Preparing exact eigenstates of the open XXZ chain on a quantum computer

The open spin-1/2 XXZ spin chain with diagonal boundary magnetic fields is the paradigmatic example of a quantum integrable model conditions. We formulate algorithm for preparing Bethe states this model, corresponding to real solutions equations. probabilistic, success probability that decreases number down spins. For state $L$ spins $M$ spins, which contains total $\binom{L}{M}\, 2^{M}\, M!$ terms, requires $L+M^2+2M$ qubits.