Variational quantum algorithms (VQAs) use classical computers as the quantum outer loop optimizer and update the circuit parameters to obtain an approximate ground state. In this article, we present a meta-learning variational quantum algorithm (meta-VQA) by recurrent unit, which uses a technique called "meta-learner." Motivated by the hybrid quantum-classical algorithms, we train classical recurrent units to assist quantum computing, learning to find approximate optima in the parameter landscape. Here, aiming to reduce the sampling number more efficiently, we use the quantum stochastic gradient descent method and introduce the adaptive learning rate. Finally, we deploy on the TensorFlow Quantum processor within approximate quantum optimization for the Ising model and variational quantum eigensolver for molecular hydrogen (H2), lithium hydride (LiH), and helium hydride cation (HeH+). Our algorithm can be expanded to larger system sizes and problem instances, which have higher performance on near-term processors.
Variational quantum algorithms (VQAs) use classical computers as the quantum outer loop optimizer and update the circuit parameters to obtain an approximate ground state. In this article, we present a meta-learning variational quantum algorithm (meta-VQA) by recurrent unit, which uses a technique called "meta-learner." Motivated by the hybrid quantum-classical algorithms, we train classical recurrent units to assist quantum computing, learning to find approximate optima in the parameter landscape. Here, aiming to reduce the sampling number more efficiently, we use the quantum stochastic gradient descent method and introduce the adaptive learning rate. Finally, we deploy on the TensorFlow Quantum processor within approximate quantum optimization for the Ising model and variational quantum eigensolver for molecular hydrogen (H2), lithium hydride (LiH), and helium hydride cation (HeH+). Our algorithm can be expanded to larger system sizes and problem instances, which have higher performance on near-term processors.
Quantum Neural Networks (QNNs) are a promising variational learning paradigm with applications to near-term quantum processors, however they still face some significant challenges. One such challenge is finding good parameter initialization heuristics that ensure rapid and consistent convergence to local minima of the parameterized quantum circuit landscape. In this work, we train classical neural networks to assist in the quantum learning process, also know as meta-learning, to rapidly find approximate optima in the parameter landscape for several classes of quantum variational algorithms. Specifically, we train classical recurrent neural networks to find approximately optimal parameters within a small number of queries of the cost function for the Quantum Approximate Optimization Algorithm (QAOA) for MaxCut, QAOA for Sherrington-Kirkpatrick Ising model, and for a Variational Quantum Eigensolver for the Hubbard model. By initializing other optimizers at parameter values suggested by the classical neural network, we demonstrate a significant improvement in the total number of optimization iterations required to reach a given accuracy. We further demonstrate that the optimization strategies learned by the neural network generalize well across a range of problem instance sizes. This opens up the possibility of training on small, classically simulatable problem instances, in order to initialize larger, classically intractably simulatable problem instances on quantum devices, thereby significantly reducing the number of required quantum-classical optimization iterations.
Abstract Variational quantum algorithms, a class of quantum heuristics, are promising candidates for the demonstration of useful quantum computation. Finding the best way to amplify the performance of these methods on hardware is an important task. Here, we evaluate the optimization of quantum heuristics with an existing class of techniques called “meta-learners.” We compare the performance of a meta-learner to evolutionary strategies, L-BFGS-B and Nelder-Mead approaches, for two quantum heuristics (quantum alternating operator ansatz and variational quantum eigensolver), on three problems, in three simulation environments. We show that the meta-learner comes near to the global optima more frequently than all other optimizers we tested in a noisy parameter setting environment. We also find that the meta-learner is generally more resistant to noise, for example, seeing a smaller reduction in performance inNoisyandSamplingenvironments, and performs better on average by a “gain” metric than its closest comparable competitor L-BFGS-B. Finally, we present evidence that indicates the meta-learner trained on small problems will generalize to larger problems. These results are an important indication that meta-learning and associated machine learning methods will be integral to the useful application of noisy near-term quantum computers.
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.
The Quantum Approximate Optimization Algorithm (QAOA) is a leading approach for solving combinatorial optimization problems on near-term quantum processors. However, finding good variational parameters remains a significant challenge due to the non-convex energy landscape, often resulting in slow convergence and poor solution quality. In this work, we propose a quantum meta-learning framework that trains advanced quantum sequence models to generate effective parameter initialization policies. We investigate four classical or quantum sequence models, including the Quantum Kernel-based Long Short-Term Memory (QK-LSTM), as learned optimizers in a "learning to learn" paradigm. Our numerical experiments on the Max-Cut problem demonstrate that the QK-LSTM optimizer achieves superior performance, obtaining the highest approximation ratios and exhibiting the fastest convergence rate across all tested problem sizes (n=10 to 13). Crucially, the QK-LSTM model achieves perfect parameter transferability by synthesizing a single, fixed set of near-optimal parameters, leading to a remarkable sustained acceleration of convergence even when generalizing to larger problems. This capability, enabled by the compact and expressive power of the quantum kernel architecture, underscores its effectiveness. The QK-LSTM, with only 43 trainable parameters, substantially outperforms the classical LSTM (56 parameters) and other quantum sequence models, establishing a robust pathway toward highly efficient parameter initialization for variational quantum algorithms in the NISQ era.
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.
This thesis explores variational quantum algorithms in order to solve optimization combinatorial problems using a meta-learning approach. This variational algorithm sare promising due to its capability to be used in the near future in the so-called NoisyIntermediate-Scale Quantum (NISQ) era, in which algorithms with high tolerance to noise could perform better than its classical counterparts. In this approach, a Recurrent Neural Network (RNN) optimizer tries to obtain the best set of parameters ofa quantum circuit for a given problem using the Qauntum Approximation Optimiza-tion Algorithm (QAOA), with the minimal amount of queries possible to a quantumcomputer. Thanks to the advances of parameter shift methods to compute the gradi-ents of parametrized quantum circuits, these algorithms could be even trained in realquantum computers without the need of highly demanding simulations. The resultspresented show that this approach is able to generalize to other problem instanceswhich the model has not seen before during training.