Abstract: 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.

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