Entanglement Induced Barren Plateaus
This addresses a critical bottleneck in quantum machine learning by identifying entanglement-induced barren plateaus as a typical issue, with potential implications for quantum neural networks and Boltzmann machines, though it is incremental in building on known barren plateau problems.
The paper tackles the problem of learning in Quantum Neural Networks by showing that excessive entanglement between visible and hidden units leads to barren plateaus, making optimization fail with high probability. It demonstrates that the Lipschitz constants of objective functions scale inversely with hidden subsystem dimensions, hindering both gradient-based and gradient-free methods.
We argue that an excess in entanglement between the visible and hidden units in a Quantum Neural Network can hinder learning. In particular, we show that quantum neural networks that satisfy a volume-law in the entanglement entropy will give rise to models not suitable for learning with high probability. Using arguments from quantum thermodynamics, we then show that this volume law is typical and that there exists a barren plateau in the optimization landscape due to entanglement. More precisely, we show that for any bounded objective function on the visible layers, the Lipshitz constants of the expectation value of that objective function will scale inversely with the dimension of the hidden-subsystem with high probability. We show how this can cause both gradient descent and gradient-free methods to fail. We note that similar problems can happen with quantum Boltzmann machines, although stronger assumptions on the coupling between the hidden/visible subspaces are necessary. We highlight how pretraining such generative models may provide a way to navigate these barren plateaus.