Noise-induced barren plateaus in variational quantum algorithms

TLDR

Variational Quantum Algorithms may provide quantum advantage on NISQ devices, but noise can induce barren plateaus distinct from those caused by random initialization. A natural question is whether noise on NISQ devices places fundamental limitations on VQA performance. 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. We prove that local Pauli noise causes the gradient to vanish exponentially with qubit number when ansatz depth scales linearly, and numerical heuristics confirm this noise‑induced barren plateau for realistic hardware 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.