  This survey summarizes several results about quantum computing related to
(mostly static) data structures. First, we describe classical data structures
for the set membership and the predecessor search problems: Perfect Hash tables
for set membership by Fredman, Koml\'{o}s and Szemer\'{e}di and a data
structure by Beame and Fich for predecessor search. We also prove results about
their space complexity (how many bits are required) and time complexity (how
many bits have to be read to answer a query). After that, we turn our attention
to classical data structures with quantum access. In the quantum access model,
data is stored in classical bits, but they can be accessed in a quantum way: We
may read several bits in superposition for unit cost. We give proofs for lower
bounds in this setting that show that the classical data structures from the
first section are, in some sense, asymptotically optimal - even in the quantum
model. In fact, these proofs are simpler and give stronger results than
previous proofs for the classical model of computation. The lower bound for set
membership was proved by Radhakrishnan, Sen and Venkatesh and the result for
the predecessor problem by Sen and Venkatesh. Finally, we examine fully quantum
data structures. Instead of encoding the data in classical bits, we now encode
it in qubits. We allow any unitary operation or measurement in order to answer
queries. We describe one data structure by de Wolf for the set membership
problem and also a general framework using fully quantum data structures in
quantum walks by Jeffery, Kothari and Magniez.
