Quantum many-body scar states are highly excited eigenstates of many-body
systems that exhibit atypical entanglement and correlation properties relative
to typical eigenstates at the same energy density. Scar states also give rise
to infinitely long-lived coherent dynamics when the system is prepared in a
special initial state having finite overlap with them. Many models with exact
scar states have been constructed, but the fate of scarred eigenstates and
dynamics when these models are perturbed is difficult to study with classical
computational techniques. In this work, we propose state preparation protocols
that enable the use of quantum computers to study this question. We present
protocols both for individual scar states in a particular model, as well as
superpositions of them that give rise to coherent dynamics. For superpositions
of scar states, we present both a system-size-linear depth unitary and a
finite-depth nonunitary state preparation protocol, the latter of which uses
measurement and postselection to reduce the circuit depth. For individual
scarred eigenstates, we formulate an exact state preparation approach based on
matrix product states that yields quasipolynomial-depth circuits, as well as a
variational approach with a polynomial-depth ansatz circuit. We also provide
proof of principle state-preparation demonstrations on superconducting quantum
hardware.Comment: 20 Pages, 15 Figures, 2 Tables. V2: corrected typo