We present efficient quantum circuits that implement high-dimensional unitary irreducible representations (irreps) of SU(n), where n>=2 is constant. For dimension N and error ?, the number of quantum gates in our circuits is polynomial in log(N) and log(1/?). Our construction relies on the Jordan-Schwinger representation, which allows us to realize ... more >>>

We present a new primitive for quantum algorithms that implements a discrete Hermite transform efficiently, in time that depends logarithmically in both the dimension and the inverse of the allowable error. This transform, which maps basis states to states whose amplitudes are proportional to the Hermite functions, can be interpreted ... more >>>