protocolli fault-tolerant e supremazia quantistica

One of the main challenges in experimentally building a quantum computer is to harness the unavoidable errors which affect quantum systems during a computation, leading to an incorrect outcome. In this work we consider a universal quantum computation model, in which quantum operations are based on the Ising Hamiltonian, a candidate for proving the supremacy of quantum computation over classical computation. We start by developing a procedure to protect quantum computation against local errors and then we propose another procedure in order to verify its outcome, that is to know if the result of the computation is correct or not. Both procedures involve quantum circuits, which are a sequence of quantum gates (unitary operations) acting on quantum states. In particular, the first procedure is able to detect and correct local errors up to any desired accuracy, provided that the probability of errors per gate is below a certain constant threshold. We calculate this threshold, which is lower than the best known ones for this type of computation, (see e.g. [1]). The second procedure allows to know if the outcome of the quantum computation is correct or not. In order to do it, we develop some particular circuits able to detect errors in the result and, in this case, reject the final outcome. We leave as an open question the calculation of the threshold for the second procedure and the proof of verifiability of the complete proposed protocol. [1]R. Raussendorf, J. Harrington and K. Goyal, Topological fault-tolerance in cluster state quantum computation. New Journal of Physics 9, 199 (2007)