  A probabilistic algorithm for preparing Bethe eigenstates of the spin-1/2
Heisenberg spin chain on a quantum computer has recently been found. We derive
an exact formula for the success probability of this algorithm in terms of the
Gaudin determinant, and we study its large-length limit. We demonstrate the
feasibility of computing antiferromagnetic ground-state spin-spin correlation
functions for short chains. However, the success probability decreases
exponentially with the chain length, which precludes the computation of these
correlation functions for chains of moderate length. Some conjectures for
estimates of the Gaudin determinant are noted in an appendix.
