Matrix-free operators and superoperators for large open-system optimal control in circuit QED

Previously, we have showed how to perform optimal control on an open spin system with the Hilbert space size of up to 2¹⁶ [1]. This is run on one or two CPU servers and does not require any special accelerators. Contrary to the common approach where the operators and superoperators appearing in the master equation are stored as dense or sparse matrices, we calculate their action on the density matrix dynamically without storing any data or only storing the diagonal. Storing the diagonal instead of recalculating it every time was found to be faster for the spin Hamiltonians that we have considered. Besides freeing up the memory, this approach also helps with utilizing the caches of the CPU in a more optimal way and helps with parallelization across the CPU cores. The adaptation of the same approach to the circuit QED is straightforward. In particular, we consider a transmon coupled to a resonator. For this system, a large Hilbert space can be required when complex non-Gaussian states are prepared and manipulated in the resonator. This can happen both when resonator is used for measurement and is strongly driven, and when the resonator is used as a memory for bosonic code states.

[1] arXiv:2409.11956