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IEEE Transactions on Quantum Engineering

Hierarchical Quantum Architecture Search for Variational Quantum Algorithms

Tong Zhao, Bo Chen, Guanting Wu, Liang Zeng

Published Jan 1, 2024• 9 citations
Publisher

Abstract

Designing efficient variational quantum algorithms (VQAs) is crucial for transforming the theoretical advantages of quantum algorithms into practical applications. In this context, quantum architecture search (QAS) has been introduced to automate the search and design of VQAs. However, current mainstream QAS algorithms typically perform both global and local searches simultaneously, which can result in high search space complexity and optimization challenges. In this paper, we propose a hierarchical quantum architecture search framework based on a two-stage search structure. In the first stage, global exploration of the overall quantum circuit structure is performed, while in the second stage, local optimization of quantum gate selection is carried out. We provide a numerical analysis of the theoretical advantages of the proposed framework in reducing the search space. To evaluate practical performance, we conduct experiments on quantum chemistry tasks with different algorithm combinations integrated into the framework. The results demonstrate the effectiveness of the hierarchical search structure in automating quantum circuit design.

DOI
10.1109/tqe.2024.3454640

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Designing efficient variational quantum algorithms (VQAs) is crucial for transforming the theoretical advantages of quantum algorithms into practical applications. In this context, quantum architecture search (QAS) has been introduced to automate the search and design of VQAs. However, current mainstream QAS algorithms typically perform both global and local searches simultaneously, which can result in high search space complexity and optimization challenges. In this paper, we propose a hierarchical quantum architecture search framework based on a two-stage search structure. In the first stage, global exploration of the overall quantum circuit structure is performed, while in the second stage, local optimization of quantum gate selection is carried out. We provide a numerical analysis of the theoretical advantages of the proposed framework in reducing the search space. To evaluate practical performance, we conduct experiments on quantum chemistry tasks with different algorithm combinations integrated into the framework. The results demonstrate the effectiveness of the hierarchical search structure in automating quantum circuit design.
Quantum architecture search (QAS) has shown significant promise in automating quantum circuit design for Variational Quantum Algorithms (VQAs). However, a central challenge remains in the high computational cost of evaluating the ground-truth performance of numerous circuit architectures during the search process. This challenge is further complicated by factors such as inefficient gradient computation, the barren plateau phenomenon, and frequent data exchange between classical and quantum systems within VQAs, all of which restrict the scalability of QAS for increasingly complex VQAs. In this study, we investigate whether quantum architectures discovered on small-scale systems can be directly extended to large-scale quantum circuits. Our results demonstrate that the performance advantage of an optimal quantum architecture, identified on a small-scale system via a layerwise construction method, can be largely preserved and effectively transferred to large-scale systems. This work establishes a viable and efficient paradigm for designing effective large-scale quantum circuits, offering a practical shortcut that bypasses the primary bottlenecks of conventional QAS.
Variational quantum algorithms (VQAs) constitute a prominent paradigm for exploring the capabilities of near-term quantum computers. As the effectiveness of VQAs depends heavily on the design of variational quantum circuits, Quantum Architecture Search (QAS) has emerged as a critical research area to automate the discovery of high-performing circuit structures. This paper reviews key advancements in current research on QAS, including its core concepts, representative methodologies, applications, and emerging trends. The content is structured to ensure broad accessibility for a diverse audience of researchers while preserving the core principles of complex methodologies. In addition, we discuss remaining challenges and suggest potential research directions to offer perspectives on future exploration in this rapidly evolving field.
Abstract Variational quantum algorithms (VQAs) are expected to be a path to quantum advantages on noisy intermediate-scale quantum devices. However, both empirical and theoretical results exhibit that the deployed ansatz heavily affects the performance of VQAs such that an ansatz with a larger number of quantum gates enables a stronger expressivity, while the accumulated noise may render a poor trainability. To maximally improve the robustness and trainability of VQAs, here we devise a resource and runtime efficient scheme termed quantum architecture search (QAS). In particular, given a learning task, QAS automatically seeks a near-optimal ansatz (i.e., circuit architecture) to balance benefits and side-effects brought by adding more noisy quantum gates to achieve a good performance. We implement QAS on both the numerical simulator and real quantum hardware, via the IBM cloud, to accomplish data classification and quantum chemistry tasks. In the problems studied, numerical and experimental results show that QAS cannot only alleviate the influence of quantum noise and barren plateaus but also outperforms VQAs with pre-selected ansatze.
A significant hurdle in the noisy intermediate-scale quantum (NISQ) era is identifying functional quantum circuits. These circuits must also adhere to the constraints imposed by current quantum hardware limitations. Variational quantum algorithms (VQAs), a class of quantum-classical optimization algorithms, were developed to address these challenges in the currently available quantum devices. However, the overall performance of VQAs depends on the initialization strategy of the variational circuit, the structure of the circuit (also known as ansatz), and the configuration of the cost function. Focusing on the structure of the circuit, in this thesis, we improve the performance of VQAs by automating the search for an optimal structure for the variational circuits using reinforcement learning (RL). Within the thesis, the optimality of a circuit is determined by evaluating its depth, the overall count of gates and parameters, and its accuracy in solving the given problem. The task of automating the search for optimal quantum circuits is known as quantum architecture search (QAS). The majority of research in QAS is primarily focused on a noiseless scenario. Yet, the impact of noise on the QAS remains inadequately explored. In this thesis, we tackle the issue by introducing a tensor-based quantum circuit encoding, restrictions on environment dynamics to explore the search space of possible circuits efficiently, an episode halting scheme to steer the agent to find shorter circuits, a double deep Q-network (DDQN) with an εεε-greedy policy for better stability. The numerical experiments on noiseless and noisy quantum hardware show that in dealing with various VQAs, our RL-based QAS outperforms existing QAS. Meanwhile, the methods we propose in the thesis can be readily adapted to address a wide range of other VQAs.
Quantum architecture search (QAS) has emerged to automate the design of high-performance quantum circuits under specific tasks and hardware constraints. We propose a noise-aware quantum architecture search (NA-QAS) framework based on variational quantum circuit design. By incorporating a noise model into the training of parameterized quantum circuits (PQCs) , the proposed framework identifies the noise-robust architectures. We introduce a hybrid Hamiltonian ε\varepsilonε -greedy strategy to optimize evaluation costs and circumvent local optima. Furthermore, an enhanced variable-depth NSGA-II algorithm is employed to navigate the vast search space, enabling an automated trade-off between architectural expressibility and quantum hardware overhead. The effectiveness of the framework is validated through binary classification and iris multi-classification tasks under a noisy condition. Compared to existing approaches, our framework can search for quantum architectures with superior performance and greater resource efficiency under a noisy condition.
Abstract Variational Quantum Algorithms (VQAs) have made great success in the Noisy Intermediate-Scale Quantum (NISQ) era due to their relative resilience to noise and high flexibility relative to quantum resources. Quantum Architecture Search (QAS) aims to enhance the performance of VQAs by refining the structure of the adopted Parameterized Quantum Circuit (PQC). QAS is garnering increased attention owing to its automation, reduced reliance on expert experience, and its ability to achieve better performance while requiring fewer quantum gates than manually designed circuits. However, existing QAS algorithms optimize the structure from scratch for each VQA without using any prior experience, rendering the process inefficient and time-consuming. Moreover, determining the number of quantum gates, a crucial hyper-parameter in these algorithms is a challenging and time-consuming task. To mitigate these challenges, we accelerate the QAS algorithm via a meta-trained generator. The proposed algorithm directly generates high-performance circuits for a new VQA by utilizing a meta-trained Variational AutoEncoder (VAE). The number of quantum gates required in the designed circuit is automatically determined based on meta-knowledge learned from a variety of training tasks. Furthermore, we have developed a meta-predictor to filter out circuits with suboptimal performance, thereby accelerating the algorithm. Simulation results on variational quantum compiling and Quantum Approximation Optimization Algorithm (QAOA) demonstrate the superior performance of our method over a state-of-the-art algorithm, namely Differentiable Quantum Architecture Search (DQAS).