Transfer Learning for Quantum Classifiers: An Information-Theoretic Generalization Analysis
This work addresses the challenge of understanding how pre-trained quantum embeddings affect classifier performance in transfer learning, which is incremental as it builds on existing quantum machine learning frameworks.
The paper tackles the problem of analyzing generalization performance in transfer learning for quantum classifiers by deriving an upper bound on the optimality gap in terms of task dissimilarity and information-theoretic measures, validated on a simple binary classification example.
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$é$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.