Which component of the Hyper-V architecture controls all communication with the physical hardware on the computer?

The answer is "Hypervisor"

Explanation:

It is software which is run on the devices, and provides a base-band or hardware to running and generate virtualization. It provides a virtual device, that operates by the hyper-visor, which is designated as a host-device, and every virtual-device is consider as a virtual platform.

In this device virtualization, runs its codes. It is also used in the virtual box.