PIRSA:09080001

The quantum adiabatic theorem and eigenpath traversal

Boixo, S. (2009). The quantum adiabatic theorem and eigenpath traversal. Perimeter Institute. https://pirsa.org/09080001

Boixo, Sergio. The quantum adiabatic theorem and eigenpath traversal. Perimeter Institute, Aug. 12, 2009, https://pirsa.org/09080001 

          @misc{ pirsa_PIRSA:09080001,
            doi = {10.48660/09080001},
            url = {https://pirsa.org/09080001},
            author = {Boixo, Sergio},
            keywords = {Quantum Information},
            language = {en},
            title = {The quantum adiabatic theorem and eigenpath traversal},
            publisher = {Perimeter Institute},
            year = {2009},
            month = {aug},
            note = {PIRSA:09080001 see, \url{https://pirsa.org}}
          }

Sergio Boixo Harvard University

DOI 10.48660/09080001
Collection
Talk Type Scientific Series
Subject

Abstract

We review situations under which standard quantum adiabatic conditions fail. We reformulate the problem of adiabatic evolution as the problem of Hamiltonian eigenpath traversal, and give cost bounds in terms of the length of the eigenpath and the minimum energy gap of the Hamiltonians. We introduce a randomized evolution method that can be used to traverse the eigenpath and show that a standard adiabatic condition is recovered. We then describe more efficient methods for the same task and show that their implementation complexity is close to optimal.