Qudit gates for high-dimensional quantum computing can be synthesized with high precision using numerical quantum optimal control techniques. Large circuits are broken down into modules and the tailored pulses for each module can be used as primitives for a qudit compiler. Application of the pulses of each module in the presence of extra modes may decrease their effectiveness due to crosstalk. In this paper, we address this problem by simulating qudit dynamics for circuit quantum electrodynamics (cQED) systems. As a test case, we take pulses for single-qudit SWAP gates optimized in isolation and then apply them in the presence of spectator modes each of which are in Fock states. We provide an experimentally relevant scaling formula that can be used as a bound on the fidelity decay. Our results show that frequency shift from spectator mode populations has to be $\lesssim 0.1\%$ of the qudit's nonlinearity in order for high-fidelity single-qudit gates to be useful in the presence of occupied spectator modes.

We propose a novel mechanism for the cosmological production of keV - GeV mass dark matter that interacts with the Standard Model through a small effective magnetic dipole moment. Such an interaction can be radiatively generated if dark matter couples to heavier charged particles. Previous studies have focused on the case where these charged states are much heavier than the reheat temperature, such that freeze-in production of dark matter is sensitive to the ultraviolet details of reheating. Here, we instead consider the possibility that these heavy states have masses comparable to the dark matter mass and are charged under a new kinetically-mixed $U(1)'$. As a result, dark matter production is dominated by the infrared freeze-in of the heavy charged states that subsequently thermalize the rest of the dark sector to a temperature much below that of the visible bath. We delineate regions of parameter space consistent with cosmological and astrophysical constraints and identify benchmark scenarios that can guide the next generation of direct detection experiments searching for spin-dependent scattering of sub-GeV dark matter.

There is a recent surge of interest and insights regarding the interplay of quantum optimal control and variational quantum algorithms. We study the framework in the context of qudits which are, for instance, definable as controllable electromagnetic modes of a superconducting cavity system coupled to a transmon. By employing recent quantum optimal control approaches described in (Petersson and Garcia, 2021), we showcase control of single-qudit operations up to eight states, and two-qutrit operations, mapped respectively onto a single mode and two modes of the resonator. We discuss the results of numerical pulse engineering on the closed system for parametrized gates useful to implement Quantum Approximate Optimization Algorithm (QAOA) for qudits. The results show that high fidelity ($>$ 0.99) is achievable with sufficient computational effort for most cases under study, and extensions to multiple modes and open, noisy systems are possible. The tailored pulses can be stored and used as calibrated primitives for a future compiler in circuit quantum electrodynamics (cQED) systems.