Predicting many properties of quantum systems with chaotic dynamics

          @misc{ scivideos_PIRSA:21120015,
            doi = {10.48660/21120015},
            url = {https://pirsa.org/21120015},
            author = {Hu, Hong-Ye},
            keywords = {Quantum Information},
            language = {en},
            title = {Predicting many properties of quantum systems with chaotic dynamics },
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2021},
            month = {dec},
            note = {PIRSA:21120015 see, \url{https://scivideos.org/pirsa/21120015}}
          }
          

Abstract

Classical shadow tomography provides an efficient method for predicting functions of an unknown quantum state from a few measurements of the state. It relies on a unitary channel that efficiently scrambles the quantum information of the state to the measurement basis. However, it is quite challenging to realize deep unitary circuits on near-term quantum devices, and an unbiased reconstruction map is non-trivial to find for arbitrary random unitary ensembles. In this talk, I will discuss our recent progress on combining classical shadow tomography with quantum chaotic dynamics. Particularly, I will introduce two new families of shadow tomography schemes: 1) Hamiltonian-driven shadow tomography and 2) Classical shadow tomography with locally scrambled quantum dynamics. In both works, I’ll derive the unbiased reconstruction map, and analyze the sample complexity. In the Hamiltonian-driven scheme, I will illustrate how to use proper time windows to achieve a more efficient tomography. In the second work, I will demonstrate advantages of shadow tomography in the shallow circuit region. Then I’ll conclude by discussing approximate shadow tomography with local Hamiltonian dynamics, and demonstrate that a single quench-disordered quantum spin chain can be used for approximate shadow tomography.

 

References:
[1] Hong-Ye Hu, Yi-Zhuang You. “Hamiltonian-Driven Shadow Tomography of Quantum States”. arXiv:2102.10132 (2021)
[2] Hong-Ye Hu, Soonwon Choi, Yi-Zhuang You. “Classical Shadow Tomography with Locally Scrambled Quantum Dynamics”. arXiv: 2107.04817 (2021)

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