Abstract In classical machine learning (ML), “overfitting” is the phenomenon occurring when a given model learns the training data excessively well, and it thus performs poorly on unseen data. A commonly employed technique in ML is the so called “dropout,” which prevents computational units from becoming too specialized, hence reducing the risk of overfitting. With the advent of quantum neural networks (QNNs) as learning models, overfitting might soon become an issue, owing to the increasing depth of quantum circuits as well as multiple embedding of classical features, which are employed to give the computational nonlinearity. Here, a generalized approach is presented to apply the dropout technique in QNN models, defining and analyzing different quantum dropout strategies to avoid overfitting and achieve a high level of generalization. This study allows to envision the power of quantum dropout in enabling generalization, providing useful guidelines on determining the maximal dropout probability for a given model, based on overparametrization theory. It also highlights how quantum dropout does not impact the features of the QNN models, such as expressibility and entanglement. All these conclusions are supported by extensive numerical simulations and may pave the way to efficiently employing deep quantum machine learning (QML) models based on state‐of‐the‐art QNNs.
Abstract In classical machine learning (ML), “overfitting” is the phenomenon occurring when a given model learns the training data excessively well, and it thus performs poorly on unseen data. A commonly employed technique in ML is the so called “dropout,” which prevents computational units from becoming too specialized, hence reducing the risk of overfitting. With the advent of quantum neural networks (QNNs) as learning models, overfitting might soon become an issue, owing to the increasing depth of quantum circuits as well as multiple embedding of classical features, which are employed to give the computational nonlinearity. Here, a generalized approach is presented to apply the dropout technique in QNN models, defining and analyzing different quantum dropout strategies to avoid overfitting and achieve a high level of generalization. This study allows to envision the power of quantum dropout in enabling generalization, providing useful guidelines on determining the maximal dropout probability for a given model, based on overparametrization theory. It also highlights how quantum dropout does not impact the features of the QNN models, such as expressibility and entanglement. All these conclusions are supported by extensive numerical simulations and may pave the way to efficiently employing deep quantum machine learning (QML) models based on state‐of‐the‐art QNNs.
Quantum convolutional neural network (QCNN), an early application for quantum computers in the noisy intermediate-scale quantum era, has been consistently proven successful as a machine learning (ML) algorithm for several tasks with significant accuracy. Derived from its classical counterpart, QCNN is prone to overfitting. Overfitting is a typical shortcoming of ML models that are trained too closely to the availed training dataset and perform relatively poorly on unseen datasets for a similar problem. In this work we study post-training approaches for mitigating overfitting in QCNNs. We find that a straightforward adaptation of a classical post-training method, known as neuron dropout, to the quantum setting leads to a significant and undesirable consequence: a substantial decrease in success probability of the QCNN. We argue that this effect exposes the crucial role of entanglement in QCNNs and the vulnerability of QCNNs to entanglement loss. Hence, we propose a parameter adaptation method as an alternative method. Our method is computationally efficient and is found to successfully handle overfitting in the test cases.
Quantum Machine Learning (QML) has been acknowledged for its transformative potential in enhancing computational capabilities beyond classical approaches, with Quantum Neural Networks (QNNs) emerging as one of the most promising models. Despite the advancements, the adaptation of effective optimization techniques such as batch normalization or regularization, which are well-established in classical Neural Networks, remains an ongoing challenge for QNNs.This adaptation is crucial, especially when considering the implementation of techniques like quantum dropout, which, although inspired by its classical counterpart to reduce the risk of overfitting by "deleting" certain model components during the forward step, exhibits distinct behaviours in a quantum context. This study introduces a novel approach to modulate the impact of dropout in QNNs through a technique we term Soft Dropout. Our method introduces a parameterized softening mechanism for gate eliminations, enabling a more nuanced control over the dropout process, thereby mitigating its adverse effects on the network’s learning capacity, and reducing at the same time the risk of overfitting.Our experimental analysis demonstrates that softening current quantum dropout consistently enhances model performance across a spectrum of configurations. This improvement is attributed to the intrinsic properties of quantum gates, which allow for a gradual adjustment of their impact on the quantum circuit up to the identity operation. The results highlight the importance of adapting classical machine learning techniques to the quantum context, considering the unique computational model of quantum processing, potentially accelerating the adoption of QML in real-world problems.
Machine Learning (ML) has changed the way computers work by letting them learn from data and make smart choices. However, traditional ML techniques encounter scalability and efficiency constraints as datasets get larger and computational problems become more complicated[1]. These restrictions could be circumvented by the new paradigms that quantum computing offers by using entanglement and superposition [2], [3]. The combination of the Quantum computing with the Machine Learning is called the Quantum Machine Learning(QML), offers efficiency improvements, new algorithmic opportunities, and speedups in certain linear algebraic operations. So, this review dives deeply into quantum-classical algorithms, with a particular emphasis on the approaches like quantum neural network and quantum support vector machines. We examine computational complexity, architectural design, benchmarking findings, and real-world applications (such as optimization, cryptography, and classification). We also discuss important issues including scalability, data encoding, and noise, and we suggest future paths for error prevention and scalable structures.
Quantum neural networks (QNNs) are a revolutionary paradigm placed at the frontier of machine learning and quantum computing. By utilizing quantum mechanical principles like superposition, entanglement, and quantum parallelism, QNNs facilitate the solution of complex machine learning problems that were thought to be impossible according to conventional models. This chapter provides a detailed study of QNNs, from elementary principles to practical applications. It begins with a rundown of the most significant concepts in machine learning and quantum computing, followed by QNN architecture, with important points including quantum gates and parameterized quantum circuits. The chapter addresses challenges in training QNNs, with special attention given to hybrid quantum-classical optimization algorithms and their utility in successful model training. It also examines multiple applications of QNNs, including simulation in quantum chemistry, optimization problems, and real-world machine learning applications, to demonstrate how they have the potential to outperform conventional algorithms in high dimensional or highly entangled data environments. This chapter provides a comparative assessment of quantum machine learning frameworks, quantum hardware platforms, and hybrid optimization methods and aids in determining the most suitable tools to design QNNs. It finally discusses possible areas of future research and research issues in the field, emphasizing the urgent need to improve quantum hardware, increase noise tolerance, and scale up. As quantum computing technology evolves, QNNs are expected to be at the center of solving some of the most complex and computationally intensive problems encountered in various industries.
Quantum machine learning (QML) holds immense potential for revolutionizing computational intelligence, yet faces significant challenges in optimizing quantum neural network architectures for practical implementation. This paper introduces Q-Drop, an innovative quantum adaptation technique that enhances parameterized quantum circuits (PQCs) for training performance. The system includes two novel optimization strategies: statistical pruning and dynamic dropout (circuit flipflops), which significantly improve the learning performance and robustness of quantum orthogonal neural networks. Evaluation results across standard (MNIST, Fashion-MNIST) and medical imaging (Pneumonia-MNIST, Retina-MNIST) datasets demonstrate substantial performance gains. Notably, the approach achieves up to 94.3 % accuracy on medical image classification and 98.7 % accuracy on standard image datasets, outperforming existing quantum machine learning methods. By addressing critical challenges in quantum neural network training, this work highlights the potential of applying quantum machine learning to enhance performance for classical computer vision tasks and QML-driven scheduling optimization in quantum networks.
Quantum machine learning is at the crossroads of two of the most exciting current areas of research: quantum computing and classical machine learning. Although the field is still in its infancy, the body of literature is already large enough to warrant several review articles [1–3]. This short survey focuses on a selection of significant recent results on the subtopic of quantum neural networks, an area that hopes to build on the enormous impact that classical neural networks have had. In particular, we concentrate on quantum generalizations of popular neural-network concepts such as Boltzmann machines, generative adversarial networks and autoencoders, as well as applications of classical neural networks to quantum information and vice versa. Examples of Boltzmann machines. In a fully connected Boltzmann machine, connections exist between all visible and hidden neurons. In a restricted Boltzmann machine (RBM), there are no connections between neurons of the same type. A deep Boltzmann machine (DBM) consists of adding one or more additional layers of hidden neurons to an RBM, with no connections between neurons in the same layer. The energy-based nature of BMs gives a natural framework for considering quantum generalizations of their behavior. The BM energy function is equivalent to the Hamiltonian of a simple Ising model and one might hope that more general Hamiltonians allowed by quantum mechanics could explain certain data sets better than classically. Amin et al. [4] adopt this approach, and take the so-called transverse field Ising Hamiltonian as the energy function. This increased generality brings certain difficulties, however, as the transverse field term makes training the quantum Boltzmann machine (QBM) non-trivial. Although the general scaling and performance of QBMs is not yet well understood, for certain small-size examples the authors observe that their QBMs can learn data distributions better than classical BMs. Kieferova and Wiebe [5] extend the formalism of Amin et al. and consider more general Hamiltonians that, unlike the transverse Ising model, are not in general believed to be classically efficiently simulatable. Furthermore, they propose new methods for training that allow for parameters corresponding to quantum terms to be learned. Finally, their QBM enables a form of quantum-state tomography that can learn non-classical data, and also generate copies of the reconstructed state. Again, small-scale numerical evidence suggests that their proposals may provide an advantage over classical BMs, although their tendency to overfit data must be investigated further. The practical value of BMs, either classical or quantum, relies in part on the ease with which they are trained. This in turn depends on sampling efficiently from the Boltzmann distribution. Classically this can be done approximately only for the special case of restricted Boltzmann machines (RBM), i.e. where connections are between visible and hidden units, and no connections exist between neurons of the same type. Wiebe et al. [6] propose two quantum algorithms for Boltzmann sampling, based on starting from a state corresponding to the product distribution that is closest to the target Boltzmann distribution. While small-scale numerical studies are encouraging, true bounds on the running time of their algorithms rely on a problem-dependent parameter κ, the scaling of which is hard to estimate. The hope remains though that empirically their algorithms work well in practice, even for multi-layer and fully connected BMs. The expressive power of BMs for compactly representing complicated probability distributions has led to another line of investigation, namely their use for representing quantum many-body wave functions. The authors apply this technique to two prototypical spin models and achieve high accuracy in both ground-state estimation and dynamical evolution, improving on existing state-of-the-art techniques. Their results indicate that RBM states can capture complex many-body correlations in an efficient manner—evidence reinforced by the work of Deng et al. [8], who show that certain topological quantum states in one, two and three dimensions can be represented by RBM states with a number of parameters only linear in the system size. In a subsequent study, however, Gao and Duan [9] prove that although RBM states can indeed represent many highly entangled states, their expressive power is limited in that they cannot represent arbitrary states generated by polynomial-sized quantum circuits, nor those that are the ground states of k-local Hamiltonians with polynomial-sized energy gaps, unless the polynomial hierarchy from computational complexity theory collapses. On the other hand, they show that these two important classes of states can be efficiently represented by a deep Boltzmann machine of three layers. Intriguingly though, another paper by Deng et al. [10] gives an analytic construction of a family of RBM states with a number of parameters linear in the system size that exhibits maximal volume-law entanglement, and that cannot be represented efficiently by either matrix product states (MPS) or tensor-network (TN) states. This shows that the expressive power of even efficiently parametrized RBM states is not limited by entanglement in the same way that other popular compact representations are. This gives the hope that RBM states may prove a valuable tool in understanding entangled quantum systems intractable by traditional methods. Levine et al. [11] establish another connection between the many-body wave function and neural networks, this time in the form of convolutional arithmetic circuits (ConvAC), a variant of the popular convolutional neural networks in widespread use today. By proving a one-to-one equivalence between a ConvAC circuit and TN quantum states, the authors are able to use tools from quantum information theory to analyze the entanglement present in the corresponding TN, and quantify the neural network's ability to model complex correlations between its inputs. This in turn can be used to obtain bounds on the expressivity of a given ConvAC architecture and be of practical use in choosing network parameters tailored to the data. While ConvAC are not widely used in practice, the authors empirically validate that the insights gained can be applied successfully to more common convolutional neural-network designs. Generative adversarial networks (GAN) are machine-learning algorithms in which two players—a generator and a discriminator—compete against each another. The generator's goal is to create and send fake data samples to the discriminator and maximize the probability that the discriminator erroneously believes that the sample comes from some true data distribution. The discriminator attempts to discern real from fake data as best as possible. Under reasonable assumptions the game converges to a point where the discriminator is unable to discriminate with probability greater than 1/2 (i.e. no better than random guessing), and the generator in fact has learned to generate data from the true distribution. Lloyd and Weedbrook [12] consider the natural extension in which one or both of the generator and discriminator are equipped with quantum information processors. When the data to be learned are a quantum state and both parties have quantum processors, the authors show that the unique end point of the adversarial game also coincides with the generator producing a quantum state corresponding to the true data statistics, and the discriminator unable to discern true from false data better than random guessing. They further argue that a different outcome may hold when the true samples are produced by the measurement of some quantum state, and the generator is purely classical. The concept of quantum supremacy is based on the assumption that there exist probability distributions accessible to a quantum computer that no classical computer can efficiently sample from. If the true data correspond to one of these distributions, then no classical generator can efficiently generate fake data reproducing the true statistics and, in principle, the discriminator can successfully discriminate true from fake data. However, whether the discriminator can efficiently find the measurements required to do so is unclear. Quantum-computing techniques have also found applications in autoencoders—neural networks where a larger number of input and output neurons are connected via a smaller number of intermediary latent neurons. The goal is to tune the weights of the network so that a training set of classical bit strings can be approximately recovered after being passed through the autoencoder. Romero et al. [13] consider instead a training set of quantum states, and ask whether a quantum circuit with a similar bottleneck structure can compress and approximately recover the data. The circuits that they consider consist of gates chosen from some set of parametrized unitary operations, and arranged in some fixed order. The parameters are then optimized classically so that the circuit best predicts the training-set labels. The authors demonstrate the validity of this approach by showing that ground states of the Hubbard model and certain molecules can indeed be compressed and recovered by such circuits. However, in general, the performance of such quantum autoencoders will be highly dependent on the kind of programmable circuit on which they are based, and at present there does not seem to be a structured way of determining this. Quantum neural networks are still in their infancy and, while the above works are important steps towards bridging our understanding between classical neural networks and quantum computing, many questions remain unanswered. If the expressivity of Boltzmann machine states is not restricted by entanglement in the same way that MPS and tensor-network states are, what is the best way of understanding their limitations? How can physicists use the correspondence between ConvAC and TN to their advantage in finding efficient, expressive representations of many-body wave functions? Can classical data distributions be learned more efficiently by quantum GAN than classical GAN? Whatever the outcome of these and many other related questions, this promises to be an exciting and active area of research in the years to come.