High-fidelity quantum tomography with imperfect measurements

Abstract

In the current work we address the problem of quantum process tomography (QPT) in the case of imperfect preparation and measurement of the states which are used for QPT. The fuzzy measurements approach which helps us to efficiently take these imperfections into account is considered. However, to implement such a procedure one should have a detailed information about the errors. An approach for obtaining the partial information about them is proposed. It is based on the tomography of the ideal identity gate. This gate could be implemented by performing the measurement right after the initial state preparation. By using the result of the identity gate tomography we were able to significantly improve further QPT procedures. The proposed approach has been tested experimentally on the IBM superconducting quantum processor. As a result, we have obtained an increase in fidelity from 89% to 98% for Hadamard transformation and from 77% to 95% for CNOT gate.

Quantum tomography for quantum systems optimization

“…There are various algorithms for performing this procedure. [12][13][14][15][16][17] In this work, we are interested in the unitary part of the evolution of quantum states, since it is responsible for the logical operations on states. In this regard, we use the first rank root parameterization for the quantum process and the maximum likelihood estimation.…”

“…In this regard, we use the first rank root parameterization for the quantum process and the maximum likelihood estimation. 15,17 Thus, in the case of a single qubit, a unitary quantum process can be described by three independent parameters (for example, the parameters from expression (1)). In the general case, the number of independent parameters for a unitary process is ν = d 2 − 1.…”

“…At the same time, quantum tomography (QT) allows one to obtain a complete description of a quantum transformation and determine how it affects any given input state. [12][13][14][15][16][17] However, at the moment, there are practically no papers where QT is used to optimize quantum transformations. The main reason for this is that QT is sensitive to quantum state preparation and measurement (SPAM) errors.…”

“…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.…”

Estimating the precision for quantum process tomography

“…One of the ways to solve this problem is to use the randomized benchmarking technique [12]. Much more detailed information can be obtained via quantum process tomography [13][14][15][16][17][18][19]27], which is a natural extension of quantum state tomography. Quantum process tomography allows predicting the effect of the quantum processes on arbitrary input states.…”