Reconquering Bell sampling on qudits: stabilizer learning and testing, quantum pseudorandomness bounds, and more

The recent paper titled 'Reconquering Bell sampling on qudits' marks a significant advancement in quantum computing by successfully generalizing Bell sampling techniques to qudits, which are quantum systems with d-levels (d ≥ 2). Previous attempts to extend Bell sampling to higher dimensions had failed to yield useful information about the quantum states being measured. However, this new approach, which incorporates a novel unitary transformation based on Lagrange's four-square theorem, allows for effective learning and testing of stabilizer states. This breakthrough not only facilitates the learning of stabilizer states in O(n^3) time with O(n) samples but also aids in solving the Hidden Stabiliser Group Problem efficiently. The implications of this work extend to various applications in quantum computing, enhancing the potential for future research and development in the field.