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AIP conference proceedings

Characterization of quantum processes with a faulty Bell-state analyzer

Masoud Mohseni, A. T. Rezakhani, Alexander I. Lvovsky

Published Jan 1, 2009• 0 citations
Publisher

Abstract

Accuracy of quantum process estimation is limited to noisy operations in the preparations and measurements devices. Such imperfections may lead to inaccuracies in the process reconstruction due to the fact that standard data analysis techniques presume ideal devices. Here, we provide a scheme for estimation of completely positive quantum maps acting on qubit systems using calibrated faulty state generator and analyzer. Specifically, we present a generalization of “Direct Characterization of Quantum Dynamics” [M. Mohseni and D. A. Lidar, 97, 170501 (2006)] with an imperfect Bell‐state analyzer.

DOI
10.1063/1.3131372

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Accuracy of quantum process estimation is limited to noisy operations in the preparations and measurements devices. Such imperfections may lead to inaccuracies in the process reconstruction due to the fact that standard data analysis techniques presume ideal devices. Here, we provide a scheme for estimation of completely positive quantum maps acting on qubit systems using calibrated faulty state generator and analyzer. Specifically, we present a generalization of “Direct Characterization of Quantum Dynamics” [M. Mohseni and D. A. Lidar, 97, 170501 (2006)] with an imperfect Bell‐state analyzer.
Performance of quantum process estimation is naturally limited by fundamental, random, and systematic imperfections of preparations and measurements. These imperfections may lead to considerable errors in the process reconstruction because standard data-analysis techniques usually presume ideal devices. Here, by utilizing generic auxiliary quantum or classical correlations, we provide a framework for the estimation of quantum dynamics via a single measurement apparatus. By construction, this approach can be applied to quantum tomography schemes with calibrated faulty-state generators and analyzers. Specifically, we present a generalization of the work begun by M. Mohseni and D. A. Lidar [Phys. Rev. Lett. 97, 170501 (2006)] with an imperfect Bell-state analyzer. We demonstrate that for several physically relevant noisy preparations and measurements, classical correlations and a small data-processing overhead suffice to accomplish the full system identification. Furthermore, we provide the optimal input states whereby the error amplification due to inversion of the measurement data is minimal.
We experimentally implement direct characterization of quantum dynamics (DCQD) algorithm of a single qubit proposed in M. Mohseni and D. A. Lidar [Phys. Rev. Lett. 97, 170501 (2006)], which does not require quantum state tomography. The number of experimental configurations is reduced by a factor of 2 compared with that of standard quantum process tomography, which can be increased four times with an ideal Bell state analyzer. We combine the DCQD algorithm with maximum-likelihood estimation to give the physical characterization of quantum dynamics. It can also be applied to obtaining partial information about quantum dynamics.
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The characterization of the dynamics of quantum systems is a task of both fundamental and practical importance. A general class of methods which have been developed in quantum information theory to accomplish this task is known as quantum process tomography (QPT). In an earlier paper [M. Mohseni and D. A. Lidar Phys. Rev. Lett. 97, 170501 (2006)] we presented an algorithm for direct characterization of quantum dynamics (DCQD) of two-level quantum systems. Here we provide a generalization by developing a theory for direct and complete characterization of the dynamics of arbitrary quantum systems. In contrast to other QPT schemes, DCQD relies on quantum error-detection techniques and does not require any quantum state tomography. We demonstrate that for the full characterization of the dynamics of nnn ddd-level quantum systems (with ddd prime), the minimal number of required experimental configurations is reduced quadratically from d4n{d}^{4n}d4n in separable QPT schemes to d2n{d}^{2n}d2n in DCQD.
The calibration of quantum measurements is limited by the ability to accurately prepare quantum states under unknown device errors. We develop an accurate calibration protocol for the measurement apparatus of a quantum computer that is `blind' to the state preparation. Blind calibration quantifies and corrects measurement errors from simple tomographic data on a noisy quantum state. Importantly, it calibrates multiple error mechanisms in a single experiment, eliminating the need for bespoke, separate calibration experiments. Using a trapped-ion quantum computer, we systematically demonstrate the accuracy of the method. We use blind calibration to estimate the native calibration parameters of the experimental system. The recovered calibrations are consistent with directly measured values and perform similarly in predicting the state properties.
Direct characterization of quantum dynamics (DCQD) introduced by Mohseni and Lidar [Phys. Rev. Lett. 97, 170501 (2006)] offers an effective way for estimation of quantum dynamical systems. Employing single-photon two-qubit states, we experimentally implement DCQD of one-qubit dynamics. The requirement of two-body interactions is thus eliminated such that the algorithm can be realized more conveniently. Both DCQD and standard quantum process tomography (SQPT) measurements are performed for several processes. The data from both methods show good agreement. Although the average process fidelities of the data obtained via DCQD are a little lower than that of SQPT, the number of experimental configurations is quadratically reduced evidencing the quadratic advantage of DCQD scheme. Partial information of the quantum dynamics can also be directly extracted via DCQD with fewer measurements.