Abstract
We construct an efficient quantum algorithm to compute the quantum Schur-Weyl transform for any value of the quantum parameter
q∈[0,∞]
. Our algorithm is a
q
-deformation of the Bacon-Chuang-Harrow algorithm, in the sense that it has the same structure and is identically equal when
q=1
. When
q=0
, our algorithm is the unitary realization of the Robinson-Schensted-Knuth (or RSK) algorithm, while when
q=∞
it is the dual RSK algorithm together with phase signs. Thus, we interpret a well-motivated quantum algorithm as a generalization of a well-known classical algorithm.