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Physical Review Applied

Adaptive fusion of training-free proxies for quantum architecture search

Zhimin He, Zhengjiang Li, Haozhen Situ, Qin Li, Jinjing Shi, Lvzhou Li

Published Aug 8, 2025• 2 citations
Publisher

Abstract

Training-free quantum architecture search (QAS) has shown substantial promise in automating quantum circuit design for variational quantum algorithms (VQAs) with minimal computational expense. However, various VQA tasks and search spaces often favor specific training-free proxies. Furthermore, circuit performance is influenced by multiple factors, such as expressibility, trainability, and circuit topology, making it challenging for a single proxy to assess circuit performance accurately. To address these limitations, we propose an adaptive QAS framework that dynamically integrates multiple training-free proxies, combining their strengths and mitigating individual biases. This framework uses a mixture-of-experts (MoE) model that adapts to different VQA tasks and search spaces. Specifically, we develop an expert model for each training-free proxy, where each expert focuses on a distinct feature, such as expressibility, trainability, or topology. A gating network then assigns weights to each expert based on the specific VQA task and search space. Our proposed QAS framework consistently outperforms state-of-the-art QAS algorithms across diverse VQAs, including variational quantum eigensolvers (VQEs) and quantum neural networks (QNNs), as well as multiple search spaces, such as gatewise, layerwise, and blockwise constructions. Moreover, our approach demonstrates transferability across different VQA tasks and search spaces.

DOI
10.1103/rbhx-3fjd

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Training-free quantum architecture search (QAS) has shown substantial promise in automating quantum circuit design for variational quantum algorithms (VQAs) with minimal computational expense. However, various VQA tasks and search spaces often favor specific training-free proxies. Furthermore, circuit performance is influenced by multiple factors, such as expressibility, trainability, and circuit topology, making it challenging for a single proxy to assess circuit performance accurately. To address these limitations, we propose an adaptive QAS framework that dynamically integrates multiple training-free proxies, combining their strengths and mitigating individual biases. This framework uses a mixture-of-experts (MoE) model that adapts to different VQA tasks and search spaces. Specifically, we develop an expert model for each training-free proxy, where each expert focuses on a distinct feature, such as expressibility, trainability, or topology. A gating network then assigns weights to each expert based on the specific VQA task and search space. Our proposed QAS framework consistently outperforms state-of-the-art QAS algorithms across diverse VQAs, including variational quantum eigensolvers (VQEs) and quantum neural networks (QNNs), as well as multiple search spaces, such as gatewise, layerwise, and blockwise constructions. Moreover, our approach demonstrates transferability across different VQA tasks and search spaces.
Variational quantum algorithm (VQA) derives advantages from its error resilience and high flexibility in quantum resource requirements, rendering it broadly applicable in the noisy intermediate-scale quantum era. As the performance of VQA highly relies on the structure of the parameterized quantum circuit, it is worthwhile to propose quantum architecture search (QAS) algorithms to automatically search for high-performance circuits. Nevertheless, existing QAS methods are time-consuming, requiring circuit training to assess circuit performance. This study pioneers training-free QAS by utilizing two training-free proxies to rank quantum circuits, in place of the expensive circuit training employed in conventional QAS. Taking into account the precision and computational overhead of the path-based and expressibility-based proxies, we devise a two-stage progressive training-free QAS (TF-QAS). Initially, directed acyclic graphs (DAGs) are employed for circuit representation, and a zero-cost proxy based on the number of paths in the DAG is designed to filter out a substantial portion of unpromising circuits. Subsequently, an expressibility-based proxy, finely reflecting circuit performance, is employed to identify high-performance circuits from the remaining candidates. These proxies evaluate circuit performance without circuit training, resulting in a remarkable reduction in computational cost compared to current training-based QAS methods. Simulations on three VQE tasks demonstrate that TF-QAS achieves a substantial enhancement of sampling efficiency ranging from 5 to 57 times compared to state-of-the-art QAS, while also being 6 to 17 times faster.
Variational Quantum Algorithms (VQAs) are central to the utility of Noisy Intermediate-Scale Quantum (NISQ) devices, but their performance is critically dependent on the design of the parameterized quantum circuit (PQC) ansatz. Manual design of these circuits is a complex, non-trivial task requiring significant expertise. To address this, Quantum Architecture Search (QAS) has emerged to automate the discovery of optimal circuit structures. However, many QAS methods incur substantial computational costs by requiring full training of candidate circuits. In this paper, we introduce QAS via iterative elimination, a novel framework that efficiently identifies high-performing circuits. Our method begins with a large, randomly generated population of circuits and iteratively prunes this set based on a composite score that evaluates both immediate performance and trainability. We introduce a dynamic weighting scheme that initially prioritizes trainability to avoid barren plateaus and gradually shifts focus to performance as the search progresses. We validate our approach on Variational Quantum Eigensolver (VQE) tasks for the 6-qubit Transverse Field Ising Model and the 5-qubit Heisenberg model. Experimental results show that our method, particularly with the dynamic weighting, discovers circuits that are competitive with those found by state-of-the-art training-free QAS methods, demonstrating a powerful balance between search efficiency and solution quality.
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).
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 propose an enhanced QAS framework that integrates a performance predictor trained through self-supervised learning with Bayesian optimization to overcome these computational barriers. To address the challenges of circuit performance evaluation, we develop a graph-isomorphism-network-based predictor pretrained using expressibility prediction, an intrinsic measure of a circuit's capacity to explore the Hilbert space uniformly. This pretraining process creates a structured and smooth latent space, significantly improving the predictor's accuracy and generalizability with minimal labeled data. Furthermore, Bayesian optimization is integrated into the QAS framework to refine the predictor iteratively, concentrating the search on regions containing high-performance circuits and thus accelerating the search process. Simulation results for VQAs involving the variational quantum eigensolver and quantum approximate optimization algorithm demonstrate that the proposed framework achieves faster convergence to optimal circuits and substantially reduces computational costs compared to existing QAS methods.
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 variational algorithms (VQAs) are highly promising to realize quantum advantages on near-term quantum devices. Existing VQAs based on a manually fixed quantum are computationally inefficient due to noise and the limited coupling maps of these devices. Previous work considers various quantum architecture search (QAS) algorithms to autodesign a quantum based on specific questions to improve the performance of VQAs. Compared to manual design, autodesign can more efficiently explore the large space of a possible and achieve better performance. However, two main challenges in utilizing QAS to design quantum circuits efficiently are the tremendous amount of space required for candidate quantum circuits, and the disconnection between quantum devices and autodesign in terms of qubit mapping and quantum noise. To address these issues, we propose an adaptive diversity-based quantum search algorithm to efficiently generate the optimal quantum circuit based on device qubit mapping and noise. By considering the diversity among different candidate circuits and adaptively adding circuit depths, our approach only needs to focus on a small optimization space at each iteration step. In addition, the synchronization of optimizing circuit structure and aligning qubit mapping enables us to generate quantum circuits while avoiding additional mapping overhead. We evaluate the performance of our algorithm on simulators and real quantum devices for quantum eigenvalue problems and classification tasks. Results demonstrate that quantum circuits generated by our method outperform both a fixed hardware-efficient and randomly generated quantum circuits in terms of final performance and resource-saving. Our algorithm provides a flexible way to efficiently generate excellent quantum circuits for significantly improving the performances of VQAs on near-term quantum devices. Published by the American Physical Society 2024