Viewing computational linguistics from the length across linear algebra and linear structure Quantum algorithms and the necessary infra were being developed; and in the 2010s programmable quantum computers became showing up Quantum is done over the complexes, which makes the normal linguistics done with the reals more powerful. want to infer the probability distribution of words based on their letters Linearity breaks down: letter combinations in not commutative; and P(letter C) + P(letter A) != P(letters CA) instead of encoding letters as one-hot vectors; we encode these letters with matrices: adds more dimensions immediate benefits: noncommutivity of matricies is a PLUS words is just the composed results into another 2x2 matricies then, to map into probability distrubtion, we map the matrix into a partial trace things create bounds from the problem: letters improve upon optimization scheme in a quantum rhelm implement this scheme on a quantum computer: https://arxiv.org/pdf/1710.10248.pdf task: NTJ reading; come up with the needed novelty