Inductive Graph Convolutional Quantum Process Tomography: A Scalable Geometric Deep Learning Approach

Quantum process tomography (QPT) is a fundamental task in quantum information science, yet it suffers from exponential scaling in the number of qubits. We introduce an inductive graph convolutional approach, IGC-QPT, that overcomes this limitation by exploiting the geometric structure of Choi matrices. The method constructs a graph based on a fast low-rank approximation of the Bures distance, then learns a GraphSAGE encoder to map measurement data to low-dimensional embeddings that preserve the local geometry of the process space. This enables efficient and accurate reconstruction of unknown quantum processes from limited measurements for systems up to seven qubits. Theoretical analysis provides sample complexity bounds with complete proofs, including a detailed analysis of the low-rank approximation error. Extensive numerical experiments on 2–7 qubit systems, with full statistical reporting, demonstrate that IGC-QPT significantly outperforms standard QPT (LS), compressed sensing (CS), and neural network methods (NN), achieving high fidelity with orders of magnitude speedup. A detailed discussion of assumptions, limitations, and practical considerations such as transfer learning for reducing training requirements is provided, along with robustness checks.