arXiv subjects

Patrick Huembeli

Publications and source records attributed to Patrick Huembeli.

16 recordsLinked to original sources

arXiv2026

A Blueprint for Equilibrium-Based Differentiable Continuous-Variable Thermodynamic Computing

To help address the escalating energy and latency demands of machine-learning workloads, we introduce a blueprint for an energy-efficient and fast thermodynamic computing stack that leverages stochastic analog processes in physical hardware. In this work, we focus on energy-based thermodynamic computing where the stochastic process is well described by Langevin dynamics with tunable energy potentials. The implementation of such potentials in physical hardware enables us to generate and sample from basic parameterized energy-based models. We demonstrate how to construct and train popular classes of machine learning models based on these hardware-native energy-based models, using the framework of probabilistic graphical models. We analyze the runtime and energy consumption of different models in this thermodynamic paradigm based on theoretical considerations and numerical studies. As a preliminary experimental realization of such hardware, we present our stochastic analog superconducting circuits driven by thermal noise. Together, these results outline a path toward energy-efficient thermodynamic hardware for probabilistic machine learning.

cs.LG↗

arXiv2022

The effect of the processing and measurement operators on the expressive power of quantum models

There is an increasing interest in Quantum Machine Learning (QML) models, how they work and for which applications they could be useful. There have been many different proposals on how classical data can be encoded and what circuit ansätze and measurement operators should be used to process the encoded data and measure the output state of an ansatz. The choice of the aforementioned operators plays a determinant role in the expressive power of the QML model. In this work we investigate how certain changes in the circuit structure change this expressivity. We introduce both numerical and analytical tools to explore the effect that these operators have in the overall performance of the QML model. These tools are based on previous work on the teacher-student scheme, the partial Fourier series and the averaged operator size. We focus our analysis on simple QML models with two and three qubits and observe that increasing the number of parameterized and entangling gates leads to a more expressive model for certain circuit structures. Also, on which qubit the measurement is performed affects the type of functions that QML models could learn. This work sketches the determinant role that the processing and measurement operators have on the expressive power of simple quantum circuits.

quant-ph↗

arXiv2022

Towards a scalable discrete quantum generative adversarial neural network

We introduce a fully quantum generative adversarial network intended for use with binary data. The architecture incorporates several features found in other classical and quantum machine learning models, which up to this point had not been used in conjunction. In particular, we incorporate noise reuploading in the generator, auxiliary qubits in the discriminator to enhance expressivity, and a direct connection between the generator and discriminator circuits, obviating the need to access the generator's probability distribution. We show that, as separate components, the generator and discriminator perform as desired. We empirically demonstrate the expressive power of our model on both synthetic data as well as low energy states of an Ising model. Our demonstrations suggest that the model is not only capable of reproducing discrete training data, but also of potentially generalizing from it.

quant-ph↗

arXiv2022

Entanglement Forging with generative neural network models

The optimal use of quantum and classical computational techniques together is important to address problems that cannot be easily solved by quantum computations alone. This is the case of the ground state problem for quantum many-body systems. We show here that probabilistic generative models can work in conjunction with quantum algorithms to design hybrid quantum-classical variational ansätze that forge entanglement to lower quantum resource overhead. The variational ansätze comprise parametrized quantum circuits on two separate quantum registers, and a classical generative neural network that can entangle them by learning a Schmidt decomposition of the whole system. The method presented is efficient in terms of the number of measurements required to achieve fixed precision on expected values of observables. To demonstrate its effectiveness, we perform numerical experiments on the transverse field Ising model in one and two dimensions, and fermionic systems such as the t-V Hamiltonian of spinless fermions on a lattice.

quant-ph↗

arXiv2022

Modern applications of machine learning in quantum sciences

In this book, we provide a comprehensive introduction to the most recent advances in the application of machine learning methods in quantum sciences. We cover the use of deep learning and kernel methods in supervised, unsupervised, and reinforcement learning algorithms for phase classification, representation of many-body quantum states, quantum feedback control, and quantum circuits optimization. Moreover, we introduce and discuss more specialized topics such as differentiable programming, generative models, statistical approach to machine learning, and quantum machine learning.

quant-ph↗

arXiv2021

Exploring Quantum Perceptron and Quantum Neural Network structures with a teacher-student scheme

Near-term quantum devices can be used to build quantum machine learning models, such as quantum kernel methods and quantum neural networks (QNN) to perform classification tasks. There have been many proposals how to use variational quantum circuits as quantum perceptrons or as QNNs. The aim of this work is to systematically compare different QNN architectures and to evaluate their relative expressive power with a teacher-student scheme. Specifically, the teacher model generates the datasets mapping random inputs to outputs which then have to be learned by the student models. This way, we avoid training on arbitrary data sets and allow to compare the learning capacity of different models directly via the loss, the prediction map, the accuracy and the relative entropy between the prediction maps. We focus particularly on a quantum perceptron model inspired by the recent work of Tacchino et. al. \cite{Tacchino1} and compare it to the data re-uploading scheme that was originally introduced by Pérez-Salinas et. al. \cite{data_re-uploading}. We discuss alterations of the perceptron model and the formation of deep QNN to better understand the role of hidden units and non-linearities in these architectures.

quant-ph↗

arXiv2021

Quadratic Unconstrained Binary Optimisation via Quantum-Inspired Annealing

We present a classical algorithm to find approximate solutions to instances of quadratic unconstrained binary optimisation. The algorithm can be seen as an analogue of quantum annealing under the restriction of a product state space, where the dynamical evolution in quantum annealing is replaced with a gradient-descent based method. This formulation is able to quickly find high-quality solutions to large-scale problem instances, and can naturally be accelerated by dedicated hardware such as graphics processing units. We benchmark our approach for large scale problem instances with tuneable hardness and planted solutions. We find that our algorithm offers a similar performance to current state of the art approaches within a comparably simple gradient-based and non-stochastic setting.

quant-ph↗

arXiv2021

Avoiding local minima in Variational Quantum Algorithms with Neural Networks

Variational Quantum Algorithms have emerged as a leading paradigm for near-term quantum computation. In such algorithms, a parameterized quantum circuit is controlled via a classical optimization method that seeks to minimize a problem-dependent cost function. Although such algorithms are powerful in principle, the non-convexity of the associated cost landscapes and the prevalence of local minima means that local optimization methods such as gradient descent typically fail to reach good solutions. In this work we suggest a method to improve gradient-based approaches to variational quantum circuit optimization, which involves coupling the output of the quantum circuit to a classical neural network. The effect of this neural network is to peturb the cost landscape as a function of its parameters, so that local minima can be escaped or avoided via a modification to the cost landscape itself. We present two algorithms within this framework and numerically benchmark them on small instances of the Max-Cut optimization problem. We show that the method is able to reach deeper minima and lower cost values than standard gradient descent based approaches. Moreover, our algorithms require essentially the same number of quantum circuit evaluations per optimization step as the standard approach since, unlike the gradient with respect to the circuit, the neural network updates can be estimated in parallel via the backpropagation method. More generally, our approach suggests that relaxing the cost landscape is a fruitful path to improving near-term quantum computing algorithms.

quant-ph↗

arXiv2021

Hessian-based toolbox for reliable and interpretable machine learning in physics

Machine learning (ML) techniques applied to quantum many-body physics have emerged as a new research field. While the numerical power of this approach is undeniable, the most expressive ML algorithms, such as neural networks, are black boxes: The user does neither know the logic behind the model predictions nor the uncertainty of the model predictions. In this work, we present a toolbox for interpretability and reliability, agnostic of the model architecture. In particular, it provides a notion of the influence of the input data on the prediction at a given test point, an estimation of the uncertainty of the model predictions, and an extrapolation score for the model predictions. Such a toolbox only requires a single computation of the Hessian of the training loss function. Our work opens the road to the systematic use of interpretability and reliability methods in ML applied to physics and, more generally, science.

quant-ph↗

arXiv2021

Unsupervised phase discovery with deep anomaly detection

We demonstrate how to explore phase diagrams with automated and unsupervised machine learning to find regions of interest for possible new phases. In contrast to supervised learning, where data is classified using predetermined labels, we here perform anomaly detection, where the task is to differentiate a normal data set, composed of one or several classes, from anomalous data. Asa paradigmatic example, we explore the phase diagram of the extended Bose Hubbard model in one dimension at exact integer filling and employ deep neural networks to determine the entire phase diagram in a completely unsupervised and automated fashion. As input data for learning, we first use the entanglement spectra and central tensors derived from tensor-networks algorithms for ground-state computation and later we extend our method and use experimentally accessible data such as low-order correlation functions as inputs. Our method allows us to reveal a phase-separated region between supersolid and superfluid parts with unexpected properties, which appears in the system in addition to the standard superfluid, Mott insulator, Haldane-insulating, and density wave phases.

quant-ph↗

arXiv2021

Characterizing the loss landscape of variational quantum circuits

Machine learning techniques enhanced by noisy intermediate-scale quantum (NISQ) devices and especially variational quantum circuits (VQC) have recently attracted much interest and have already been benchmarked for certain problems. Inspired by classical deep learning, VQCs are trained by gradient descent methods which allow for efficient training over big parameter spaces. For NISQ sized circuits, such methods show good convergence. There are however still many open questions related to the convergence of the loss function and to the trainability of these circuits in situations of vanishing gradients. Furthermore, it is not clear how "good" the minima are in terms of generalization and stability against perturbations of the data and there is, therefore, a need for tools to quantitatively study the convergence of the VQCs. In this work, we introduce a way to compute the Hessian of the loss function of VQCs and show how to characterize the loss landscape with it. The eigenvalues of the Hessian give information on the local curvature and we discuss how this information can be interpreted and compared to classical neural networks. We benchmark our results on several examples, starting with a simple analytic toy model to provide some intuition about the behavior of the Hessian, then going to bigger circuits, and also train VQCs on data. Finally, we show how the Hessian can be used to adjust the learning rate for faster convergence during the training of variational circuits.

quant-ph↗

arXiv2020

Phase Detection with Neural Networks: Interpreting the Black Box

Neural networks (NNs) usually hinder any insight into the reasoning behind their predictions. We demonstrate how influence functions can unravel the black box of NN when trained to predict the phases of the one-dimensional extended spinless Fermi-Hubbard model at half-filling. Results provide strong evidence that the NN correctly learns an order parameter describing the quantum transition in this model. We demonstrate that influence functions allow to check that the network, trained to recognize known quantum phases, can predict new unknown ones within the data set. Moreover, we show they can guide physicists in understanding patterns responsible for the phase transition. This method requires no a priori knowledge on the order parameter, has no dependence on the NN's architecture or the underlying physical model, and is therefore applicable to a broad class of physical models or experimental data.

quant-ph↗

arXiv2019

Automated discovery of characteristic features of phase transitions in many-body localization

We identify a new "order parameter" for the disorder driven many-body localization (MBL) transition by leveraging artificial intelligence. This allows us to pin down the transition, as the point at which the physics changes qualitatively, from vastly fewer disorder realizations and in an objective and cleaner way than is possible with the existing zoo of quantities. Contrary to previous studies, our method is almost entirely unsupervised. A game theoretic process between neural networks defines an adversarial setup with conflicting objectives to identify what characteristic features to base efficient predictions on. This reduces the numerical effort for mapping out the phase diagram by a factor of ~100x. This approach of automated discovery is applicable specifically to poorly understood phase transitions and exemplifies the potential of machine learning assisted research in physics.

quant-ph↗

arXiv2019

Towards a heralded eigenstate preserving measurement of multi-qubit parity in circuit QED

Eigenstate-preserving multi-qubit parity measurements lie at the heart of stabilizer quantum error correction, which is a promising approach to mitigate the problem of decoherence in quantum computers. In this work we explore a high-fidelity, eigenstate-preserving parity readout for superconducting qubits dispersively coupled to a microwave resonator, where the parity bit is encoded in the amplitude of a coherent state of the resonator. Detecting photons emitted by the resonator via a current biased Josephson junction yields information about the parity bit. We analyse theoretically the measurement back-action in the limit of a strongly coupled fast detector and show that in general such a parity measurement, while approximately Quantum Non-Demolition (QND) is not eigenstate-preserving. To remediate this shortcoming we propose a simple dynamical decoupling technique during photon detection, which greatly reduces decoherence within a given parity subspace. Furthermore, by applying a sequence of fast displacement operations interleaved with the dynamical decoupling pulses, the natural bias of this binary detector can be efficiently suppressed. Finally, we introduce the concept of a heralded parity measurement, where a detector click guarantees successful multi-qubit parity detection even for finite detection efficiency.

quant-ph↗

arXiv2019

QuCumber: wavefunction reconstruction with neural networks

As we enter a new era of quantum technology, it is increasingly important to develop methods to aid in the accurate preparation of quantum states for a variety of materials, matter, and devices. Computational techniques can be used to reconstruct a state from data, however the growing number of qubits demands ongoing algorithmic advances in order to keep pace with experiments. In this paper, we present an open-source software package called QuCumber that uses machine learning to reconstruct a quantum state consistent with a set of projective measurements. QuCumber uses a restricted Boltzmann machine to efficiently represent the quantum wavefunction for a large number of qubits. New measurements can be generated from the machine to obtain physical observables not easily accessible from the original data.

quant-ph↗

arXiv2018

Identifying Quantum Phase Transitions with Adversarial Neural Networks

The identification of phases of matter is a challenging task, especially in quantum mechanics, where the complexity of the ground state appears to grow exponentially with the size of the system. We address this problem with state-of-the-art deep learning techniques: adversarial domain adaptation. We derive the phase diagram of the whole parameter space starting from a fixed and known subspace using unsupervised learning. The input data set contains both labeled and unlabeled data instances. The first kind is a system that admits an accurate analytical or numerical solution, and one can recover its phase diagram. The second type is the physical system with an unknown phase diagram. Adversarial domain adaptation uses both types of data to create invariant feature extracting layers in a deep learning architecture. Once these layers are trained, we can attach an unsupervised learner to the network to find phase transitions. We show the success of this technique by applying it on several paradigmatic models: the Ising model with different temperatures, the Bose-Hubbard model, and the SSH model with disorder. The input is the ground state without any manual feature engineering, and the dimension of the parameter space is unrestricted. The method finds unknown transitions successfully and predicts transition points in close agreement with standard methods. This study opens the door to the classification of physical systems where the phases boundaries are complex such as the many-body localization problem or the Bose glass phase.

cond-mat.stat-mech↗