Current structure optimization algorithms optimize the structure of quantum circuit from scratch for each new task of variational quantum algorithms (VQAs) without using any prior experience, which is inefficient and time-consuming. Besides, the number of quantum gates is a hyper-parameter of these algorithms, which is difficult and time-consuming to determine. In this paper, we propose a rapid structure optimization algorithm for VQAs which automatically determines the number of quantum gates and directly generates the optimal structures for new tasks with the meta-trained graph variational autoencoder (VAE) on a number of training tasks. We also develop a meta-trained predictor to filter out circuits with poor performances to further accelerate the algorithm. Simulation results show that our method output structures with lower loss and it is 70 times faster in running time compared to a state-of-the-art algorithm, namely DQAS.
Current structure optimization algorithms optimize the structure of quantum circuit from scratch for each new task of variational quantum algorithms (VQAs) without using any prior experience, which is inefficient and time-consuming. Besides, the number of quantum gates is a hyper-parameter of these algorithms, which is difficult and time-consuming to determine. In this paper, we propose a rapid structure optimization algorithm for VQAs which automatically determines the number of quantum gates and directly generates the optimal structures for new tasks with the meta-trained graph variational autoencoder (VAE) on a number of training tasks. We also develop a meta-trained predictor to filter out circuits with poor performances to further accelerate the algorithm. Simulation results show that our method output structures with lower loss and it is 70 times faster in running time compared to a state-of-the-art algorithm, namely DQAS.
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).
Abstract Variational quantum algorithms (VQAs) have been successfully applied to quantum approximate optimization algorithms, variational quantum compiling and quantum machine learning models. The performances of VQAs largely depend on the architecture of parameterized quantum circuits (PQCs). Quantum architecture search (QAS) aims to automate the design of PQCs in different VQAs with classical optimization algorithms. However, current QAS algorithms do not use prior experiences and search the quantum architecture from scratch for each new task, which is inefficient and time consuming. In this paper, a meta quantum architecture search (MetaQAS) algorithm is proposed, which learns good initialization heuristics of the architecture (i.e., meta‐architecture), along with the meta‐parameters of quantum gates from a number of training tasks such that they can adapt to new tasks with fewer gradient updates, which leads to fast learning on new tasks. The proposed MetaQAS can be used with arbitrary gradient‐based QAS algorithms. Simulation results on variational quantum compiling (VQC) and quantum approximate optimization algorithm (QAOA) show that the architectures optimized by MetaQAS converge faster than a state‐of‐the‐art gradient‐based QAS algorithm, namely DQAS. MetaQAS also achieves a better solution than DQAS after fine‐tuning of gate parameters.
In the Noisy Intermediate-Scale Quantum (NISQ) era, using variational quantum algorithms (VQAs) to solve optimization problems has become a key application. However, these algorithms face significant challenges, such as choosing an effective initial set of parameters and the limited quantum processing time that restricts the number of optimization iterations. In this study, we introduce a new framework for optimizing parameterized quantum circuits (PQCs) that employs a classical optimizer, inspired by Model-Agnostic Meta-Learning (MAML) technique. This approach aim to achieve better parameter initialization that ensures fast convergence. Our framework features a classical neural network, called Learner, which interacts with a PQC using the output of Learner as an initial parameter. During the pre-training phase, Learner is trained with the meta objective function. In the adaptation phase, the framework requires only a few PQC updates to converge to a more accurate value, while the learner remains unchanged. This method is highly adaptable and is effectively extended to various Hamiltonian optimization problems. We validate our approach through experiments, including distribution function mapping and optimization of the Heisenberg XYZ Hamiltonian. The result implies that the Learner successfully estimates initial parameters that generalize across the problem space, enabling fast adaptation.
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.
Variational quantum algorithms (VQAs) have been successfully applied to quantum approximate optimization algorithms, variational quantum compiling, and quantum machine learning models. The performance of VQAs is significantly influenced by the architecture of parameterized quantum circuits (PQCs). Quantum architecture search aims to automatically discover high-performance quantum circuits for specific VQA tasks. Quantum architecture search algorithms that utilize both SuperCircuit training and a parameter-sharing approach can save computational resources. If we directly follow the parameter-sharing approach, the SuperCircuit has to be trained to compensate for the worse search space. To address the challenges posed by the worse search space, we introduce an optimization strategy known as the efficient continuous evolutionary approach using Non-dominated Sorting Genetic Algorithm-II (NSGA-II). Then, we leverage prior information (symmetric property) designing Structure Symmetric Pruning for removing redundant gates of the searched ansatz. Experiments show that the efficient continuous evolutionary approach can search for more quantum architectures with better performance; the number of high-performance ansatzes obtained by our method is 10% higher than that in the literature (Du et al. in npj Quantum Inf. 8:62, 2022 ). The application of Structure Symmetric Pruning effectively reduces the number of parameters in quantum circuits without compromising their performance significantly. In binary classification tasks, the pruned quantum circuits exhibit an average accuracy reduction of 0.044 compared to their unpruned counterparts.
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.