Theory and Experimental Demonstration of Wigner Tomography of Unknown Unitary Quantum Gates

• URL: http://arxiv.org/abs/2411.05404v2
• Date: Wed, 18 Dec 2024 14:02:57 GMT
• Title: Theory and Experimental Demonstration of Wigner Tomography of Unknown Unitary Quantum Gates
• Authors: Amit Devra, Léo Van Damme, Frederik vom Ende, Emanuel Malvetti, Steffen J. Glaser,
• Abstract summary: We investigate the tomography of unknown unitary quantum processes within the framework of a finite-dimensional Wigner-type representation. These shapes can be experimentally tomographed using a scanning-based phase-space tomography approach.
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• Abstract: We investigate the tomography of unknown unitary quantum processes within the framework of a finite-dimensional Wigner-type representation. This representation provides a rich visualization of quantum operators by depicting them as shapes assembled as a linear combination of spherical harmonics. These shapes can be experimentally tomographed using a scanning-based phase-space tomography approach. However, so far, this approach was limited to $\textit{known}$ target processes and only provided information about the controlled version of the process rather than the process itself. To overcome this limitation, we introduce a general protocol to extend Wigner tomography to $\textit{unknown}$ unitary processes. This new method enables experimental tomography by combining a set of experiments with classical post-processing algorithms introduced herein to reconstruct the unknown process. We also demonstrate the tomography approach experimentally on IBM quantum devices and present the specific calibration circuits required for quantifying undesired errors in the measurement outcomes of these demonstrations.

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