Trainability of Dissipative Perceptron-Based Quantum Neural Networks

Sharma, Kunal; Cerezo, M.; Cincio, Lukasz; Coles, Patrick J.

doi:10.1103/physrevlett.128.180505

Trainability of Dissipative Perceptron-Based Quantum Neural Networks

Journal Article · Fri May 06 00:00:00 EDT 2022 · Physical Review Letters

DOI:https://doi.org/10.1103/physrevlett.128.180505· OSTI ID:1992248

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Los Alamos National Laboratory (LANL), Los Alamos, NM (United States). Theoretical Division; Louisiana State University, Baton Rouge, LA (United States)
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States). Theoretical Division; Los Alamos National Laboratory (LANL), Los Alamos, NM (United States). Center for Nonlinear Studies (CNLS)
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States). Theoretical Division

Several architectures have been proposed for quantum neural networks (QNNs), with the goal of efficiently performing machine learning tasks on quantum data. Rigorous scaling results are urgently needed for specific QNN constructions to understand which, if any, will be trainable at a large scale. Here, we analyze the gradient scaling (and hence the trainability) for a recently proposed architecture that we call dissipative QNNs (DQNNs), where the input qubits of each layer are discarded at the layer’s output. We find that DQNNs can exhibit barren plateaus, i.e., gradients that vanish exponentially in the number of qubits. Moreover, we provide quantitative bounds on the scaling of the gradient for DQNNs under different conditions, such as different cost functions and circuit depths, and show that trainability is not always guaranteed. Here our work represents the first rigorous analysis of the scalability of a perceptron-based QNN.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1992248

Report Number(s):: LA-UR-20-23484

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 18 Vol. 128; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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