[Paper Review] Learning to learn with quantum neural networks via classical neural networks

Guillaume Verdon, Michael Broughton+6 more|arXiv (Cornell University)|Jul 11, 2019

Quantum Computing Algorithms and Architecture98 citations

TL;DR

The paper trains classical recurrent neural networks to act as meta-optimizers for quantum variational algorithms, improving initialization and reducing quantum-classical optimization iterations for QAOA and VQE tasks, with demonstrated cross-size generalization.

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.

Motivation & Objective

• Address poor parameter initialization in quantum neural networks (QNNs) for near-term devices.
• Develop a meta-learning approach where a classical RNN learns parameter-update heuristics.
• Demonstrate that RNN-based initialization speeds up convergence for QAOA and VQE on representative problem classes.
• Show generalization of learned optimization strategies to larger problem instances than those seen during training.

Proposed method

• Model a hybrid quantum-classical variational loop where a QNN is optimized by a classical optimizer.
• Use a recurrent neural network (RNN), specifically an LSTM, as a meta-optimizer that outputs QNN parameter updates.
• Train the RNN on distributions of small, classically simulatable QNN instances for targeted problem classes (QAOA MaxCut, QAOA Ising SK, Hubbard VQE).
• Define a meta-learning loss L(phi) based on observed improvements in the QNN cost across timesteps to train the RNN.
• Integrate the RNN initializer with a local optimizer (e.g., Nelder-Mead) to refine parameters after initialization.
• Draw on quantum-alternating operator ansatze (QAOA style) where the QNN parameters act as hyperparameters of the gradient-descent-like landscape.

Experimental results

Research questions

• RQ1 Can a classical RNN meta-optimizer learn effective parameter-update heuristics for QNNs in QAOA and VQE settings?
• RQ2 Do RNN-learned initializations reduce the number of optimization iterations to reach a desired accuracy compared to standard initialization strategies?
• RQ3 Do strategies learned on small, classically simulatable instances generalize to larger problem sizes?
• RQ4 Is the RNN-based initializer robust across different problem classes within quantum variational algorithms (MaxCut QAOA, Ising SK QAOA, Hubbard VQE)?

Key findings

• A recurrent neural network trained as a meta-optimizer yields significant improvement in the total number of optimization iterations to reach a given accuracy.
• The learned initialization generalizes well across a range of problem instance sizes beyond the training set.
• The RNN initializer outperforms other standard parameter initialization methods when used to initialize local optimizers like Nelder-Mead.
• Training can be performed on small, classically simulatable QNN instances and then applied to larger, harder-to-simulate instances on quantum devices.
• This work demonstrates the first successful application of meta-learning to enhance quantum machine learning algorithms.