  We present an algorithm to design networks that feature pretty good state
transfer (PGST), which is of interest for high-fidelity transfer of information
in quantum computing. Realizations of PGST networks have so far mostly relied
either on very special network geometries or imposed conditions such as
transcendental on-site potentials. However, it was recently shown [Eisenberg et
al., arXiv:1804.01645] that PGST generally arises when a network's eigenvectors
and the factors $P_{\pm}$ of its characteristic polynomial $P$ fulfill certain
conditions, where $P_{\pm}$ correspond to eigenvectors which have $\pm 1$
parity on the input and target sites. We combine this result with the so-called
isospectral reduction of a network to obtain $P_{\pm}$ from a dimensionally
reduced form of the Hamiltonian. Equipped with the knowledge of the factors
$P_{\pm}$, we show how a variety of setups can be equipped with PGST by proper
tuning of $P_{\pm}$. Having demonstrated a method of designing networks
featuring pretty good state transfer of single site excitations, we further
show how the obtained networks can be manipulated such that they allow for
robust storage of qubits. We hereby rely on the concept of compact localized
states, which are eigenstates of a Hamiltonian localized on a small subdomain,
and whose amplitudes completely vanish outside of this domain. Such states are
natural candidates for the storage of quantum information, and we show how
certain Hamiltonians featuring pretty good state transfer of single site
excitation can be equipped with compact localized states such that their
transfer is made possible.
