Estimating the precision for quantum process tomography

Abstract

Quantum tomography is a widely applicable tool for complete characterization of quantum states and processes. In the present work, we develop a method for precision-guaranteed quantum process tomography. With the use of the Choi-Jamiokowski isomorphism, we generalize the recently suggested extended norm minimization estimator for the case of quantum processes. Our estimator is based on the Hilbert-Schmidt distance for quantum processes. Specifically, we discuss the application of our method for characterizing quantum gates of a superconducting quantum processor in the framework of the IBM Q Experience.

Random density matrices: analytical results for mean root fidelity and mean square Bures distance

“…These PDF's are shown in Figs. 6 and the mean square Bures distances are illustrated in Figs. 7 and 8.…”

“…Various distance measures between quantum states play a crucial role in quantum information theory and find applications in diverse problems, such as quantum communication protocols, quantification of quantum correlations, quantum algorithms in machine learning, and quantum-state tomography [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Roughly speaking, distance measures quantify the degree of closeness of two given quantum states.…”

“…2 and derived exact analytical expressions for its mean square between a fixed density matrix and a random density matrix, and also between two random density matrices. These results serve as useful references for comparing Hilbert-Schmidt distance between quantum states and are of relevance in applications such as construction of entanglement witness operators [13,14], variational hybrid quantum-classical algorithms in machine learning [7,[15][16][17], precision quantum-state tomography [4][5][6], etc. Unfortunately, as far as distinguishability criterion is concerned, Hilbert-Schmidt distance has its limitations since it is not a monotone [1-3, 53, 54].…”

Confidence polytopes for quantum process tomography

“…The bootstrapping approach from the QST domain [4] has been extended to the QPT case [24], but without provable accuracy and with high computational costs. The generalization of the precision-guaranteed QST scheme [8] for quantum processes has also been proposed [25]. Although this approach is computationally efficient, it is limited to the consideration of the Hilbert-Schmidt distance between true Choi state and the corresponding point estimator.…”

Confidence polytopes for quantum process tomography

“…The bootstrapping approach from the QST domain [4] has been generarlized for the QPT case [24] but without provable accuracy, and it is computationally intensive. The generalization of the precision-guaranteed QST scheme [8] for quantum processes has also been proposed [25]. However, this approach is computationally efficient, but it is limited to the consideration of the Hilbert-Schmidt distance between true Choi state and the corresponding point estimator.…”