Hamiltonian supermaps: Higher-order quantum transformations of unknown Hamiltonian dynamics

          @misc{ scivideos_PIRSA:23100031,
            doi = {10.48660/23100031},
            url = {https://pirsa.org/23100031},
            author = {Murao, Mio},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Hamiltonian supermaps: Higher-order quantum transformations of unknown Hamiltonian dynamics},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2023},
            month = {oct},
            note = {PIRSA:23100031 see, \url{https://scivideos.org/pirsa/23100031}}
          }
          

Abstract

Supermaps are higher-order transformations taking maps as input.  We consider quantum algorithms implementing supermaps for the input given by unknown Hamiltonian dynamics, which can be regarded as infinitely divisible unitary operations.  We first show a quantum algorithm that approximately but universally transforms black-box Hamiltonian dynamics into controlled Hamiltonian dynamics utilizing a higher-order transformation called neutralization.  Then, we present another universal algorithm that efficiently simulates linear transformations of any Hamiltonian consisting of a polynomial number of terms in system size, using only controlled-Pauli gates and time-correlated randomness.  This algorithm for implementing Hamiltonian supermaps is an instance of quantum functional programming, where the desired function is specified as a concatenation of higher-order quantum transformations. As examples, we demonstrate the simulation of negative time-evolution and time-reversal, and perform a Hamiltonian learning task.

References:

Q. Dong, S. Nakayama, A. Soeda and M. Murao, arXiv:1911.01645v3
T. Odake, Hlér Kristjánsson, A. Soeda M. Murao, arXiv:2303.09788

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