Selective and Efficient Quantum Process Tomography

TL;DR

This paper presents a detailed and generalized method for efficient quantum process tomography that scales polynomially with system size, enabling precise estimation of the process matrix elements with minimal resources.

Contribution

It generalizes a previous quantum process tomography method, introducing efficient estimation techniques using 2-designs and detailing state preparation and detection methods.

Findings

Efficient estimation of $oldsymbol{ ext{chi}}$-matrix elements using random sampling.

Diagonal elements can be estimated without ancillary qubits.

Off-diagonal elements require an additional clean qubit.

Abstract

In this paper we describe in detail and generalize a method for quantum process tomography that was presented in [A. Bendersky, F. Pastawski, J. P. Paz, Physical Review Letters 100, 190403 (2008)]. The method enables the efficient estimation of any element of the $\chi$--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 to implement it scale polynomically with the number of qubits 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 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.