L2O-$g^{\dagger}$: Learning to Optimize Parameterized Quantum Circuits with Fubini-Study Metric Tensor

TL;DR

This paper introduces L2O-$g^{ abla}$, a quantum-aware learned optimizer that incorporates quantum geometry via the Fubini-Study metric tensor, achieving superior performance and generalization in variational quantum algorithms on NISQ devices.

Contribution

The work presents a novel quantum-aware learned optimizer leveraging the Fubini-Study metric tensor and LSTM, improving optimization of VQAs without hyperparameter tuning and demonstrating strong out-of-distribution generalization.

Findings

Outperforms state-of-the-art hand-designed optimizers

Shows strong out-of-distribution generalization

Achieves effective optimization with training on a single PQC instance

Abstract

Before the advent of fault-tolerant quantum computers, variational quantum algorithms (VQAs) play a crucial role in noisy intermediate-scale quantum (NISQ) machines. Conventionally, the optimization of VQAs predominantly relies on manually designed optimizers. However, learning to optimize (L2O) demonstrates impressive performance by training small neural networks to replace handcrafted optimizers. In our work, we propose L2O-$g^{\dagger}$, a $\textit{quantum-aware}$ learned optimizer that leverages the Fubini-Study metric tensor ($g^{\dagger}$) and long short-term memory networks. We theoretically derive the update equation inspired by the lookahead optimizer and incorporate the quantum geometry of the optimization landscape in the learned optimizer to balance fast convergence and generalization. Empirically, we conduct comprehensive experiments across a range of VQA problems. Our results demonstrate that L2O-$g^{\dagger}$ not only outperforms the current SOTA hand-designed optimizer without any hyperparameter tuning but also shows strong out-of-distribution generalization compared to previous L2O optimizers. We achieve this by training L2O-$g^{\dagger}$ on just a single generic PQC instance. Our novel $\textit{quantum-aware}$ learned optimizer, L2O-$g^{\dagger}$, presents an advancement in addressing the challenges of VQAs, making it a valuable tool in the NISQ era.