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This thesis presents an efficient quantum algorithm and explicit circuits forgenerating eigenstates of arbitrary SU(2) and SU(3) representations. Theseinclude a wide variety of highly entangled states. The algorithm uses Schurtransform that rotates the input computational basis states to the output Schurbasis states with resources polynomial in number of qudits n. Using the factthat quantum logic is reversible, we accomplish the desired result using theinverse Schur transform. The algorithm can be easily generalized to anyarbitrary higher groups.

An Efficient Quantum Algorithm and Circuit to Generate Eigenstates of SU(2) and SU(3) Representations