Semidefinite Programming (SDP) is a work horse of computational quantum information theory (QIT). The optimization problems that are typically encountered in QIT have constraints that are formulated in terms of Pauli matrices. The aim of this project is to develop a computational method to symmetry-reduce such Pauli-constrained SDPs, making existing solvers for such cases vastly more efficient.
Reference: https://arxiv.org/abs/1608.02090
Many interesting objects in quantum information come in the form of highly structured matrices. Examples are absolutely maximally entangled states, mutually unbiased bases, and stabilizer quantum codes. The aim of this project is to develop a reinforcement learning algorithm for finding such type of objects across scales.
Reference: https://www.nature.com/articles/s41586-022-05172-4
The Terwilliger algebra can be used to block-diagonalizes the n-qubit space of permutation symmetric matrices, satisfying \pi A \pi^{-1} = A for all permutations \pi of the symmetric group S_n. In analogy to determinant and immanant inequalities, the aim of this project is to find inequalities for positive semidefinite matrices that relate different subspaces.
Reference: https://arxiv.org/abs/2103.04317