Noise-induced barren plateaus in variational quantum algorithms

By Samson Wang, Enrico Fontana, M. Cerezo, Akira Sone, Lukasz Cincio, Patrick J. Coles. Nature Communications, 2020

964 citations recorded by the source corpus.

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. Variational quantum algorithms (VQAs) are a leading candidate for useful applications of near-term quantum computing, but limitations due to unavoidable noise have not been clearly characterized. Here, the authors prove that local Pauli noise can cause vanishing gradients rendering VQAs untrainable.

Subfields: Artificial Intelligence

View Paper: https://www.semanticscholar.org/paper/a7da6cf3820d94f250349d658a09004a36b14ff0

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Citations in the corpus

Training Variational Quantum Algorithms Is NP-Hard. (2021, background): “Also, sources of randomness given by noise in the gate implementations can cause similar effects [13].”
Entanglement Induced Barren Plateaus (2020, background): “Another type of a barren plateau emerges from hardware noise in the system [15].”
Challenges and opportunities in quantum machine learning (2022, background): “Local minima are not the only issue facing QML, as it has been shown that quantum landscapes can exhibit a fascinating property known as a barren plateau [58, 77– 89].”
Fundamental limits of quantum error mitigation (2021, neutral): “, p̂ 1⁄4 p̂ð1Þ p̂ðKÞ and q̂ 1⁄4 q̂ð1Þ q̂ðKÞ , it holds that: DLMðp̂; q̂Þ 1⁄4 Dtrðp̂; q̂Þ: (25)”
Quantum error mitigation (2022, background): “Since the Clifford group is a unitary 2-design, the loss function satisfies L C ( ⃗ θ ) = L U ( ⃗ θ ) (Wang et al. , 2021c).”
Barren plateaus in variational quantum computing (2024, neutral): “By contrast, there exists a second type of concentration, known as deterministic BPs, where all of the landscape is truly flat 24–27 .”
Absence of Barren Plateaus in Quantum Convolutional Neural Networks (2020, background): “[37] Samson Wang, Enrico Fontana, Marco Cerezo, Kunal Sharma, Akira Sone, Lukasz Cincio, and Patrick J Coles, “Noise-induced barren plateaus in variational quantum algorithms,” arXiv preprint arXiv:2007.”
The power of quantum neural networks (2020, background): “As shown in [24], barren plateaus may be noiseinduced, where certain noise models are assumed on the hardware.”
Variational quantum algorithms (2020, background): “[173, 174] it was also shown that in the presence of local Pauli noise, the cost landscape concentrated exponentially with the depth of the ansatz around the value of the cost associated with the maximally mixed state.”