Robust Qudit Hamiltonian Engineering: A General Theory

Dynamical decoupling and Hamiltonian engineering lie at the cornerstone of modern quantum science and engineering. For qubits, conditions that determine whether a given pulse sequence transforms a native interaction into a desired form are straightforward to obtain due to the intimate connection between single qubit gates and rotations in three dimensions. In this talk, we extend this characterization to generic qudit systems with strongly anharmonic level structures. Utilizing results from group theory we show how the Clebsch-Gordon coefficients of particular irreducible representations of SU(d) lead to simple analytic conditions for the cancellation of generic qudit interactions. We further use them to give a natural parameterization of engineerable Hamiltonians. Lastly, we analytically construct experimentally robust pulse sequences satisfying our cancellation conditions, leveraging the algebraic properties of the generalized Clifford group. Motivated by the prominence of modern qutrit quantum simulation and computation experiments, special attention will be given to this d=3 special case. These results offer an efficient, analytical design tool for modern quantum simulators, opening the door to exotic many-body physics lacking any analog in qubit systems.