ABSTRACT
We show that the minimum experimental effort to estimate the average error of a quantum gate scales as 2(n) for n qubits and requires classical computational resources â¼n(2)2(3n) when no specific assumptions on the gate can be made. This represents a reduction by 2(n) compared to the best currently available protocol, Monte Carlo characterization. The reduction comes at the price of either having to prepare entangled input states or obtaining bounds rather than the average fidelity itself. It is achieved by applying Monte Carlo sampling to so-called 2-designs or two classical fidelities. For the specific case of Clifford gates, the original version of Monte Carlo characterization based on the channel-state isomorphism remains an optimal choice. We provide a classification of the available efficient strategies to determine the average gate error in terms of the number of required experimental settings, average number of actual measurements, and classical computational resources.
ABSTRACT
We introduce and discuss the concept of modular entanglement. This is the entanglement that is established between the end points of modular systems composed by sets of interacting moduli of arbitrarily fixed size. We show that end-to-end modular entanglement scales in the thermodynamic limit and rapidly saturates with the number of constituent moduli. We clarify the mechanisms underlying the onset of entanglement between distant and noninteracting quantum systems and its optimization for applications to quantum repeaters and entanglement distribution and sharing.
