The authors demonstrate that parametrized quantum circuits possess a better expressive power than classical neural networks, such as restricted and deep Boltzmann machines. Based on the advanced expressive power, the authors propose a Bayesian quantum circuit that enables parametrized quantum circuits to perform machine learning tasks
Parameterized quantum circuits (PQCs) have been broadly used as a hybrid\nquantum-classical machine learning scheme to accomplish generative tasks.\nHowever, whether PQCs have better expressive power than classical generative\nneural networks, such as restricted or deep Boltzmann machines, remains an open\nissue. In this paper, we prove that PQCs with a simple structure already\noutperform any classical neural network for generative tasks, unless the\npolynomial hierarchy collapses. Our proof builds on known results from tensor\nnetworks and quantum circuits (in particular, instantaneous quantum polynomial\ncircuits). In addition, PQCs equipped with ancillary qubits for post-selection\nhave even stronger expressive power than those without post-selection. We\nemploy them as an application for Bayesian learning, since it is possible to\nlearn prior probabilities rather than assuming they are known. We expect that\nit will find many more applications in semi-supervised learning where prior\ndistributions are normally assumed to be unknown. Lastly, we conduct several\nnumerical experiments using the Rigetti Forest platform to demonstrate the\nperformance of the proposed Bayesian quantum circuit.
Quantum Computing (QC) is fastly growing to replace current computing systems for many high-performance applications. Due to the rapid increase of computational power, machine learning models based on artificial neural networks (ANN) have become highly effective. Even though classical machine learning models have been performing well, quantum computing with machine learning, i.e., Quantum Machine Learning (QML), will enhance the performance in multiple ways. Subsequently, DeepQlearning is a prominent approach to reinforcement learning used in solving complex applications for a desired performance. But this performance can be improved using a quantum computer. This paper proposes a quantum-enhanced Deep Q Learning algorithm to see its advantages over its classical counterparts. We implement our approach using parametrized quantum circuit (PQC). The evaluation of the proposed method achieves the metrics rewards and episodes up to 500 points and 1200, respectively. The performance shows that it collects roughly four times more rewards in a given time and takes significantly fewer episodes to converge compared to the classical approach.
The quantum kernel method is one of the key approaches to quantum machine learning, which has the advantage of not requiring optimization and its theoretical simplicity. By virtue of these properties, several experimental demonstrations and discussions of the potential advantages have been developed so far. However, as is the case in classical machine learning, not all quantum machine learning models could be regarded as kernel methods. In this work, we explore a quantum machine learning model with a deep parametrized quantum circuit and aim to go beyond the conventional quantum kernel method. In this case, the expressive power and performance are expected to be enhanced, while the training process might be a bottleneck because of the barren plateaus. Moreover, the high computational cost of gradient-based optimization and the large search space of the gradient-free optimization directly make the training intractable. However, we find that parameters of a deep enough quantum circuit do not move much from their initial values during training, allowing for a first-order expansion with respect to the parameters. This behavior is similar to that of the neural tangent kernel in classical machine learning, and such a quantum machine learning with deep variational quantum circuits can be described by another emergent kernel, the . We show that the proposed quantum tangent kernel has the potential to outperform the conventional quantum kernel method by performing a classification task on an ansatz-generated dataset. This work provides a different direction beyond the conventional quantum kernel method and explores the potential power of quantum machine learning with deep parametrized quantum circuits. Published by the American Physical Society 2024
The astounding acceleration in Artificial Intelligence and Quantum Computing advances naturally gives rise to a line of research, which unrolls the potential advantages of quantum computing on classical Machine Learning tasks, known as Quantum Machine Learning or Quantum Machine Intelligence. The typical objectives are either (1) exploring the potential quantum advantages on classical learning tasks or (2) levering well-established classical ML algorithms to tackle quantum-related problems on Noisy Intermediate-Scale Quantum (NISQ) devices. Along the second research direction, we study Quantum Neural Networks (QNNs) to accomplish the purpose of Bayesian learning. By observing a wide range of studies on QNNs, in which the sole training method is based on frequentist training, we find that Bayesian learning benefits QNNs from two aspects. First, Bayesian-trained models enjoy a high level of generalization due to the prior and posterior distribution usage compared to frequentist training, which will be justified by this paper’s theoretical study of model capacity. Second, Bayesian Inference offers epistemic uncertainty estimation, which merits the decision-making process. It is worth mentioning that frequentist-trained QNNs generally lack this desirable property. Under the Bayesian training procedure, our derived models can be considered a new class of QNNs (called BayesianQNNs) which possesses both desirable properties of Bayesian Inference while maintaining comparable predictive performance as frequentist counterparts. The proposed Bayesian Quantum Neural Networks is justified by empirical evidence from numerical experiments.
Parameterized quantum circuits (PQCs) have emerged as a promising approach for quantum neural networks. However, understanding their expressive power in accomplishing machine learning tasks remains a crucial question. This paper investigates the expressivity of PQCs for approximating general multivariate function classes. Unlike previous Universal Approximation Theorems for PQCs, which are either nonconstructive or rely on parameterized classical data processing, we explicitly construct data re-uploading PQCs for approximating multivariate polynomials and smooth functions. We establish the first non-asymptotic approximation error bounds for these functions in terms of the number of qubits, quantum circuit depth, and number of trainable parameters. Notably, we demonstrate that for approximating functions that satisfy specific smoothness criteria, the quantum circuit size and number of trainable parameters of our proposed PQCs can be smaller than those of deep ReLU neural networks. We further validate the approximation capability of PQCs through numerical experiments. Our results provide a theoretical foundation for designing practical PQCs and quantum neural networks for machine learning tasks that can be implemented on near-term quantum devices, paving the way for the advancement of quantum machine learning.
Quantum machine learning promises great speedups over classical algorithms, but it often requires repeated computations to achieve a desired level of accuracy for its point estimates. Bayesian learning focuses more on sampling from posterior distributions than on point estimation, thus it might be more forgiving in the face of additional quantum noise. We propose a quantum algorithm for Bayesian neural network inference, drawing on recent advances in quantum deep learning, and simulate its empirical performance on several tasks. We find that already for small numbers of qubits, our algorithm approximates the true posterior well, while it does not require any repeated computations and thus fully realizes the quantum speedups.