On quantum backpropagation, information reuse, and cheating measurement collapse

Amira Abbas, Robbie King, Hsin-Yuan Huang, William J. Huggins, Ramis Movassagh, Dar Gilboa, Jarrod Ryan McClean

Keywords: Backpropagation, quantum computing, shadow tomography, gentle measurement

TL;DR: We prove that resources to compute gradients of parameterized quantum models will not scale as efficiently as neural networks equipped with backpropagation, by reduction to a well-known problem in quantum information theory.

Abstract: The success of modern deep learning hinges on the ability to train neural networks at scale. Through clever reuse of intermediate information, backpropagation facilitates training through gradient computation at a total cost roughly proportional to running the function, rather than incurring an additional factor proportional to the number of parameters -- which can now be in the trillions. Naively, one expects that quantum measurement collapse entirely rules out the reuse of quantum information as in backpropagation. But recent developments in shadow tomography, which assumes access to multiple copies of a quantum state, have challenged that notion. Here, we investigate whether parameterized quantum models can train as efficiently as classical neural networks. We show that achieving backpropagation scaling is impossible without access to multiple copies of a state. With this added ability, we introduce an algorithm with foundations in shadow tomography that matches backpropagation scaling in quantum resources while reducing classical auxiliary computational costs to open problems in shadow tomography. These results highlight the nuance of reusing quantum information for practical purposes and clarify the unique difficulties in training large quantum models, which could alter the course of quantum machine learning.

Submission Number: 6864