Quantum tomography of noisy ion-based qudits

Abstract

Quantum tomography makes it possible to obtain a comprehensive information about certain logical elements of a quantum computer. In this regard, it is a promising tool for debugging quantum computers. The practical application of tomography, however, is still limited by systematic measurement errors. Their main source are errors in the quantum state preparation and measurement procedures. In this work, we investigate the possibility of suppressing these errors in the case of trapped-ion-based qudits. First, we will show that one can construct a quantum tomography protocol that contains no more than a single quantum operation in each measurement circuit. Such a protocol is more robust to errors than the measurements in mutually unbiased bases, where the number of operations increases in proportion to the square of the qudit dimension. After that, we will demonstrate the possibility of determining and accounting for the state initialization and readout errors. Together, the measures described can significantly improve the accuracy of quantum tomography of real ion-based qudits.

Quantum tomography for quantum systems optimization

“…Here we consider the most common standard protocol. 21,30,31 For a single qubit it consists of m P = 4 input states and m M = 3 measurement bases.…”

“…Using this model, it is possible to obtain a consistent estimate of a quantum state or a quantum process. 17,20,21,24 Note, however, that this requires knowing the SPAM parameters with sufficient accuracy. Below we consider a possible experimental procedures for estimating these parameters in the trapped ion system.…”

“…To avoid this, the QT model must take into account SPAM errors. [17][18][19][20][21][22][23][24] One way to achieve this is through the use of machine learning methods. 25,26 However, errors in the training data can lead to the overestimated accuracy of subsequent results.…”

Linear optical circuits characterization by means of thermal field correlation measurement

“…A general approach for multichannel quantum optical process characterization is based on quantum state and quantum process tomography technique [23][24][25][26][27][28][29]. In works [30,31] an unknown two-mode process was probed by coherent states and a homodyne tomography of the output states was performed.…”