Wigner process tomography: Visualization of spin propagators and their spinor properties

Abstract

We study the tomography of propagators for spin systems in the context of finite-dimensional Wigner representations, which completely characterize and visualize operators using shapes assembled from linear combinations of spherical harmonics. The Wigner representation of a propagator can be experimentally recovered by measuring expectation values of rotated axial spherical tensor operators in an augmented system with an additional ancilla qubit. The methodology is experimentally demonstrated for standard one-qubit quantum gates using nuclear magnetic resonance spectroscopy. In particular, this approach provides a direct and compelling visualization of the spinor property of the propagators corresponding to the rotation of a spin 1/2 particle.

arXiv comment18 pages, 10 figures

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Cited by in corpus (8)

• Overview of the phase space formulation of quantum mechanics with application to quantum technologies
• Continuous phase-space representations for finite-dimensional quantum states and their tomography
• New Phase Space Formulations and Quantum Dynamics Approaches
• Implementing efficient selective quantum process tomography of superconducting quantum gates on the IBM quantum processor
• Continuous phase spaces and the time evolution of spins: star products and spin-weighted spherical harmonics
• Phase Spaces, Parity Operators, and the Born-Jordan Distribution
• Symmetry-adapted decomposition of tensor operators and the visualization of coupled spin systems
• Wigner State and Process Tomography on Near-Term Quantum Devices