Optimal circuit depths for shadow tomography in the presence of noise
Kartiek Agarwal
Shadow tomography is a novel way of performing tomography on quantum states wherein measurements on the state are used to compile classical data into a form that succinctly captures the quantum state. This data, called classical shadows, can then be postprocessed in a way specified by the tomography protocol, to infer many, say M, properties of the state, using only order log(M) number of measurements. In this talk, I will spend some time introducing the shadow tomography framework, and our work, which deals with understanding how such tomography can be performed on noisy quantum hardware. I will also discuss towards the end how classical shadows can be used (hopefully, this is work in progress!) as a variational approach to finding the ground state properties of quantum Hamiltonians in arbitrary dimensions efficiently, that is, in polynomial time, as long as we are prepared to give up on ascertaining very high order correlation functions.