Quantum generative adversarial learning in a superconducting quantum circuit

Generative Quantum Machine Learning via Denoising Diffusion Probabilistic Models

Deep generative models are key-enabling technology to computer vision, text generation, and large language models. Denoising diffusion probabilistic models (DDPMs) have recently gained much attention due to their ability to generate diverse and high-quality samples in many computer vision tasks, as well as to incorporate flexible model architectures and a relatively simple training scheme. Quantum generative models, empowered by entanglement and superposition, have brought new insight to learning classical and quantum data. Inspired by the classical counterpart, we propose the quantum denoising diffusion probabilistic model (QuDDPM) to enable efficiently trainable generative learning of quantum data. QuDDPM adopts sufficient layers of circuits to guarantee expressivity, while it introduces multiple intermediate training tasks as interpolation between the target distribution and noise to avoid barren plateau and guarantee efficient training. We provide bounds on the learning error and demonstrate QuDDPM's capability in learning correlated quantum noise model, quantum many-body phases, and topological structure of quantum data. The results provide a paradigm for versatile and efficient quantum generative learning.

Quantum conditional generative adversarial network based on patch method for abnormal electrocardiogram generation

To address the scarcity and class imbalance of abnormal electrocardiogram (ECG) databases, which are crucial in AI-driven diagnostic tools for potential cardiovascular disease detection, this study proposes a novel quantum conditional generative adversarial algorithm (QCGAN-ECG) for generating abnormal ECG signals. The QCGAN-ECG constructs a quantum generator based on patch method. In this method, each sub-generator generates distinct features of abnormal heartbeats in different segments. This patch-based generative algorithm conserves quantum resources and makes QCGAN-ECG practical for near-term quantum devices. Additionally, QCGAN-ECG introduces quantum registers as control conditions. It encodes information about the types and probability distributions of abnormal heartbeats into quantum registers, rendering the entire generative process controllable. Simulation experiments on Pennylane demonstrated that the QCGAN-ECG could generate completely abnormal heartbeats with an average accuracy of 88.8%. Moreover, the QCGAN-ECG can accurately fit the probability distribution of various abnormal ECG data. In the anti-noise experiments, the QCGAN-ECG showcased outstanding robustness across various levels of quantum noise interference. These results demonstrate the effectiveness and potential applicability of the QCGAN-ECG for generating abnormal ECG signals, which will further promote the development of AI-driven cardiac disease diagnosis systems. The source code is available at github.com/VanSWK/QCGAN_ECG.

Quantum generative adversarial learning in photonics

Quantum generative adversarial networks (QGANs), an intersection of quantum computing and machine learning, have attracted widespread attention due to their potential advantages over classical analogs. However, in the current era of noisy intermediate-scale quantum (NISQ) computing, it is essential to investigate whether QGANs can perform learning tasks on near-term quantum devices usually affected by noise and even defects. In this Letter, using a programmable silicon quantum photonic chip, we experimentally demonstrate the QGAN model in photonics for the first time to our knowledge and investigate the effects of noise and defects on its performance. Our results show that QGANs can generate high-quality quantum data with a fidelity higher than 90%, even under conditions where up to half of the generator's phase shifters are damaged, or all of the generator and discriminator's phase shifters are subjected to phase noise up to 0.04π. Our work sheds light on the feasibility of implementing QGANs on the NISQ-era quantum hardware.

Recent Advances for Quantum Neural Networks in Generative Learning

Quantum computers are next-generation devices that hold promise to perform calculations beyond the reach of classical computers. A leading method towards achieving this goal is through quantum machine learning, especially quantum generative learning. Due to the intrinsic probabilistic nature of quantum mechanics, it is reasonable to postulate that quantum generative learning models (QGLMs) may surpass their classical counterparts. As such, QGLMs are receiving growing attention from the quantum physics and computer science communities, where various QGLMs that can be efficiently implemented on near-term quantum machines with potential computational advantages are proposed. In this paper, we review the current progress of QGLMs from the perspective of machine learning. Particularly, we interpret these QGLMs, covering quantum circuit Born machines, quantum generative adversarial networks, quantum Boltzmann machines, and quantum variational autoencoders, as the quantum extension of classical generative learning models. In this context, we explore their intrinsic relations and their fundamental differences. We further summarize the potential applications of QGLMs in both conventional machine learning tasks and quantum physics. Last, we discuss the challenges and further research directions for QGLMs.

Enhanced Synaptic Behaviors in Chitosan Electrolyte-Based Electric-Double-Layer Transistors with Poly-Si Nanowire Channel Structures

In this study, we enhance the synaptic behavior of artificial synaptic transistors by utilizing nanowire (NW)-type polysilicon channel structures. The high surface-to-volume ratio of the NW channels enables efficient modulation of the channel conductance, which is interpreted as the synaptic weight. As a result, NW-type synaptic transistors exhibit a larger hysteresis window compared to film-type synaptic transistors, even within the same gate voltage sweeping range. Moreover, NW-type synaptic transistors demonstrate superior short-term facilitation and long-term memory transition compared with film-type ones, as evidenced by the measured paired-pulse facilitation and excitatory post-synaptic current characteristics at varying frequencies and pulse numbers. Additionally, we observed gradual potentiation/depression characteristics, making these artificial synapses applicable to artificial neural networks. Furthermore, the NW-type synaptic transistors exhibit improved Modified National Institute of Standards and Technology pattern recognition rate of 91.2%. In conclusion, NW structure channels are expected to be a promising technology for next-generation artificial intelligence (AI) semiconductors, and the integration of NW structure channels has significant potential to advance AI semiconductor technology.

Quantum Adversarial Transfer Learning

Adversarial transfer learning is a machine learning method that employs an adversarial training process to learn the datasets of different domains. Recently, this method has attracted attention because it can efficiently decouple the requirements of tasks from insufficient target data. In this study, we introduce the notion of quantum adversarial transfer learning, where data are completely encoded by quantum states. A measurement-based judgment of the data label and a quantum subroutine to compute the gradients are discussed in detail. We also prove that our proposal has an exponential advantage over its classical counterparts in terms of computing resources such as the gate number of the circuits and the size of the storage required for the generated data. Finally, numerical experiments demonstrate that our model can be successfully trained, achieving high accuracy on certain datasets.

Deep quantum neural networks on a superconducting processor

Deep learning and quantum computing have achieved dramatic progresses in recent years. The interplay between these two fast-growing fields gives rise to a new research frontier of quantum machine learning. In this work, we report an experimental demonstration of training deep quantum neural networks via the backpropagation algorithm with a six-qubit programmable superconducting processor. We experimentally perform the forward process of the backpropagation algorithm and classically simulate the backward process. In particular, we show that three-layer deep quantum neural networks can be trained efficiently to learn two-qubit quantum channels with a mean fidelity up to 96.0% and the ground state energy of molecular hydrogen with an accuracy up to 93.3% compared to the theoretical value. In addition, six-layer deep quantum neural networks can be trained in a similar fashion to achieve a mean fidelity up to 94.8% for learning single-qubit quantum channels. Our experimental results indicate that the number of coherent qubits required to maintain does not scale with the depth of the deep quantum neural network, thus providing a valuable guide for quantum machine learning applications with both near-term and future quantum devices.

Quantum reinforcement learning in the presence of thermal dissipation

A study of the effect of thermal dissipation on quantum reinforcement learning is performed. For this purpose, a nondissipative quantum reinforcement learning protocol is adapted to the presence of thermal dissipation. Analytical calculations as well as numerical simulations are carried out, obtaining evidence that dissipation does not significantly degrade the performance of the quantum reinforcement learning protocol for sufficiently low temperatures, in some cases even being beneficial. Quantum reinforcement learning under realistic experimental conditions of thermal dissipation opens an avenue for the realization of quantum agents to be able to interact with a changing environment, as well as adapt to it, with many plausible applications inside quantum technologies and machine learning.

Presence and Absence of Barren Plateaus in Tensor-Network Based Machine Learning

Tensor networks are efficient representations of high-dimensional tensors with widespread applications in quantum many-body physics. Recently, they have been adapted to the field of machine learning, giving rise to an emergent research frontier that has attracted considerable attention. Here, we study the trainability of tensor-network based machine learning models by exploring the landscapes of different loss functions, with a focus on the matrix product states (also called tensor trains) architecture. In particular, we rigorously prove that barren plateaus (i.e., exponentially vanishing gradients) prevail in the training process of the machine learning algorithms with global loss functions. Whereas, for local loss functions the gradients with respect to variational parameters near the local observables do not vanish as the system size increases. Therefore, the barren plateaus are absent in this case and the corresponding models could be efficiently trainable. Our results reveal a crucial aspect of tensor-network based machine learning in a rigorous fashion, which provide a valuable guide for both practical applications and theoretical studies in the future.

Resource-efficient high-dimensional subspace teleportation with a quantum autoencoder

Quantum autoencoders serve as efficient means for quantum data compression. Here, we propose and demonstrate their use to reduce resource costs for quantum teleportation of subspaces in high-dimensional systems. We use a quantum autoencoder in a compress-teleport-decompress manner and report the first demonstration with qutrits using an integrated photonic platform for future scalability. The key strategy is to compress the dimensionality of input states by erasing redundant information and recover the initial states after chip-to-chip teleportation. Unsupervised machine learning is applied to train the on-chip autoencoder, enabling the compression and teleportation of any state from a high-dimensional subspace. Unknown states are decompressed at a high fidelity (~0.971), obtaining a total teleportation fidelity of ~0.894. Subspace encodings hold great potential as they support enhanced noise robustness and increased coherence. Laying the groundwork for machine learning techniques in quantum systems, our scheme opens previously unidentified paths toward high-dimensional quantum computing and networking.

Quantum machine learning for chemistry and physics

Machine learning (ML) has emerged as a formidable force for identifying hidden but pertinent patterns within a given data set with the objective of subsequent generation of automated predictive behavior. In recent years, it is safe to conclude that ML and its close cousin, deep learning (DL), have ushered in unprecedented developments in all areas of physical sciences, especially chemistry. Not only classical variants of ML, even those trainable on near-term quantum hardwares have been developed with promising outcomes. Such algorithms have revolutionized materials design and performance of photovoltaics, electronic structure calculations of ground and excited states of correlated matter, computation of force-fields and potential energy surfaces informing chemical reaction dynamics, reactivity inspired rational strategies of drug designing and even classification of phases of matter with accurate identification of emergent criticality. In this review we shall explicate a subset of such topics and delineate the contributions made by both classical and quantum computing enhanced machine learning algorithms over the past few years. We shall not only present a brief overview of the well-known techniques but also highlight their learning strategies using statistical physical insight. The objective of the review is not only to foster exposition of the aforesaid techniques but also to empower and promote cross-pollination among future research in all areas of chemistry which can benefit from ML and in turn can potentially accelerate the growth of such algorithms.

Entangling Quantum Generative Adversarial Networks

Generative adversarial networks (GANs) are one of the most widely adopted machine learning methods for data generation. In this work, we propose a new type of architecture for quantum generative adversarial networks (an entangling quantum GAN, EQ-GAN) that overcomes limitations of previously proposed quantum GANs. Leveraging the entangling power of quantum circuits, the EQ-GAN converges to the Nash equilibrium by performing entangling operations between both the generator output and true quantum data. In the first multiqubit experimental demonstration of a fully quantum GAN with a provably optimal Nash equilibrium, we use the EQ-GAN on a Google Sycamore superconducting quantum processor to mitigate uncharacterized errors, and we numerically confirm successful error mitigation with simulations up to 18 qubits. Finally, we present an application of the EQ-GAN to prepare an approximate quantum random access memory and for the training of quantum neural networks via variational datasets.

Efficient Bipartite Entanglement Detection Scheme with a Quantum Adversarial Solver

The recognition of entanglement states is a notoriously difficult problem when no prior information is available. Here, we propose an efficient quantum adversarial bipartite entanglement detection scheme to address this issue. Our proposal reformulates the bipartite entanglement detection as a two-player zero-sum game completed by parameterized quantum circuits, where a two-outcome measurement can be used to query a classical binary result about whether the input state is bipartite entangled or not. In principle, for an N-qubit quantum state, the runtime complexity of our proposal is O(poly(N)T) with T being the number of iterations. We experimentally implement our protocol on a linear optical network and exhibit its effectiveness to accomplish the bipartite entanglement detection for 5-qubit quantum pure states and 2-qubit quantum mixed states. Our work paves the way for using near-term quantum machines to tackle entanglement detection on multipartite entangled quantum systems.

Quantum semi-supervised generative adversarial network for enhanced data classification

In this paper, we propose the quantum semi-supervised generative adversarial network (qSGAN). The system is composed of a quantum generator and a classical discriminator/classifier (D/C). The goal is to train both the generator and the D/C, so that the latter may get a high classification accuracy for a given dataset. Hence the qSGAN needs neither any data loading nor to generate a pure quantum state, implying that qSGAN is much easier to implement than many existing quantum algorithms. Also the generator can serve as a stronger adversary than a classical one thanks to its rich expressibility, and it is expected to be robust against noise. These advantages are demonstrated in a numerical simulation.

Quantum State Tomography with Conditional Generative Adversarial Networks

Quantum state tomography (QST) is a challenging task in intermediate-scale quantum devices. Here, we apply conditional generative adversarial networks (CGANs) to QST. In the CGAN framework, two dueling neural networks, a generator and a discriminator, learn multimodal models from data. We augment a CGAN with custom neural-network layers that enable conversion of output from any standard neural network into a physical density matrix. To reconstruct the density matrix, the generator and discriminator networks train each other on data using standard gradient-based methods. We demonstrate that our QST-CGAN reconstructs optical quantum states with high fidelity, using orders of magnitude fewer iterative steps, and less data, than both accelerated projected-gradient-based and iterative maximum-likelihood estimation. We also show that the QST-CGAN can reconstruct a quantum state in a single evaluation of the generator network if it has been pretrained on similar quantum states.

F-Divergences and Cost Function Locality in Generative Modelling with Quantum Circuits

Generative modelling is an important unsupervised task in machine learning. In this work, we study a hybrid quantum-classical approach to this task, based on the use of a quantum circuit born machine. In particular, we consider training a quantum circuit born machine using f-divergences. We first discuss the adversarial framework for generative modelling, which enables the estimation of any f-divergence in the near term. Based on this capability, we introduce two heuristics which demonstrably improve the training of the born machine. The first is based on f-divergence switching during training. The second introduces locality to the divergence, a strategy which has proved important in similar applications in terms of mitigating barren plateaus. Finally, we discuss the long-term implications of quantum devices for computing f-divergences, including algorithms which provide quadratic speedups to their estimation. In particular, we generalise existing algorithms for estimating the Kullback-Leibler divergence and the total variation distance to obtain a fault-tolerant quantum algorithm for estimating another f-divergence, namely, the Pearson divergence.

Universal adversarial examples and perturbations for quantum classifiers

Quantum machine learning explores the interplay between machine learning and quantum physics, which may lead to unprecedented perspectives for both fields. In fact, recent works have shown strong evidence that quantum computers could outperform classical computers in solving certain notable machine learning tasks. Yet, quantum learning systems may also suffer from the vulnerability problem: adding a tiny carefully crafted perturbation to the legitimate input data would cause the systems to make incorrect predictions at a notably high confidence level. In this paper, we study the universality of adversarial examples and perturbations for quantum classifiers. Through concrete examples involving classifications of real-life images and quantum phases of matter, we show that there exist universal adversarial examples that can fool a set of different quantum classifiers. We prove that, for a set of k classifiers with each receiving input data of n qubits, an O(ln [k]/2 ⁿ ) increase of the perturbation strength is enough to ensure a moderate universal adversarial risk. In addition, for a given quantum classifier, we show that there exist universal adversarial perturbations, which can be added to different legitimate samples to make them adversarial examples for the classifier. Our results reveal the universality perspective of adversarial attacks for quantum machine learning systems, which would be crucial for practical applications of both near-term and future quantum technologies in solving machine learning problems.

Natural evolutionary strategies for variational quantum computation

Natural evolutionary strategies (NES) are a family of gradient-free black-box optimization algorithms. This study illustrates their use for the optimization of randomly initialized parameterized quantum circuits (PQCs) in the region of vanishing gradients. We show that using the NES gradient estimator the exponential decrease in variance can be alleviated. We implement two specific approaches, the exponential and separable NES, for parameter optimization of PQCs and compare them against standard gradient descent. We apply them to two different problems of ground state energy estimation using variational quantum eigensolver and state preparation with circuits of varying depth and length. We also introduce batch optimization for circuits with larger depth to extend the use of ES to a larger number of parameters. We achieve accuracy comparable to state-of-the-art optimization techniques in all the above cases with a lower number of circuit evaluations. Our empirical results indicate that one can use NES as a hybrid tool in tandem with other gradient-based methods for optimization of deep quantum circuits in regions with vanishing gradients.

Experimental Quantum Principal Component Analysis via Parametrized Quantum Circuits

Principal component analysis (PCA) is a widely applied but rather time-consuming tool in machine learning techniques. In 2014, Lloyd, Mohseni, and Rebentrost proposed a quantum PCA (qPCA) algorithm [Lloyd, Mohseni, and Rebentrost, Nat. Phys. 10, 631 (2014)NPAHAX1745-247310.1038/nphys3029] that still lacks experimental demonstration due to the experimental challenges in preparing multiple quantum state copies and implementing quantum phase estimations. Here, we propose a new qPCA algorithm using the hybrid classical-quantum control, where parameterized quantum circuits are optimized with simple measurement observables, which significantly reduces the experimental complexity. As one important PCA application, we implement a human face recognition process using the images from the Yale Face Dataset. By training our quantum processor, the eigenface information in the training dataset is encoded into the parameterized quantum circuit, and the quantum processor learns to recognize new face images from the test dataset with high fidelities. Our work paves a new avenue toward the study of qPCA applications in theory and experiment.

Machine Learning in Nanoscience: Big Data at Small Scales

Recent advances in machine learning (ML) offer new tools to extract new insights from large data sets and to acquire small data sets more effectively. Researchers in nanoscience are experimenting with these tools to tackle challenges in many fields. In addition to ML's advancement of nanoscience, nanoscience provides the foundation for neuromorphic computing hardware to expand the implementation of ML algorithms. In this Mini Review, we highlight some recent efforts to connect the ML and nanoscience communities by focusing on three types of interaction: (1) using ML to analyze and extract new insights from large nanoscience data sets, (2) applying ML to accelerate material discovery, including the use of active learning to guide experimental design, and (3) the nanoscience of memristive devices to realize hardware tailored for ML. We conclude with a discussion of challenges and opportunities for future interactions between nanoscience and ML researchers.

Training of quantum circuits on a hybrid quantum computer

Generative modeling is a flavor of machine learning with applications ranging from computer vision to chemical design. It is expected to be one of the techniques most suited to take advantage of the additional resources provided by near-term quantum computers. Here, we implement a data-driven quantum circuit training algorithm on the canonical Bars-and-Stripes dataset using a quantum-classical hybrid machine. The training proceeds by running parameterized circuits on a trapped ion quantum computer and feeding the results to a classical optimizer. We apply two separate strategies, Particle Swarm and Bayesian optimization to this task. We show that the convergence of the quantum circuit to the target distribution depends critically on both the quantum hardware and classical optimization strategy. Our study represents the first successful training of a high-dimensional universal quantum circuit and highlights the promise and challenges associated with hybrid learning schemes.