Mode connectivity in the loss landscape of parameterized quantum circuits

Kathleen E. Hamilton; Emily Lynn; Raphael C. Pooser

doi:10.1007/s42484-021-00059-5

Mode connectivity in the loss landscape of parameterized quantum circuits

Kathleen E. Hamilton, Emily Lynn, Raphael C. Pooser

Quantum Computational Science

Research output: Contribution to journal › Article › peer-review

Abstract

Variational training of parameterized quantum circuits (PQCs) underpins many workflows employed on near-term noisy intermediate scale quantum (NISQ) devices. It is a hybrid quantum-classical approach that minimizes an associated cost function in order to train a parameterized ansatz. In this paper we adapt the qualitative loss landscape characterization for neural networks introduced in Goodfellow et al. (2014); Li et al. (2017) and tests for connectivity used in Draxler et al. (2018) to study the loss landscape features in PQC training. We present results for PQCs trained on a simple regression task, using the bilayer circuit ansatz, which consists of alternating layers of parameterized rotation gates and entangling gates. Multiple circuits are trained with 3 different batch gradient optimizers: stochastic gradient descent, the quantum natural gradient, and Adam. We identify large features in the landscape that can lead to faster convergence in training workflows.

Original language	English
Article number	10
Journal	Quantum Machine Intelligence
Volume	4
Issue number	1
DOIs	https://doi.org/10.1007/s42484-021-00059-5
State	Published - Jun 2022

Funding

This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan. ( http://energy.gov/downloads/doe-public-279access-plan ). This work was partially supported as part of the ASCR Testbed Pathfinder Program at Oak Ridge National Laboratory under FWP ERKJ332. This work was partially supported as part of the ASCR Fundamental Algorithmic Research for Quantum Computing Program at Oak Ridge National Laboratory under FWP ERKJ354. This work was partially supported as part of the ASCR QCAT Program at Oak Ridge National Laboratory under FWP #ERKJ347. EL was supported by the U.S. Department of Energy, Office of Science, Office of Workforce Development for Teachers and Scientists (WDTS) under the Science Undergraduate Laboratory Internship program.

Funders	Funder number
Office of Workforce Development for Teachers
U.S. Department of Energy
Office of Science
Advanced Scientific Computing Research
Oak Ridge National Laboratory	FWP ERKJ332, FWP ERKJ354, FWP #ERKJ347

Keywords

Circuit design
Gradient-based optimization
Mode connectivity
Quantum machine learning
Visualization

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10.1007/s42484-021-00059-5

Cite this

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Mode connectivity in the loss landscape of parameterized quantum circuits

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