Deterministic Bethe state preparation
Quantum 8, 1510 (2024).
https://doi.org/10.22331/q-2024-10-24-1510
We present an explicit quantum circuit that prepares an arbitrary $U(1)$-eigenstate on a quantum computer, including the exact eigenstates of the spin-$1/2 XXZ$ quantum spin chain with either open or closed boundary conditions. The algorithm is deterministic, does not require ancillary qubits, and does not require QR decompositions. The circuit prepares such an $L$-qubit state with $M$ down-spins using $binom{L}{M}-1$ multi-controlled rotation gates and $2M(L-M)$ CNOT-gates.
“Bethe state preparation”, Simons Center, May 2024: http://scgp.stonybrook.edu/video_portal/video.php?id=6518
“Preparing exact eigenstates on a quantum computer”, Australian Institute of Physics Theoretical Seminar, July 2024:
https://www.aip.org.au/Theoretical-Physics-(TPG)/13382858