Learning to learn with quantum neural networks via classical neural networks

Abstract

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.

The Presence and Absence of Barren Plateaus in Tensor-network Based Machine Learning

“…Consequently, although we can prove the absence of barren plateaus for general tensor-network based learning models with local losses, training them may still be infeasible when scaling up due to the intrinsic difficulty in computing the derivatives. We mention that a variety of strategies, such as specific parameter initialization [80] and pre-training [108], have been proposed to escape barren plateaus for variational quantum circuits. These strategies may also apply for tensor-network based learning and a further investigation along this line is highly desirable.…”

The Optimization Landscape of Hybrid Quantum-Classical Algorithms: from Quantum Control to NISQ Applications

“…In Ref. [75], the idea of pretraining is introduced, i.e., the parameters are pretrained by classical neural networks, which are then transferred to the quantum neural network and fine tuned. In this way, the total number of optimization iterations required to reach a given accuracy can be significantly improved.…”

Meta Hamiltonian Learning

“…It has been shown that metalearned optimization outperforms generic hand-designed competitors in many tasks [29]. The application of this concept to the quantum domain has been recently considered in the context of the variational quantum algorithms [33,34].…”

“…It is also possible to use derivativefree methods, such as Bayesian optimization for the same task [16]. Meta-learning can again be used in this context to develop task-specific optimizers [33,40]. In this approach, it is only necessary to have gradient information during the training.…”