Toward Neural Network Simulation of Variational Quantum Algorithms
This work addresses the challenge of establishing computational advantage for VQAs over classical methods, with implications for quantum computing research, but it is incremental as it builds on existing variational Monte Carlo approaches.
The paper investigates whether classical stochastic optimization algorithms, using neural networks instead of quantum circuits, can parallel variational quantum algorithms (VQAs), specifically applying this to the variational quantum linear solver (VQLS) and suggesting potential extension to similar VQAs.
Variational quantum algorithms (VQAs) utilize a hybrid quantum-classical architecture to recast problems of high-dimensional linear algebra as ones of stochastic optimization. Despite the promise of leveraging near- to intermediate-term quantum resources to accelerate this task, the computational advantage of VQAs over wholly classical algorithms has not been firmly established. For instance, while the variational quantum eigensolver (VQE) has been developed to approximate low-lying eigenmodes of high-dimensional sparse linear operators, analogous classical optimization algorithms exist in the variational Monte Carlo (VMC) literature, utilizing neural networks in place of quantum circuits to represent quantum states. In this paper we ask if classical stochastic optimization algorithms can be constructed paralleling other VQAs, focusing on the example of the variational quantum linear solver (VQLS). We find that such a construction can be applied to the VQLS, yielding a paradigm that could theoretically extend to other VQAs of similar form.