Weak Schur sampling with logarithmic quantum memory

TimeDec 15, 2023, 4pm (Taipei Time)
SpeakerEnrique Cervero Martín
TitleWeak Schur sampling with logarithmic quantum memory
AbstractThe quantum Schur transform maps the computational basis of a system of n qudits onto a Schur basis, which spans the minimal invariant subspaces of the representations of the unitary and the symmetric groups acting on the state space of n qudits. We introduce a new algorithm for the task of weak Schur sampling. Our algorithm efficiently determines both the Young label which indexes the irreducible representations and the multiplicity label of the symmetric group. There are two major advantages of our algorithm for weak Schur sampling  when compared to existing approaches which proceed via quantum Schur transform algorithm or Generalized Phase Estimation algorithm. First, our algorihtm is suitable for streaming applications and second it is exponentially more efficient in its memory usage.  We show that an instance of our weak Schur sampling algorithm on n qudits requires only logarithmically many qudits of memory to implement.
Reference https://arxiv.org/abs/2309.11947
Personal informationEnrique obtained his Master’s degree at the University of Copenhagen under the supervision of Laura Mančinska in 2021 and is now a Ph.D. candidate in mathematics at the Centre for Quantum Technologies, Singapore, supervised by Marco Tomamichel. His research interests lie in the areas of quantum information, cryptography, machine learning and algorithms.