Symbolic Pauli Propagation for Gradient-Enabled Pre-Training of Quantum Circuits

TL;DR

This paper introduces a symbolic Pauli propagation method for efficient gradient estimation in quantum circuit training, enabling scalable pre-training and improved accuracy for quantum machine learning models.

Contribution

It presents a novel symbolic representation of observables using Pauli propagation, allowing scalable and accurate gradient estimation for larger quantum systems.

Findings

Effective for Variational Quantum Eigensolver tasks

Enables classical pre-training of quantum circuits

Achieves accurate results with tractable computations

Abstract

Quantum Machine Learning models typically require expensive on-chip training procedures and often lack efficient gradient estimation methods. By employing Pauli propagation, it is possible to derive a symbolic representation of observables as analytic functions of a circuit's parameters. Although the number of terms in such functional representations grows rapidly with circuit depth, suitable choices of ansatz and controlled truncations on Pauli weights and frequency components yield accurate yet tractable estimators of the target observables. With the right ansatz design, this approach can be extended to system sizes beyond the reach of classical simulation, enabling scalable training for larger quantum systems. This also enables a form of classical pre-training through gradient-based optimization prior to deployment on quantum hardware. The proposed approach is demonstrated on the Variational Quantum Eigensolver for obtaining the ground state of a spin model, showing that accurate results can be achieved with a scalable and computationally efficient procedure.