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/2508.01470, 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
Quantum codes are an indispensable component for quantum computers. The aim of this project to derive bounds on entanglement-assisted quantum codes through the theory of quantum weight enumerators.
Reference: https://arxiv.org/abs/1708.06298, https://arxiv.org/abs/2206.13040
Multi-qubit states show an intricate geometry. For a one-qubit system, the Bloch sphere characterizes the state space, but for two or more parties this simple description breaks down. The aim of the project is to derive existing state space inequalities and to find new ones using a moment matrix approach.
Reference: https://arxiv.org/abs/2303.11400
The sharing of multipartite entanglement is constrained by monogamy inequalities. The aim of the project is to derive higher-order purity inequalities from the generalized shadow inequalities, and to apply them to the disprove the existence of certain quantum codes.
Reference: https://arxiv.org/abs/1807.09165, https://arxiv.org/abs/2002.12887
The project aims to understand and characterize the difference between classical and quantum moment inequalities.
Reference: https://arxiv.org/abs/2306.05761
The project aims to formalize a simple proof from quantum information in the Interactive theorem proving system Lean.
Reference: https://www.youtube.com/watch?v=I2zaPoj3G50