Markovian Errors in Higher-Dimensional Quantum Systems

We extend the error generator formalism for noisy quantum processes to quantum systems with local Hilbert spaces of arbitrary dimension. In particular, we consider error bases adapted to the symmetries of various model systems. Central to this generalization is a notion of locality (or sparseness) of errors not only for collections of local degrees of freedom, but within each local Hilbert space. This work provides a theoretical foundation for building efficient models of small Markovian errors in quantum computing platforms beyond those based on qubits, with potential applications to tomography and benchmarking.