Pairwise projected Choi matrix tomography for efficient error characterization in qudits

Qudit-based quantum computation offers several practical advantages over qubit systems. By fully utilizing these d-dimensional Hilbert spaces, we can reduce encoding overhead (by log₂d) and suppress leakage as a destructive error. Moreover, several qubit platforms are in fact qudit systems which experience leakage outside the computational subspace. As a result, robust and precise qudit tomography becomes essential to accurately characterize, verify, and validate (QCVV) operations on (and control of) these larger logical spaces. In this work, we utilize the canonical Hamiltonian (obtained with minimizing the Haar-average dissipator norm) of Hayden and Sorce (2022) to develop a pairwise subspace tomography method, and we benchmark its performance and effectiveness against theoretical models. This method employs the O(d²) Choi matrix elements corresponding to pairwise subspaces of the qudit Hilbert space (instead of the usual O(d⁴) Choi matrix elements), efficiently obtaining a qudit Hamiltonian and dissipator under the assumption of Markovian dynamics. We also explore in detail the consequences of various gauge choices in this tomography procedure, and the error in the estimation, quantified by a distance between the estimated and actual Hamiltonian. Finally, we discuss potential applications of this approach in the context of qudit codes and qubit leakage. This can be implemented and tested in state-of-the art ion trap and superconducting quantum processors.