Merging automatic differentiation and the adjoint method for photonic inverse design
Alexander Luce,
Rasoul Alaee,
Fabian Knorr,
Florian Marquardt
Machine Learning: Science and Technology
5
(2)
025076
(2024)
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Optimizing the shapes and topology of physical devices is crucial for both scientific and technological advancements, given their wide-ranging implications across numerous industries and research areas. Innovations in shape and topology optimization have been observed across a wide range of fields, notably structural mechanics, fluid mechanics, and more recently, photonics. Gradient-based inverse design techniques have been particularly successful for photonic and optical problems, resulting in integrated, miniaturized hardware that has set new standards in device performance. To calculate the gradients, there are typically two approaches: namely, either by implementing specialized solvers using automatic differentiation (AD) or by deriving analytical solutions for gradient calculation and adjoint sources by hand. In this work, we propose a middle ground and present a hybrid approach that leverages and enables the benefits of AD for handling gradient derivation while using existing, proven but black-box photonic solvers for numerical solutions. Utilizing the adjoint method, we make existing numerical solvers differentiable and seamlessly integrate them into an AD framework. Further, this enables users to integrate the optimization environment seamlessly with other autodifferentiable components such as machine learning, geometry generation, or intricate post-processing which could lead to better photonic design workflows. We illustrate the approach through two distinct photonic optimization problems: optimizing the Purcell factor of a magnetic dipole in the vicinity of an optical nanocavity and enhancing the light extraction efficiency of a µLED.
No-Collapse Accurate Quantum Feedback Control via Conditional State Tomography
Sangkha Borah,
Bijita Sarma
Physical Review Letters
131
210803
(2023)
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The effectiveness of measurement-based feedback control (MBFC) protocols is hindered by the presence of measurement noise, which impairs the ability to accurately infer the underlying dynamics of a quantum system from noisy continuous measurement records. To circumvent this limitation, a real-time stochastic state estimation approach is proposed in this work, that enables noise-free monitoring of the conditional dynamics, including the full density matrix of the quantum system, despite using noisy measurement data. This, in turn, enables the development of precise MBFC strategies that leads to effective control of quantum systems by essentially mitigating the constraints imposed by measurement noise, and has potential applications in various feedback quantum control scenarios. This approach is particularly important for machine learning-based control, where the AI controller can be trained with arbitrary conditional averages of observables, including the full density matrix, to quickly and accurately learn control strategies.
Realizing a deep reinforcement learning agent discovering real-time feedback control strategies for a quantum system
Kevin Reuer,
Jonas Landgraf,
Thomas Fösel,
James O'Sullivan,
Liberto Beltrán,
Abdulkadir Akin,
Graham J. Norris,
Ants Remm,
Michael Kerschbaum, et al.
Nature Communications
14
7138
(2023)
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Realizing the full potential of quantum technologies requires precise real-time control on time scales much shorter than the coherence time. Model-free reinforcement learning promises to discover efficient feedback strategies from scratch without relying on a description of the quantum system. However, developing and training a reinforcement learning agent able to operate in real-time using feedback has been an open challenge. Here, we have implemented such an agent for a single qubit as a sub-microsecond-latency neural network on a field-programmable gate array (FPGA). We demonstrate its use to efficiently initialize a superconducting qubit and train the agent based solely on measurements. Our work is a first step towards adoption of reinforcement learning for the control of quantum devices and more generally any physical device requiring low-latency feedback.<br>
Deep Bayesian Experimental Design for Quantum Many-Body Systems
Leopoldo Sarra,
Florian Marquardt
Machine Learning: Science and Technology
(4)
045022
(2023)
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Bayesian experimental design is a technique that allows to efficiently select measurements to characterize a physical system by maximizing the expected information gain. Recent developments in deep neural networks and normalizing flows allow for a more efficient approximation of the posterior and thus the extension of this technique to complex high-dimensional situations. In this paper, we show how this approach holds promise for adaptive measurement strategies to characterize present-day quantum technology platforms. In particular, we focus on arrays of coupled cavities and qubit arrays. Both represent model systems of high relevance for modern applications, like quantum simulations and computing, and both have been realized in platforms where measurement and control can be exploited to characterize and counteract unavoidable disorder. Thus, they represent ideal targets for applications of Bayesian experimental design.
Restoration of the non-Hermitian bulk-boundary correspondence viatopological amplification
Matteo Brunelli,
Clara C. Wanjura,
Andreas Nunnenkamp
Non-Hermitian (NH) lattice Hamiltonians display a unique kind of energy gap and ex- treme sensitivity to boundary conditions. Due to the NH skin effect, the separation between edge and bulk states is blurred and the (conventional) bulk-boundary corre- spondence is lost. Here, we restore the bulk-boundary correspondence for the most paradigmatic class of NH Hamiltonians, namely those with one complex band and with- out symmetries. We obtain the desired NH Hamiltonian from the mean-field evolution of driven-dissipative cavity arrays, in which NH terms—in the form of non-reciprocal hopping amplitudes, gain and loss—are explicitly modeled via coupling to (engineered and non-engineered) reservoirs. This approach removes the arbitrariness in the defini- tion of the topological invariant, as point-gapped spectra differing by a complex-energy shift are not treated as equivalent; the origin of the complex plane provides a common reference (base point) for the evaluation of the topological invariant. This implies that topologically non-trivial Hamiltonians are only a strict subset of those with a point gap and that the NH skin effect does not have a topological origin. We analyze the NH Hamil- tonians so obtained via the singular value decomposition, which allows to express the NH bulk-boundary correspondence in the following simple form: an integer value ν of the topological invariant defined in the bulk corresponds to |ν| singular vectors exponen- tially localized at the system edge under open boundary conditions, in which the sign of ν determines which edge. Non-trivial topology manifests as directional amplification of a coherent input with gain exponential in system size. Our work solves an outstanding problem in the theory of NH topological phases and opens up new avenues in topological photonics.
Deep-Learning Approach for the Atomic Configuration Interaction Problem on Large Basis Sets
Pavlo Bilous,
Adriana Pálffy,
Florian Marquardt
Physical Review Letters
131
(13)
(2023)
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High-precision atomic structure calculations require accurate modeling of electronic correlations typically addressed via the configuration interaction (CI) problem on a multiconfiguration wave function expansion. The latter can easily become challenging or infeasibly large even for advanced supercomputers. Here, we develop a deep-learning approach which allows us to preselect the most relevant configurations out of large CI basis sets until the targeted energy precision is achieved. The large CI computation is thereby replaced by a series of smaller ones performed on an iteratively expanding basis subset managed by a neural network. While dense architectures as used in quantum chemistry fail, we show that a convolutional neural network naturally accounts for the physical structure of the basis set and allows for robust and accurate CI calculations. The method was benchmarked on basis sets of moderate size allowing for the direct CI calculation, and further demonstrated on prohibitively large sets where the direct computation is not possible.
Cooling microwave fields into general multimode Gaussian states
Nahid Yazdi,
Juan José García-Ripoll,
Diego Porras,
Carlos Navarrete-Benlloch
New Journal of Physics
25
083052
(2023)
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We show that a collection of lossy multi-chromatically modulated qubits can be used to dissipa- tively engineer arbitrary Gaussian states of a set of bosonic modes. Our ideas are especially suited to superconducting-circuit architectures, where all the required ingredients are experimentally avail- able. The generation of such multimode Gaussian states is necessary for many applications, most notably measurement-based quantum computation. We build upon some of our previous proposals, where we showed how to generate single-mode and two-mode squeezed states through cooling and lasing. Special care must be taken when extending these ideas to many bosonic modes, and we discuss here how to overcome all the limitations and hurdles that naturally appear. We illustrate our ideas with a fully worked out example consisting of GHZ states, but have also tested several other examples such as cluster states. All these examples allow us to show that it is possible to use a set of N lossy qubits to cool down a bosonic chain of N modes to any desired Gaussian state.
Roadmap on structured waves
Konstantin Y Bliokh,
Ebrahim Karimi,
Miles J Padgett,
Miguel A Alonso,
Mark R Dennis,
Angela Dudley,
Andrew Forbes,
Sina Zahedpour,
Scott W Hancock, et al.
Journal of Optics
25
103001
(2023)
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Structured waves are ubiquitous for all areas of wave physics, both classical and quantum, where the wavefields are inhomogeneous and cannot be approximated by a single plane wave. Even the interference of two plane waves, or of a single inhomogeneous (evanescent) wave, provides a number of nontrivial phenomena and additional functionalities as compared to a single plane wave. Complex wavefields with inhomogeneities in the amplitude, phase, and polarization, including topological structures and singularities, underpin modern nanooptics and photonics, yet they are equally important, e.g. for quantum matter waves, acoustics, water waves, etc. Structured waves are crucial in optical and electron microscopy, wave propagation and scattering, imaging, communications, quantum optics, topological and non-Hermitian wave systems, quantum condensed-matter systems, optomechanics, plasmonics and metamaterials, optical and acoustic manipulation, and so forth. This Roadmap is written collectively by prominent researchers and aims to survey the role of structured waves in various areas of wave physics. Providing background, current research, and anticipating future developments, it will be of interest to a wide cross-disciplinary audience.
Self-learning Machines based on Hamiltonian Echo Backpropagation
Victor Lopez-Pastor,
Florian Marquardt
Physical Review X
13
(3)
031020
(2023)
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A physical self-learning machine can be defined as a nonlinear dynamical system that can be trained on data (similar to artificial neural networks), but where the update of the internal degrees of freedom that serve as learnable parameters happens autonomously. In this way, neither external processing and feedback nor knowledge of (and control of) these internal degrees of freedom is required. We introduce a general scheme for self-learning in any time-reversible Hamiltonian system. We illustrate the training of such a self-learning machine numerically for the case of coupled nonlinear wave fields.
Quadrature nonreciprocity in bosonic networks without breaking time-reversal symmetry
Clara C. Wanjura,
Jesse J. Slim,
Javier del Pino,
Matteo Brunelli,
Ewold Verhagen,
Andreas Nunnenkamp
Nature Physics
19
1429-1436
(2023)
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Nonreciprocity means that the transmission of a signal depends on its direction of propagation. Despite vastly different platforms and underlying working principles, the realizations of nonreciprocal transport in linear, time-independent systems rely on Aharonov–Bohm interference among several pathways and require breaking time-reversal symmetry. Here we extend the notion of nonreciprocity to unidirectional bosonic transport in systems with a time-reversal symmetric Hamiltonian by exploiting interference between beamsplitter (excitation-preserving) and two-mode-squeezing (excitation non-preserving) interactions. In contrast to standard nonreciprocity, this unidirectional transport manifests when the mode quadratures are resolved with respect to an external reference phase. Accordingly, we dub this phenomenon ‘quadrature nonreciprocity’. We experimentally demonstrate it in the minimal system of two coupled nanomechanical modes orchestrated by optomechanical interactions. Next, we develop a theoretical framework to characterize the class of networks exhibiting quadrature nonreciprocity based on features of their particle–hole graphs. In addition to unidirectionality, these networks can exhibit an even–odd pairing between collective quadratures, which we confirm experimentally in a four-mode system, and an exponential end-to-end gain in the case of arrays of cavities.
Efficient approaches to quantum control and feedback are essential for quantum technologies, from sensing to quantum computation. Open-loop control tasks have been successfully solved using optimization techniques, including methods such as gradient-ascent pulse engineering (GRAPE) , relying on a differentiable model of the quantum dynamics. For feedback tasks, such methods are not directly applicable, since the aim is to discover strategies conditioned on measurement outcomes. In this work, we introduce feedback GRAPE, which borrows some concepts from model-free reinforcement learning to incorporate the response to strong stochastic (discrete or continuous) measurements, while still performing direct gradient ascent through the quantum dynamics. We illustrate its power considering various scenarios based on cavity-QED setups. Our method yields interpretable feedback strategies for state preparation and stabilization in the presence of noise. Our approach could be employed for discovering strategies in a wide range of feedback tasks, from calibration of multiqubit devices to linear-optics quantum computation strategies, quantum enhanced sensing with adaptive measurements, and quantum error correction.
Deep recurrent networks predicting the gap evolution in adiabatic quantum computing
Naeimeh Mohseni,
Carlos Navarrete-Benlloch,
Tim Byrnes,
Florian Marquardt
One of the main challenges in quantum physics is predicting efficiently the dynamics of observables in many-body problems out of equilibrium. A particular example occurs in adiabatic quantum computing, where finding the structure of the instantaneous gap of the Hamiltonian is crucial in order to optimize the speed of the computation. Inspired by this challenge, in this work we explore the potential of deep learning for discovering a mapping from the parameters that fully identify a problem Hamiltonian to the full evolution of the gap during an adiabatic sweep applying different network architectures. Through this example, we find that a limiting factor for the learnability of the dynamics is the size of the input, that is, how the number of parameters needed to identify the Hamiltonian scales with the system size. We demonstrate that a long short-term memory network succeeds in predicting the gap when the parameter space scales linearly with system size. Remarkably, we show that once this architecture is combined with a convolutional neural network to deal with the spatial structure of the model, the gap evolution can even be predicted for system sizes larger than the ones seen by the neural network during training. This provides a significant speedup in comparison with the existing exact and approximate algorithms in calculating the gap.
Classical Phase Space Crystals in Open Environment
Ali Emami Kopaei,
Krzysztof Sacha,
Lingzhen Guo
Physical Review B
107
214302
(2023)
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It was recently discovered that a crystalline many-body state can exist in the phase space of a closed dynamical system. A phase space crystal can be an anomalous Chern insulator that supports chiral topological transport without breaking physical time-reversal symmetry [L. Guo et al., Phys. Rev. B 105, 094301 (2022)]. In this work, we further study the effects of an open dissipative environment with thermal noise and identify the existence condition of classical phase space crystals in realistic scenarios. By defining a crystal order parameter, we plot the phase diagram in the parameter space of dissipation rate, interaction, and temperature. Our present work paves the way to realize phase space crystals and explore anomalous chiral transport in experiments.
Quench-drive spectroscopy and high-harmonic generation in BCS superconductors
Matteo Puviani,
Rafael Haenel,
Dirk Manske
Physical Review B
(107)
094501
(2023)
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In pump-probe spectroscopies, THz pulses are used to quench a system, which is subsequently probed by either a THz or optical pulse. In contrast, third-harmonic generation experiments employ a single multicycle driving pulse and measure the induced third harmonic. In this work, we analyze a spectroscopy setup where both a quench and a drive are applied and two-dimensional spectra as a function of time and quench-drive delay are recorded. We calculate the time evolution of the nonlinear current generated in the superconductor within an Anderson-pseudospin framework and characterize all experimental signatures using a quasiequilibrium approach. We analyze the superconducting response in Fourier space with respect to both the frequencies corresponding to the real time and the quench-drive delay time. In particular, we show the presence of a transient modulation of higher harmonics, induced by a wave mixing process of the drive with the quench pulse, which probes both quasiparticle and collective excitations of the superconducting condensate.
Learning Quantum Systems
Valentin Gebhart,
Raffaele Santagati,
Antonio Andrea Gentile,
Erik Gauger,
David Craig,
Natalia Ares,
Leonardo Banchi,
Florian Marquardt,
Luca Pezzè, et al.
Nature Reviews Physics
5
141-156
(2023)
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The future development of quantum technologies relies on creating and manipulating quantum systems of increasing complexity, with key applications in computation, simulation and sensing. This poses severe challenges in the efficient control, calibration and validation of quantum states and their dynamics. Although the full simulation of large-scale quantum systems may only be possible on a quantum computer, classical characterization and optimization methods still play an important role. Here, we review different approaches that use classical post-processing techniques, possibly combined with adaptive optimization, to learn quantum systems, their correlation properties, dynamics and interaction with the environment. We discuss theoretical proposals and successful implementations across different multiple-qubit architectures such as spin qubits, trapped ions, photonic and atomic systems, and superconducting circuits. This Review provides a brief background of key concepts recurring across many of these approaches with special emphasis on the Bayesian formalism and neural networks.<br><br>
Tunneling-induced fractal transmission in Valley Hall waveguides
Tirth Shah,
Florian Marquardt,
Vittorio Peano
Physical Review B
107
054304
(2023)
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The valley Hall effect provides a popular route to engineer robust waveguides for bosonic excitations such as photons and phonons. The almost complete absence of backscattering in many experiments has its theoretical underpinning in a smooth-envelope approximation that neglects large momentum transfer and is accurate only for small bulk band gaps and/or smooth domain walls. For larger bulk band gaps and hard domain walls, backscattering is expected to become significant. Here, we show that in this experimentally relevant regime, the reflection of a wave at a sharp corner becomes highly sensitive to the orientation of the outgoing waveguide relative to the underlying lattice. Enhanced backscattering can be understood as being triggered by resonant tunneling transitions in quasimomentum space. Tracking the resonant tunneling energies as a function of the waveguide orientation reveals a self-repeating fractal pattern that is also imprinted in the density of states and the backscattering rate at a sharp corner.<br><br>
Investigation of inverse design of multilayer thin-films with conditional invertible Neural Networks
Alexander Luce,
Ali Mahdavi,
Heribert Wankerl,
Florian Marquardt
Machine Learning: Science and Technology
4
(1)
015014
(2023)
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In this work, we apply conditional invertible neural networks (cINN) to inversely design multilayer thin-films given an optical target in order to overcome limitations of state-of-the-art optimization approaches. Usually, state-of-the-art algorithms depend on a set of carefully chosen initial thin-film parameters or employ neural networks which must be retrained for every new application. We aim to overcome those limitations by training the cINN to learn the loss landscape of all thin-film configurations within a training dataset. We show that cINNs can generate a stochastic ensemble of proposals for thin-film configurations that are reasonably close to the desired target depending only on random variables. By refining the proposed configurations further by a local optimization, we show that the generated thin-films reach the target with significantly greater precision than comparable state-of-the-art approaches. Furthermore, we tested the generative capabilities on samples which are outside of the training data distribution and found that the cINN was able to predict thin-films for out-of-distribution targets, too. The results suggest that in order to improve the generative design of thin-films, it is instructive to use established and new machine learning methods in conjunction in order to obtain the most favorable results.<br><br>
Complex decoherence-free interactions between giant atoms
Lei Du,
Lingzhen Guo,
Yong Li
Physical Review A
107
023705
(2023)
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Giant atoms provide a promising platform for engineering decoherence-free interactions, which is a major task in modern quantum technologies. Here we study systematically how to implement complex decoherence-free interactions among giant atoms resorting to periodic coupling modulations and suitable arrangements of coupling points. We demonstrate that the phase of the modulation, which is tunable in experiments, can be encoded into the decoherence-free interactions and thus enables phase-dependent dynamics when the giant atoms constitute an effective closed loop. Moreover, we consider the influence of non-Markovian retardation effect arising from large separations of the coupling points and study its dependence on the modulation parameters.
Artificial Intelligence and Machine Learning for Quantum Technologies
Mario Krenn,
Jonas Landgraf,
Thomas Fösel,
Florian Marquardt
Physical Review A
107
010101
(2023)
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In recent years the dramatic progress in machine learning has begun to impact many areas of science and technology significantly. In the present perspective article, we explore how quantum technologies are benefiting from this revolution. We showcase in illustrative examples how scientists in the past few years have started to use machine learning and more broadly methods of artificial intelligence to analyze quantum measurements, estimate the parameters of quantum devices, discover new quantum experimental setups, protocols, and feed- back strategies, and generally improve aspects of quantum computing, quantum communication, and quantum simulation. We highlight open challenges and future possibilities and conclude with some speculative visions for the next decade.
Contact
Theory Division Prof. Florian Marquardt
Max Planck Institute for the Science of Light Staudtstr. 2 91058 Erlangen, Germany
