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Abstract: In this paper we describe in detail and generalize a method for quantumprocess tomography that was presented in A. Bendersky, F. Pastawski, J. P.Paz, Physical Review Letters 100, 190403 2008. The method enables theefficient estimation of any element of the $\chi$-matrix of a quantum process.Such elements are estimated as averages over experimental outcomes with aprecision that is fixed by the number of repetitions of the experiment.Resources required to implement it scale polynomically with the number ofqubits of the system. The estimation of all diagonal elements of the$\chi$-matrix can be efficiently done without any ancillary qubits. In turn,the estimation of all the off-diagonal elements requires an extra clean qubit.The key ideas of the method, that is based on efficient estimation by randomsampling over a set of states forming a 2-design, are described in detail.Efficient methods for preparing and detecting such states are explicitly shown.

Autor: Ariel Bendersky, Fernando Pastawski, Juan Pablo Paz


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