Transfer Learning for Quantum Classifiers: An Information-Theoretic Generalization Analysis

TL;DR

This paper analyzes the generalization performance of transfer learning in quantum classifiers, introducing a new task similarity measure and deriving bounds on excess risk based on information-theoretic quantities.

Contribution

It proposes a novel task (dis)similarity measure for quantum classification and derives an upper bound on the excess risk using information-theoretic and complexity measures.

Findings

Theoretical bounds are validated on a binary classification example.

A new measure of task (dis)similarity based on trace distances is introduced.

The excess risk depends on task similarity, mutual information, and complexity measures.

Abstract

A key component of a quantum machine learning model operating on classical inputs is the design of an embedding circuit mapping inputs to a quantum state. This paper studies a transfer learning setting in which classical-to-quantum embedding is carried out by an arbitrary parametric quantum circuit that is pre-trained based on data from a source task. At run time, a binary quantum classifier of the embedding is optimized based on data from the target task of interest. The average excess risk, i.e., the optimality gap, of the resulting classifier depends on how (dis)similar the source and target tasks are. We introduce a new measure of (dis)similarity between the binary quantum classification tasks via the trace distances. An upper bound on the optimality gap is derived in terms of the proposed task (dis)similarity measure, two R$\'e$nyi mutual information terms between classical input and quantum embedding under source and target tasks, as well as a measure of complexity of the combined space of quantum embeddings and classifiers under the source task. The theoretical results are validated on a simple binary classification example.