Barren plateaus in quantum neural network training landscapes

TL;DR

This paper demonstrates that training quantum neural networks with random circuits faces exponential difficulty due to barren plateaus, where gradients vanish exponentially with increasing qubits, hindering effective optimization.

Contribution

It reveals the exponential vanishing of gradients in random quantum circuits, highlighting a fundamental challenge in training quantum neural networks on larger systems.

Findings

Gradients vanish exponentially with the number of qubits.

Random circuits exhibit barren plateaus hindering training.

Solutions to mitigate this problem are necessary for scalable quantum machine learning.

Abstract

Many experimental proposals for noisy intermediate scale quantum devices involve training a parameterized quantum circuit with a classical optimization loop. Such hybrid quantum-classical algorithms are popular for applications in quantum simulation, optimization, and machine learning. Due to its simplicity and hardware efficiency, random circuits are often proposed as initial guesses for exploring the space of quantum states. We show that the exponential dimension of Hilbert space and the gradient estimation complexity make this choice unsuitable for hybrid quantum-classical algorithms run on more than a few qubits. Specifically, we show that for a wide class of reasonable parameterized quantum circuits, the probability that the gradient along any reasonable direction is non-zero to some fixed precision is exponentially small as a function of the number of qubits. We argue that this is related to the 2-design characteristic of random circuits, and that solutions to this problem must be studied.