IQC Math and CS seminar featuring Yanglin Hu

Unitary Schur sampling with applications in state tomography

Yanglin Hu | National University of Singapore

The Schur transform is a ubiquitous tool in quantum information theory. In many applications, the full transform is not necessary, as the Young label and the unitary group register of an input m qudit state are sufficient. We formalize this more specialized task as unitary Schur sampling, and we generalize it to mixed Schur-Weyl duality. We further provide a streaming/online algorithm which achieves an exponential reduction in the memory complexity. For input states with limited rank, we also show a reduction in the gate and memory complexities of our streaming algorithm as well as the algorithms for the Schur and mixed Schur transforms.

A natural application of unitary Schur sampling is quantum state tomography, the fundamental physical task of learning a complete classical description of an unknown quantum state. The complexity of this task is commonly characterized by its sample-complexity, the minimal number of samples needed to reach a certain target precision of the description. While the sample complexity of quantum state tomography has been well studied, the memory complexity has not been investigated in depth. In this work, we leverage our streaming algorithm for unitary Schur sampling to obtain a quantum state tomography algorithm which retains sample-optimality but is also memory-efficient.

Location

• Online on Zoom

  • Meeting ID: 922 3130 1548

    Passcode: 182556