Quantum state preparation plays a crucial role in several areas of quantum
information science, in applications such as quantum simulation, quantum
metrology and quantum computing. However, typically state preparation requires
resources that scale exponentially with the problem size, due to their
probabilistic nature or otherwise, making studying such models challenging. In
this article, we propose a method to prepare the ground state of the
Affleck-Lieb-Kennedy-Tasaki (AKLT) model deterministically using an
measurement-based imaginary time evolution (MITE) approach. By taking advantage
of the special properties of the AKLT state, we show that it can be prepared
efficiently using the MITE approach. Estimates based on the convergence of a
sequence of local projections, as well as direct evolution of the MITE
algorithm suggest a constant scaling with respect to the number of AKLT sites,
which is an exponential improvement over the naive estimate for convergence. We
show that the procedure is compatible with qubit-based simulators, and show
that using a variational quantum algorithm for circuit recompilation, the
measurement operator required for MITE can be well approximated by a circuit
with a much shallower circuit depth compared with the one obtained using the
default Qiskit method.Comment: 11 pages, 7 figure