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 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.
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.
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 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.
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.
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.
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.