Noise-Induced Barren Plateaus in Variational Quantum Algorithms

TL;DR

This paper proves that noise in variational quantum algorithms causes the training landscape to develop barren plateaus, with gradients vanishing exponentially as the number of qubits increases, posing a fundamental limitation for NISQ devices.

Contribution

It rigorously demonstrates that local Pauli noise induces exponential vanishing gradients in VQAs, revealing a fundamental noise-induced limitation not present in noise-free scenarios.

Findings

Noise causes gradients to vanish exponentially with qubit number

NIBPs are distinct from noise-free barren plateaus

Numerical heuristics confirm NIBP in realistic noise models

Abstract

Variational Quantum Algorithms (VQAs) may be a path to quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) computers. A natural question is whether noise on NISQ devices places fundamental limitations on VQA performance. We rigorously prove a serious limitation for noisy VQAs, in that the noise causes the training landscape to have a barren plateau (i.e., vanishing gradient). Specifically, for the local Pauli noise considered, we prove that the gradient vanishes exponentially in the number of qubits $n$ if the depth of the ansatz grows linearly with $n$. These noise-induced barren plateaus (NIBPs) are conceptually different from noise-free barren plateaus, which are linked to random parameter initialization. Our result is formulated for a generic ansatz that includes as special cases the Quantum Alternating Operator Ansatz and the Unitary Coupled Cluster Ansatz, among others. For the former, our numerical heuristics demonstrate the NIBP phenomenon for a realistic hardware noise model.