Wigner State and Process Tomography on Near-Term Quantum Devices

With the growing interest and rapid development in near-term quantum devices, the migration of theoretical and experimental approaches from existing devices to near-term quantum devices are imperative. We present an experimental scanning-based tomography approach in the context of finite-dimensional Wigner representations. These representations provide a rich visualization of quantum operators using shapes assembled from a linear combination of spherical harmonics. These shapes, i.e., spherical droplets, can be recreated experimentally by measuring the expectation values of rotated axial tensor operators. This study provides a reformulation of the theory of Wigner state and process tomography for the case of a general-purpose pure-state quantum computer. 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

spherical droplets. This tomography approach can be directly accessed using python packages.