The spin-1/2 Heisenberg quantum spin chain is a paradigmatic model of theoretical physics. We consider the problem of preparing exact eigenstates of this model on a quantum computer. We begin by briefly reviewing the basics of coordinate Bethe ansatz and quantum computing. We then describe an efficient construction of Dicke states, and finally its generalization to Bethe states. The algorithm is explicit, deterministic, and does not use ancillary qubits. 

Rafael obtained his Ph.D. in physics from the University of Chicago in 1982. He held postdoctoral positions at Brandeis University (1982-84) and the University of Washington (1984-1986) before joining the University of Miami, where he is a Professor. His current research interests include quantum integrability and quantum computing.