We propose laser-based methods for the production of nuclear spin hyperpolarized molecules. Following pulsed, coherent excitation from ground-state molecules in a molecular beam to specific rotational $|J\phantom{\rule{0.16em}{0ex}}{m}_{J}\ensuremath{\rangle}$ states, the resulting hyperfine polarization beating produces desirable nuclear spin
mI population distributions and ${m}_{I}\ensuremath{-}{m}_{J}$ correlations at specific later times. At this point, selective dissociation can be used to remove undesired spin states, or a strong magnetic field can be applied, which later can be removed adiabatically to transfer the population-enhanced nuclear spin configurations to the desired nuclear spin state. Finally, the polarization beating is stopped, and the molecules are stored by cryogenic trapping. We show how these methods can be used to produce the long-lived singlet state of
15N2O and ortho
H2O, which have been proposed as magnetic tracers. We discuss how large production rates between 1 and $100 \ensuremath{\mu}\mathrm{mol}$/s with singlet-state populations between 35% and 100% can be achieved.
We generalize the canonical Hopfield model of associative memory, which stores classical states of individual spins, to store entangled quantum states. The construction is based on truncated projector-sum Hamiltonian, and we explicitly consider a special case that stores dimer singlet coverings of a spin-1/2 system. We analyze the stability of the stored memories and find that the capacity -- the number of stable patterns -- scales faster with the system size than one would expect from a naive analogy with the standard Hopfield model, suggesting a possible quantum advantage.