems in the ground states of translationally invariant Hamiltonians are local, while bigger subsystems are in general not. Our method now offers a quantitative tool for determining the regimes of non-locality in any given physical context, including scenarios involving non-equilibrium and decoherence.
Transfer learning in predicting quantum many-body dynamics: from physical observables to entanglement entropy
Philipp Schmidt,
Florian Marquardt,
Naeimeh Mohseni
Quantum Science and Technology
10
025038
(2025)
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| PDF
Deep neural networks have demonstrated remarkable efficacy in extracting meaningful representations from complex datasets. This has propelled representation learning as a compelling area of research across diverse fields. One interesting open question is how beneficial representation learning can be for quantum many-body physics, with its notoriously high-dimensional state space. In this work, we showcase the capacity of a neural network that was trained on a subset of physical observables of a many-body system to partially acquire an implicit representation of the wave function. We illustrate this by demonstrating the effectiveness of reusing the representation learned by the neural network to enhance the learning process of another quantity derived from the quantum state. In particular, we focus on how the pre-trained neural network can enhance the learning of entanglement entropy. This is of particular interest as directly measuring the entanglement in a many-body system is very challenging, while a subset of physical observables can be easily measured in experiments. We show the pre-trained neural network learns the dynamics of entropy with fewer resources and higher precision in comparison with direct training on the entanglement entropy.
Scaling the Automated Discovery of Quantum Circuits via Reinforcement Learning with Gadgets
Jan Ollé Aguilera,
Oleg M. Yevtushenko,
Florian Marquardt
Reinforcement Learning (RL) has established itself as a powerful tool for designing quantum circuits, which are essential for processing quantum information. RL applications have typically focused on circuits of small to intermediate complexity, as computation times tend to increase exponentially with growing circuit complexity. This computational explosion severely limits the scalability of RL and casts significant doubt on its broader applicability. In this paper, we propose a principled approach based on the systematic discovery and introduction of composite gates – gadgets, that enables RL scalability, thereby expanding its potential applications. As a case study, we explore the discovery of Clifford encoders for Quantum Error Correction. We demonstrate that incorporating gadgets in the form of composite Clifford gates, in addition to standard CNOT and Hadamard gates, significantly enhances the efficiency of RL agents. Specifically, the computation speed increases (by one or even two orders of magnitude), enabling RL to discover highly complex quantum codes without previous knowledge. We illustrate this advancement with examples of QEC code discovery with parameters [[n, 1, d]] for d ≤ 7 and [[n, k, 6]] for k ≤ 7. We note that the most complicated circuits of these classes were not previously found. We highlight the advantages and limitations of the gadget-based approach. Our method paves the way for scaling the RL-based automatic discovery of complicated quantum circuits for various tasks, which may include designing logical operations between logical qubits or discovering quantum algorithms.
Meta-learning characteristics and dynamics of quantum systems
Lucas Schorling,
Pranav Vaidhyanathan,
Jonas Schuff,
Miguel J. Carballido,
Dominik Zumbühl,
Gerard Milburn,
Florian Marquardt,
Jakob Foerster,
Michael A. Osborne, et al.
While machine learning holds great promise for quantum technologies, most current methods fo- cus on predicting or controlling a specific quantum system. Meta-learning approaches, however, can adapt to new systems for which little data is available, by leveraging knowledge obtained from previ- ous data associated with similar systems. In this paper, we meta-learn dynamics and characteristics of closed and open two-level systems, as well as the Heisenberg model. Based on experimental data of a Loss-DiVincenzo spin-qubit hosted in a Ge/Si core/shell nanowire for different gate voltage config- urations, we predict qubit characteristics i.e. g-factor and Rabi frequency using meta-learning. The algorithm we introduce improves upon previous state-of-the-art meta-learning methods for physics- based systems by introducing novel techniques such as adaptive learning rates and a global optimizer for improved robustness and increased computational efficiency. We benchmark our method against other meta-learning methods, a vanilla transformer, and a multilayer perceptron, and demonstrate improved performance.
dCG—differentiable connected geometries for AI-compatible multi-domain optimization and inverse design
Alexander Luce,
Daniel Grünbaum,
Florian Marquardt
Machine Learning: Science and Technology
6
015055
(2025)
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In the domain of geometry and topology optimization, discovering geometries that optimally satisfy specific problem criteria is a complex challenge in both engineering and scientific research. In this work, we propose a new approach for the creation of multidomain connected geometries that are designed to work with automatic differentiation. We introduce the concept of differentiable Connected Geometries (dCG), discussing its theoretical aspects and illustrating its application through a simple toy examples and a more sophisticated photonic optimization task. Since these geometries are built upon the principles of automatic differentiation, they are compatible with existing deep learning frameworks, a feature we demonstrate via the application examples. This methodology provides a systematic way to approach geometric design and optimization in computational fields involving dependent geometries, potentially improving the efficiency and effectiveness of optimization tasks in scientific and engineering applications.
Neural-Network-Based Selective Configuration Interaction Approach to Molecular Electronic Structure
Yorick L. A. Schmerwitz,
Louis Thirion,
Gianluca Levi,
Elvar Ö. Jónsson,
Pavlo Bilous,
Hannes Jónsson,
Philipp Hansmann
Journal of Chemical Theory and Computation
21
2301-2310
(2025)
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By combining Hartree–Fock with a neural-network-supported quantum-cluster solver proposed recently in the context of solid-state lattice models, we formulate a scheme for selective neural-network configuration interaction (NNCI) calculations and implement it with various options for the type of basis set and boundary conditions. The method’s performance is evaluated in studies of several small molecules as a step toward calculations of larger systems. In particular, the correlation energy in the N₂ molecule is compared with published full CI calculations that included nearly 10¹⁰ Slater determinants, and the results are reproduced with only 4 × 10⁵ determinants using NNCI. A clear advantage is seen from increasing the set of orbitals included rather than approaching full CI for a smaller set. The method’s high efficiency and implementation in a condensed matter simulation software expands the applicability of CI calculations to a wider range of problems, even extended systems through an embedding approach.
SOLAX: A Python solver for fermionic quantum systems with neural network
support
Numerical modeling of fermionic many-body quantum systems presents similar challenges across various research domains, necessitating universal tools, including state-of-the-art machine learning techniques. Here, we introduce SOLAX, a Python library designed to compute and analyze fermionic quantum systems using the formalism of second quantization. SOLAX provides a modular framework for constructing and manipulating basis sets, quantum states, and operators, facilitating the simulation of electronic structures and determining many-body quantum states in finite-size Hilbert spaces. The library integrates machine learning capabilities to mitigate the exponential growth of Hilbert space dimensions in large quantum clusters. The core low-level functionalities are implemented using the recently developed Python library JAX. Demonstrated through its application to the Single Impurity Anderson Model, SOLAX offers a flexible and powerful tool for researchers addressing the challenges of many-body quantum systems across a broad spectrum of fields, including atomic physics, quantum chemistry, and condensed matter physics.
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)
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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.
From Dyson Models to many-body Quantum Chaos
Alexei Andreanov,
Matteo Carrega,
Jeff Murugan,
Jan Olle,
Dario Rosa,
Ruth Shir
A deep understanding of the mechanisms underlying many-body quantum chaos is one of the big challenges in contemporary theoretical physics. We tackle this problem in the context of a set of perturbed quadratic Sachdev-Ye-Kitaev (SYK) Hamiltonians defined on graphs. This allows us to disentangle the geometrical properties of the underlying single-particle problem and the importance of the interaction terms, showing that the former is the dominant feature ensuring the single-particle to many-body chaotic transition. Our results are verified numerically with state-of-the-art numerical techniques, capable of extracting eigenvalues in a desired energy window of very large Hamiltonians. Our approach essentially provides a new way of viewing many-body chaos from a single-particle perspective.
Non-Markovian Feedback for Optimized Quantum Error Correction
Matteo Puviani,
Sangkha Borah,
Remmy Augusta Menzata Zen,
Jan Ollé Aguilera,
Florian Marquardt
Physical Review Letters
134
020601
(2025)
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| PDF
Bosonic codes allow the encoding of a logical qubit in a single component device, utilizing the infinitely large Hilbert space of a harmonic oscillator. In particular, the Gottesman-Kitaev-Preskill code has recently been demonstrated to be correctable well beyond the break-even point of the best passive encoding in the same system. Current approaches to quantum error correction (QEC) for this system are based on protocols that use feedback, but the response is based only on the latest measurement outcome. In our work, we use the recently proposed feedback-GRAPE (gradient-ascent pulse engineering with feedback) method to train a recurrent neural network that provides a QEC scheme based on memory, responding in a non-Markovian way to the full history of previous measurement outcomes, optimizing all subsequent unitary operations. This approach significantly outperforms current strategies and paves the way for more powerful measurement-based QEC protocols.
Neural-network-supported basis optimizer for the configuration interaction problem in quantum many-body clusters: Feasibility study and numerical proof
Pavlo Bilous,
Louis Thirion,
Henri Menke,
Maurits W. Haverkort,
Adriana Pálffy,
Philipp Hansmann
Physical Review B
111
035124
(2025)
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| PDF
A neural-network approach to optimize the selection of Slater determinants in configuration interaction for correlated electron systems is presented. We apply our algorithm to the selection of determinants in the discrete version of the single-impurity Anderson model, scaling up to large systems with as many as 299 determinants in a basis with 299 bath sites. By employing a neural network classifier and active learning, our approach significantly enhances computational efficiency by iteratively refining the selection of the most relevant determinants. We compare our method against a conventional basis truncation scheme without machine learning and demonstrate that our algorithm achieves a more compact and computationally efficient determinant selection while maintaining high accuracy. Given its straightforward applicability, our method offers a promising advancement for selective configuration interaction calculations in the study of correlated condensed matter systems.
Preparing Schrödinger cat states in a microwave cavity using a neural network
Hector Hutin,
Pavlo Bilous,
Chengzhi Ye,
Sepideh Abdollahi,
Loris Cros,
Tom Dvir,
Tirth Shah,
Yonatan Cohen,
Audrey Bienfait, et al.
Scaling up quantum computing devices requires solving ever more complex quantum control tasks. Machine learning has been proposed as a promising approach to tackle the resulting challenges. However, experimental implementations are still scarce. In this work, we demonstrate experimentally a neural-network-based preparation of Schrödinger cat states in a cavity coupled dispersively to a qubit. We show that it is possible to teach a neural network to output optimized control pulses for a whole family of quantum states. After being trained in simulations, the network takes a description of the target quantum state as input and rapidly produces the pulse shape for the experiment, without any need for time-consuming additional optimization or retraining for different states. Our experimental results demonstrate more generally how deep neural networks and transfer learning can produce efficient simultaneous solutions to a range of quantum control tasks, which will benefit not only state preparation but also parametrized quantum gates.
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Theorie-Abteilung Prof. Florian Marquardt
Max-Planck-Institut für die Physik des Lichts Staudtstr. 2 91058 Erlangen
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