2009/06/16 by Ariel Bendersky, Fernando Pastawski, Juan Pablo Paz · 47 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Computer science #Density matrix #Diagonal #Diagonal matrix #Element (criminal law) #Geometry #Key (lock) #Mathematics #Matrix (chemical analysis) #Physics #Process (computing) #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Quantum process #Quantum state #Quantum tomography #Qubit #Scale (ratio) #Set (abstract data type) #Theoretical computer science #quant-ph
paper · pdf · doi:10.1103/physreva.80.032116
published in Physical Review A 80(3) (American Physical Society) · 9 pages, 5 figures
arxiv created 2009/06/16 · openalex publication_date 2009/09/24 · arxiv updated 2015/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 \ensuremathχ 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 \ensuremathχ 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.