Adding a notebook on POVM implementation

[petr-ivashkov]

Summary

Implementing generalized measurements in the form of positive operator valued measurements (POVM) is non-trivial, and to this end, several methods have been proposed. To compare contrasting approaches, we focus on two methods: Naimark's extension and the binary tree search methods, which significantly differ in terms of their scaling with the size of the POVM set and the hardware resources necessary to implement them.

Details and comments

In this tutorial, we first introduce the theory behind generalized measurements and show how they can be implemented in Qiskit using Naimark's extension. After that, we demonstrate the implementation of the binary search tree approach using the protocol described by Andersson and Oi for a tetrad POVM using a single auxiliary qubit, thus demonstrating a promising application of mid-circuit measurements and feed-forward capabilities of near-term quantum devices.

Contributors: Alireza Seif, Derek Wang, Gideon Uchehara, Peter Ivashkov

This project was carried out within QAMP Fall 2022.

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