# Wigner State and Process Tomography on Near-Term Quantum Devices

## TL;DR

This paper introduces a Wigner-based tomography method for near-term quantum devices, providing visualization tools, experimental procedures, and software to facilitate state and process characterization on quantum computers.

## Contribution

It adapts a previously known ensemble-based tomography approach to pure-state quantum devices, with software tools and experimental validation on IBM quantum hardware.

## Key findings

- Successful implementation of Wigner tomography on IBM quantum devices
- Development of software package DROPStomo for practical use
- Effective estimation of density and process matrices from Wigner functions

## Abstract

We present an experimental scanning-based tomography approach for near-term quantum devices. The underlying method has previously been introduced in an ensemble-based NMR setting. Here we provide a tutorial-style explanation along with suitable software tools to guide experimentalists in its adaptation to near-term pure-state quantum devices. The approach is based on a Wigner-type representation of quantum states and operators. These representations provide a rich visualization of quantum operators using shapes assembled from a linear combination of spherical harmonics. These shapes (called droplets in the following) can be experimentally tomographed by measuring the expectation values of rotated axial tensor operators. We present an experimental framework for implementing the scanning-based tomography technique for circuit-based quantum computers and showcase results from IBM quantum experience. We also present a method for estimating the density and process matrices from experimentally tomographed Wigner functions (droplets). This tomography approach can be directly implemented using the Python-based software package \texttt{DROPStomo}.