Quantum Architecture Search (QAS) is a promising approach to designing quantum circuits for variational quantum algorithms (VQAs). However, existing QAS algorithms require to evaluate a large number of quantum circuits during the search process, which makes them computationally demanding and limits their applications to large-scale quantum circuits. Recently, predictor-based QAS has been proposed to alleviate this problem by directly estimating the performances of circuits according to their structures with a predictor trained on a set of labeled quantum circuits. However, the predictor is trained by purely supervised learning, which suffers from poor generalization ability when labeled training circuits are scarce. It is very time-consuming to obtain a large number of labeled quantum circuits because the gate parameters of quantum circuits need to be optimized until convergence to obtain their ground-truth performances. To overcome these limitations, we propose GSQAS, a graph self-supervised QAS, which trains a predictor based on self-supervised learning. Specifically, we first pre-train a graph encoder on a large number of unlabeled quantum circuits using a well-designed pretext task in order to generate meaningful representations of circuits. Then the downstream predictor is trained on a small number of quantum circuits' representations and their labels. Once the encoder is trained, it can apply to different downstream tasks. In order to better encode the spatial topology information and avoid the huge dimension of feature vectors for large-scale quantum circuits, we design a scheme to encode quantum circuits as graphs. Simulation results on searching circuit structures for variational quantum eigensolver and quantum state classification show that GSQAS outperforms the state-of-the-art predictor-based QAS, achieving better performance with fewer labeled circuits.
Quantum Architecture Search (QAS) is a promising approach to designing quantum circuits for variational quantum algorithms (VQAs). However, existing QAS algorithms require to evaluate a large number of quantum circuits during the search process, which makes them computationally demanding and limits their applications to large-scale quantum circuits. Recently, predictor-based QAS has been proposed to alleviate this problem by directly estimating the performances of circuits according to their structures with a predictor trained on a set of labeled quantum circuits. However, the predictor is trained by purely supervised learning, which suffers from poor generalization ability when labeled training circuits are scarce. It is very time-consuming to obtain a large number of labeled quantum circuits because the gate parameters of quantum circuits need to be optimized until convergence to obtain their ground-truth performances. To overcome these limitations, we propose GSQAS, a graph self-supervised QAS, which trains a predictor based on self-supervised learning. Specifically, we first pre-train a graph encoder on a large number of unlabeled quantum circuits using a well-designed pretext task in order to generate meaningful representations of circuits. Then the downstream predictor is trained on a small number of quantum circuits' representations and their labels. Once the encoder is trained, it can apply to different downstream tasks. In order to better encode the spatial topology information and avoid the huge dimension of feature vectors for large-scale quantum circuits, we design a scheme to encode quantum circuits as graphs. Simulation results on searching circuit structures for variational quantum eigensolver and quantum state classification show that GSQAS outperforms the state-of-the-art predictor-based QAS, achieving better performance with fewer labeled circuits.
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.
Unsupervised representation learning presents new opportunities for advancing Quantum Architecture Search (QAS) on Noisy Intermediate-Scale Quantum (NISQ) devices. QAS is designed to optimize quantum circuits for Variational Quantum Algorithms (VQAs). Most QAS algorithms tightly couple the search space and search algorithm, typically requiring the evaluation of numerous quantum circuits, resulting in high computational costs and limiting scalability to larger quantum circuits. Predictor-based QAS algorithms mitigate this issue by estimating circuit performance based on structure or embedding. However, these methods often demand time-intensive labeling to optimize gate parameters across many circuits, which is crucial for training accurate predictors. Inspired by the classical neural architecture search algorithm A r c h 2 v e c , we investigate the potential of unsupervised representation learning for QAS without relying on predictors. Our framework decouples unsupervised architecture representation learning from the search process, enabling the learned representations to be applied across various downstream tasks. Additionally, it integrates an improved quantum circuit graph encoding scheme, addressing the limitations of existing representations and enhancing search efficiency. This predictor-free approach removes the need for large labeled datasets. During the search, we employ REINFORCE and Bayesian Optimization to explore the latent representation space and compare their performance against baseline methods. We further validate our approach by executing the best-discovered MaxCut circuits on IBM's ibm_sherbrooke quantum processor, confirming that the architectures retain optimal performance even under real hardware noise. Our results demonstrate that the framework efficiently identifies high-performing quantum circuits with fewer search iterations.
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).
Variational quantum algorithms (VQAs) are widely speculated to deliver quantum advantages for practical problems under the quantum–classical hybrid computational paradigm in the near term. Both theoretical and practical developments of VQAs share many similarities with those of deep learning. For instance, a key component of VQAs is the design of task-dependent parameterized quantum circuits (PQCs) as in the case of designing a good neural architecture in deep learning. Partly inspired by the recent success of AutoML and neural architecture search (NAS), quantum architecture search (QAS) is a collection of methods devised to engineer an optimal task-specific PQC. It has been proven that QAS-designed VQAs can outperform expert-crafted VQAs in various scenarios. In this work, we propose to use a neural network based predictor as the evaluation policy for QAS. We demonstrate a neural predictor guided QAS can discover powerful quantum circuit ansatz, yielding state-of-the-art results for various examples from quantum simulation and quantum machine learning. Notably, neural predictor guided QAS provides a better solution than that by the random-search baseline while using an order of magnitude less of circuit evaluations. Moreover, the predictor for QAS as well as the optimal ansatz found by QAS can both be transferred and generalized to address similar problems.
Abstract Quantum architecture search (QAS) has attracted increasing attention owing to its remarkable ability to automate the design of quantum circuits for variational quantum algorithms (VQAs). However, evaluating the performance of numerous quantum circuits is essential to provide feedback for the search strategy, which inevitably renders QAS computationally expensive. Performance predictors have emerged as highly efficient evaluation methods to mitigate this challenge. However, the performance predictor faces a critical challenge in reducing the required number of circuit‐performance pairs for training. This study encodes circuit architecture by representing a quantum circuit as a relational graph that emphasizes message exchange. Subsequently, valuable information about circuit architecture is extracted through three types of graph measures, including distance‐based, degree‐based, and cluster‐based measures. The graph measures define a smooth space related to circuit performance, facilitating the training of the performance predictor. The effectiveness of the proposed method is assessed across three tasks within variational quantum eigensolvers (VQE): identifying the ground states of the Transverse Field Ising Model (TFIM), the Heisenberg model, and the molecule. The simulation results demonstrate notable enhancements in predictive accuracy achieved by our method, coupled with a substantial reduction in the required number of training samples for the predictor.
Abstract With the ongoing advances in noisy intermediate-scale quantum hardware, variational quantum algorithms have demonstrated significant potential in a range of quantum applications. However, obtaining high-performance, shallow-parameterized quantum circuits typically requires repeated optimization of the gate parameters over a large set of candidate circuits, resulting in prohibitively high evaluation costs. To address this challenge, this study proposes a novel predictor-based quantum architecture search (PQAS-ZX) method that leverages ZX-calculus. In this approach, a quantum circuit is first represented as a ZX diagram that supports multi-step equivalent simplifications at the diagram level. By applying these equivalence transformations, multiple circuit variants that share the same performance metric are generated, thereby significantly expanding the training dataset and enhancing the ability of the predictor to manage diverse circuit structures. ZX diagrams offer more flexible characterizations of multi-qubit entanglement and phase interactions, as well as higher-level equivalent transformations, compared with the state-of-the-art predictor-based quantum architecture search with graph measures (PQAS-GM). Numerical simulations of three variational quantum eigensolver tasks, namely the transverse-field Ising, Heisenberg, and BeH2 molecular models, demonstrated that PQAS-ZX required only approximately 80.9%, 82.9%, and 76.1% of the queries required by PQAS-GM, respectively, to achieve the same probability of reaching the target ground-state energy. These results highlight the advantage of using ZX diagrams to identify high-quality circuits efficiently and alleviate the evaluation burden of quantum architecture searches.