Mode connectivity in the loss landscape of parameterized quantum circuits

• URL: http://arxiv.org/abs/2111.05311v1
• Date: Tue, 9 Nov 2021 18:28:46 GMT
• Title: Mode connectivity in the loss landscape of parameterized quantum circuits
• Authors: Kathleen E. Hamilton and Emily Lynn and Raphael C. Pooser
• Abstract summary: Variational training of parameterized quantum circuits (PQCs) underpins many employed on near-term noisy intermediate scale quantum (NISQ) devices. We adapt the qualitative loss landscape characterization for neural networks introduced in citegoodfellowqualitatively,li 2017visualizing and tests for connectivity used in citedraxler 2018essentially to study the loss landscape features in PQC training.
• Score: 1.7546369508217283
• License: http://creativecommons.org/licenses/by/4.0/
• 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 \cite{goodfellow2014qualitatively,li2017visualizing} and tests for connectivity used in \cite{draxler2018essentially} 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.

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