Variational quantum algorithms (VQAs) have emerged as the leading strategy to obtain quantum advantages on the current noisy intermediate-scale devices. However, their entanglement-trainability correlation indicates that deep circuits are generally untrainable due to the barren plateau phenomenon, which challenges their applications. In this work, we suggest a gate-to-tensor encoding method for parametrized quantum circuits (PQCs), with which two long short-term memory networks are trained to predict both entangling capability and trainability. We call these LG networks. The remarkable capabilities of LG networks afford a statistical way to investigate the entanglement-trainability correlation of PQCs within a data set encompassing millions of generated circuits. This machine-learning-driven method first confirms the negative correlation between entanglement and trainability. Then, we observe that circuits with any values of entangling capability and trainability exist. These circuits with high entanglement and high trainability possess an appropriate high portion of nearest-neighbor nonlocal gates. Furthermore, the trained LG networks can be employed to construct PQCs with specific entanglement and trainability, demonstrating their practical applications in VQAs.
Variational quantum algorithms (VQAs) have emerged as the leading strategy to obtain quantum advantages on the current noisy intermediate-scale devices. However, their entanglement-trainability correlation indicates that deep circuits are generally untrainable due to the barren plateau phenomenon, which challenges their applications. In this work, we suggest a gate-to-tensor encoding method for parametrized quantum circuits (PQCs), with which two long short-term memory networks are trained to predict both entangling capability and trainability. We call these LG networks. The remarkable capabilities of LG networks afford a statistical way to investigate the entanglement-trainability correlation of PQCs within a data set encompassing millions of generated circuits. This machine-learning-driven method first confirms the negative correlation between entanglement and trainability. Then, we observe that circuits with any values of entangling capability and trainability exist. These circuits with high entanglement and high trainability possess an appropriate high portion of nearest-neighbor nonlocal gates. Furthermore, the trained LG networks can be employed to construct PQCs with specific entanglement and trainability, demonstrating their practical applications in VQAs.
Abstract Barren plateaus are the main obstacle to training quantum machine-learning models. On a barren plateau, the cost-function gradient shrinks exponentially as the circuit grows, and training stalls. Today the only reliable test is to measure it. That means sampling many gradients for every candidate circuit, which is expensive. We ask a different question. Can a classical model predict trainability from the circuit architecture alone? The architecture here means qubit count, depth, ansatz type, entanglement pattern, entangler gate, and cost-observable locality. We test this directly. We use an exact statevector simulator to build a dataset of \Nrows{} random variational circuits. For each circuit we estimate the gradient variance Var[∂C/∂θ] from \Samples{} random parameter vectors, using the parameter-shift rule. This variance is the label. A gradient-boosted regressor then predicts log10Var with $R^2 = \RsqHold{}$ on held-out architectures. A classifier separates barren from trainable circuits with an area under the ROC curve of \AucHold{}. We also test transfer to larger circuits. We train only on small circuits and test on the two largest unseen sizes (n=11,12). The model still reaches $R^2 = \RsqExtrap{}$. Permutation importance then recovers established theory. Cost-observable locality and entanglement structure matter most. We make no quantum-advantage claim. This is classical machine learning about quantum circuits. It offers a cheap way to screen ans\"atze, and it shows which design choices cause untrainability.
While recent breakthroughs have proven the ability of noisy intermediate-scale quantum (NISQ) devices to achieve quantum advantage in classically-intractable sampling tasks, the use of these devices for solving more practically relevant computational problems remains a challenge. Proposals for attaining practical quantum advantage typically involve parametrized quantum circuits (PQCs), whose parameters can be optimized to find solutions to diverse problems throughout quantum simulation and machine learning. However, training PQCs for real-world problems remains a significant practical challenge, largely due to the phenomenon of barren plateaus in the optimization landscapes of randomly-initialized quantum circuits. In this work, we introduce a scalable procedure for harnessing classical computing resources to provide pre-optimized initializations for PQCs, which we show significantly improves the trainability and performance of PQCs on a variety of problems. Given a specific optimization task, this method first utilizes tensor network (TN) simulations to identify a promising quantum state, which is then converted into gate parameters of a PQC by means of a high-performance decomposition procedure. We show that this learned initialization avoids barren plateaus, and effectively translates increases in classical resources to enhanced performance and speed in training quantum circuits. By demonstrating a means of boosting limited quantum resources using classical computers, our approach illustrates the promise of this synergy between quantum and quantum-inspired models in quantum computing, and opens up new avenues to harness the power of modern quantum hardware for realizing practical quantum advantage.
Quantum machine learning methods, including quantum kernels and variational quantum algorithms (VQAs), are poised to demonstrate quantum advantages in machine learning, chemistry, condensed matter physics, and materials science. However, these methods face critical challenges hindering practical quantum advantates: quantum kernels require meticulous design to outperform classical alternatives, while VQA training is obstructed by barren plateaus (BPs) in the optimization landscape. To address these issues, this thesis proposes two novel frameworks to guide quantum kernel design and tackle quantum neural network (QNN) training challenges in VQAs. Specifically, to resolve quantum kernel design challenges, we propose a data-driven method for automatic quantum kernel design, leveraging classical machine learning to learn from input data and identify optimal kernel structures. Experiments show this method finds suitable quantum kernels that avoid vanishing similarity, a common flaw in traditional designs. To improve VQA trainability, we propose an encoder-decoder parameter prediction framework, where a graph neural network (GNN) acts as the encoder to process information based on the QNN’s directed acyclic graph (DAG). Experiments confirm the parameters from this framework significantly enhance VQAs’ robustness, convergence speed, and trainability. In conclusion, we propose two schemes, QuKerNet and QuGHN, for automatic quantum kernel design and enhanced VQA trainability. QuKerNet considers optimal circuit layouts and variational parameters, and is more resource-efficient for contemporary quantum hardware by accounting for qubit topology and count. QuGHN is versatile, applicable to circuits with varying qubits, ansatzes, and tasks; its parameters enable faster convergence and more stable VQA solutions. These advancements enhance quantum machine learning practicality on near-term machines and its utility in large-scale quantum circuit simulations.
Abstract A new paradigm for data science has emerged, with quantum data, quantum models, and quantum computational devices. This field, called quantum machine learning (QML), aims to achieve a speedup over traditional machine learning for data analysis. However, its success usually hinges on efficiently training the parameters in quantum neural networks, and the field of QML is still lacking theoretical scaling results for their trainability. Some trainability results have been proven for a closely related field called variational quantum algorithms (VQAs). While both fields involve training a parametrized quantum circuit, there are crucial differences that make the results for one setting not readily applicable to the other. In this work, we bridge the two frameworks and show that gradient scaling results for VQAs can also be applied to study the gradient scaling of QML models. Our results indicate that features deemed detrimental for VQA trainability can also lead to issues such as barren plateaus in QML. Consequently, our work has implications for several QML proposals in the literature. In addition, we provide theoretical and numerical evidence that QML models exhibit further trainability issues not present in VQAs, arising from the use of a training dataset. We refer to these as dataset-induced barren plateaus. These results are most relevant when dealing with classical data, as here the choice of embedding scheme (i.e., the map between classical data and quantum states) can greatly affect the gradient scaling.
Abstract Combining classical optimization with parameterized quantum circuit evaluation, variational quantum algorithms (VQAs) are among the most promising algorithms in near-term quantum computing. However, the training of variational quantum circuits (VQCs) is susceptible to a phenomenon known as barren plateaus (BPs). Various approaches have been proposed to mitigate this issue, such as using neural networks to generate VQC parameters. In this paper, we improve the NN-based BP mitigation approach by refining the neural network architecture and extend its applicability to a more generalized scenario that includes random quantum inputs and VQC structures. We evaluate the effectiveness of the approach by comparing the convergence speed before and after it is utilized. Furthermore, we give an explanation for the effectiveness of the NN-based BP mitigation approach by utilizing a loss landscape visualization technique and the expressibility metric of VQC. The smoothness of the loss landscape offers an intuitive insight into the approach’s utility, while the reduction in expressibility accounts for the enhanced trainability. Our research highlights the universal applicability of the NN-based BP mitigation approach, underscoring its potential to drive progress in the development of VQAs across diverse domains.
In the field of quantum machine learning (QML), parametrized quantum circuits (PQCs)─constructed using a combination of fixed and tunable quantum gates─provide a promising hybrid framework for tackling complex machine learning problems. Despite numerous proposed applications, there remains limited exploration of data sets relevant to quantum chemistry. In this study, we investigate the potential benefits and limitations of PQCs on two chemically meaningful data sets: (1) the BSE49 data set, containing bond separation energies for 49 different classes of chemical bonds, and (2) a data set of water conformers, where coupled-cluster singles and doubles (CCSD) wave functions are predicted from lower-level electronic structure methods using the data-driven coupled-cluster (DDCC) approach. We construct a comprehensive set of 168 PQCs by combining 14 data encoding strategies with 12 variational ansätze, and evaluate their performance on circuits with 5 and 16 qubits. Our initial analysis examines the impact of circuit structure on model performance using state-vector simulations. We then explore how circuit depth and training set size influence model performance. Finally, we assess the performance of the best-performing PQCs on current quantum hardware, using both noisy simulations ("fake" backends) and real quantum devices. Our findings underscore the challenges of applying PQCs to chemically relevant problems that are straightforward for classical machine learning methods but remain nontrivial for quantum approaches.