Verification of Quantum Computations and Quantum Supremacy

Quantum computers hold the promise to decidedly increase our computing capacity, providing a huge speed-up in the solution of a certain class of problems which are believed to be intractable by classical devices. An example of that is represented by the simulation of microscopic systems,
which is one of the central problems in modern science and has a wide range of applications - from drug design to nuclear physics to quantum
chemistry and biology. For instance, while there is no known classical algorithm able to efficiently simulate microscopic systems, it is widely
believed that "quantum simulators" will someday be able to simulate interesting microscopic systems. Since many experimental challenges still
make the road to a universal quantum computer a hard one, intermediate non-universal machines are nowadays regarded with great interest and
might possibly be built in the following decades. However, a fundamental question concerning their "certification" arises: how can a classical
observer certify the correctness of the outcome of a quantum simulator? How can he get confidence about the correct functioning of the machine,
if the outcome he obtains has never been obtained by means of a classical device?
My PhD project is focused on the study and the development of protocols for the certification of quantum simulators. In particular, I will initially
try to optimise already existing protocols whose objective is to give an answer to the questions addressed above, while I will subsequently try to
adapt them to apply in realistic settings, e.g. in an actual experiment with the presence of noise.