Layerwise learning for quantum neural networks

Quantum Machine Intelligence, vol. 3

Abstract

Abstract With the increased focus on quantum circuit learning for near-term applications on quantum devices, in conjunction with unique challenges presented by cost function landscapes of parametrized quantum circuits, strategies for effective training are becoming increasingly important. In order to ameliorate some of these challenges, we investigate a layerwise learning strategy for parametrized quantum circuits. The circuit depth is incrementally grown during optimization, and only subsets of parameters are updated in each training step. We show that when considering sampling noise, this strategy can help avoid the problem of barren plateaus of the error surface due to the low depth of circuits, low number of parameters trained in one step, and larger magnitude of gradients compared to training the full circuit. These properties make our algorithm preferable for execution on noisy intermediate-scale quantum devices. We demonstrate our approach on an image-classification task on handwritten digits, and show that layerwise learning attains an 8% lower generalization error on average in comparison to standard learning schemes for training quantum circuits of the same size. Additionally, the percentage of runs that reach lower test errors is up to 40% larger compared to training the full circuit, which is susceptible to creeping onto a plateau during training.

Authors 5

1. Andrea Skolik corresponding Aachen

   Leiden University · Ludwig-Maximilians-Universität München

   Affiliation as printed

   Leiden University, Niels Bohrweg 1, 2333, CA, Leiden, The Netherlands

   Ludwig Maximilian University, 80333, Munich, Germany

   Volkswagen Data:Lab, Ungererstraße 69, 80805, Munich, Germany

2. Jarrod R. McClean

   Google (United States)

   Affiliation as printed

   Google Research, 340 Main Street, Venice, CA, 90291, USA

3. Masoud Mohseni

   Google (United States)

   Affiliation as printed

   Google Research, 340 Main Street, Venice, CA, 90291, USA

4. Patrick van der Smagt

   Eötvös Loránd University · Volkswagen Group (Germany)

   Affiliation as printed

   Eötvös Loránd University, Budapest, Hungary

   Volkswagen Group Machine Learning Research Lab, Munich, Germany

5. Martin Leib
   Affiliation as printed

   Volkswagen Data:Lab, Ungererstraße 69, 80805, Munich, Germany