On quantum computation by variation of a quantum circuits parameters to minimise an effective Hamiltonian iteratively realised by local measurements

Modern quantum processors enable the execution of short quantum circuits. These quantum circuits can be iteratively tuned to minimise an objective function and solve problem instances. This is known as variational quantum computation: local measurements are repeated and modified to determine the expected value of a effective Hamiltonian. Whereas solving practical problems appears to remain out of reach, many questions of theoretical interest surround the variational model. I will explain some recent negative results found in collaboration, including reachability deficits in variational quantum approximate optimisation. I will also explain some more forward looking findings, including my proof that the variational model is, in theory, a universal model of quantum computation.
This talk is based on Phys. Rev. A 103, L030401 (2021) available open access at https://journals.aps.org/pra/abstract/10.1103/PhysRevA.103.L030401