PIRSA:19080087

Coherence in logical quantum channels

Iverson, J. (2019). Coherence in logical quantum channels. Perimeter Institute. https://pirsa.org/19080087

Iverson, Joseph. Coherence in logical quantum channels. Perimeter Institute, Aug. 28, 2019, https://pirsa.org/19080087 

          @misc{ pirsa_PIRSA:19080087,
            doi = {10.48660/19080087},
            url = {https://pirsa.org/19080087},
            author = {Iverson, Joseph},
            keywords = {Other},
            language = {en},
            title = {Coherence in logical quantum channels},
            publisher = {Perimeter Institute},
            year = {2019},
            month = {aug},
            note = {PIRSA:19080087 see, \url{https://pirsa.org}}
          }

Joseph Iverson

California Institute of Technology

Talk number
PIRSA:19080087
Collection
Talk Type
Subject
Abstract

In quantum error correcting codes, there is a distinction
between coherent and incoherent noise. Coherent noise can cause the
average infidelity to accumulate quadratically when a fixed channel is
applied many times in succession, rather than linearly as in the case
of incoherent noise. I will present a proof that unitary single qubit
noise in the 2D toric code with minimum weight decoding is mapped to
less coherent logical noise, and as the code size grows, the coherence
of the logical noise channel is suppressed. In the process, I will
describe how to characterize the coherence of noise using either the
growth of infidelity or the relation between the diamond distance from
identity and the average infidelity. I will explain how coherence in
the noise on physical qubits is transformed by error correction in
stabilizer codes. Then, I will sketch the proof that coherence is
suppressed for the 2D toric code. The result holds even when the
single qubit unitary rotation are allowed to have arbitrary directions
and angles, so long as the angles are below a threshold, and even when
the rotations are correlated. Joint work with John Preskill.