I will explain how a quantum circuit together with measurement apparatuses and EPR sources can be fully verified without any reference to some other trusted set of quantum devices. Our main assumption is that the physical system we are working with consists of several identifiable sub-systems, on which we can apply some given gates locally.
To achieve our goal we define the notions of simulation and equivalence. The concept of simulation refers to producing the correct probabilities when measuring physical systems. The notion of equivalence is used to enable the efficient testing of the composition of quantum operations. Unlike simulation, which refers to measured quantities (i.e., probabilities of outcomes), equivalence relates mathematical objects like states, subspaces or gates.
Using these two concepts, we prove that if a system satisfies some simulation conditions, then it is equivalent to the one it is supposed to implement. In addition, with our formalism, we can show that these statements are robust, and the degree of robustness can be made explicit. Finally, we design a test for any quantum circuit whose complexity is linear in the number of gates and qubits, and polynomial in the required precision.
Joint work with Frederic Magniez, Dominic Mayers and Harold Ollivier.