Selective and efficient quantum process tomography

ARIEL BENDERSKY; FERNANDO PASTAWSKI; JUAN PABLO PAZ

PHYSICAL REVIEW A - ATOMIC, MOLECULAR AND OPTICAL PHYSICS

AMER PHYSICAL SOC

Lugar: New York; Año: 2009 vol. 80 p. 32116 - 32116

1050-2947

In this paper we describe in detail and generalize a method for quantum process tomography that was presented by Bendersky et al. [Phys. Rev. Lett. 100, 190403 (2008)]. The method enables the efficient estimation of any element of the χ matrix of a quantum process. Such elements are estimated as averages over experimental outcomes with a precision that is fixed by the number of repetitions of the experiment. Resources required implementing it scale polynomially with the number of qubits of the system. The estimation of all diagonal elements of the χ 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, which is based on efficient estimation by random sampling over a set of states forming a 2-design, are described in detail. Efficient methods for preparing and detecting such states are explicitly shown.