  Quantum state preparation in high-dimensional systems is an essential
requirement for many quantum-technology applications. The engineering of an
arbitrary quantum state is, however, typically strongly dependent on the
experimental platform chosen for implementation, and a general framework is
still missing. Here we show that coined quantum walks on a line, which
represent a framework general enough to encompass a variety of different
platforms, can be used for quantum state engineering of arbitrary
superpositions of the walker's sites. We achieve this goal by identifying a set
of conditions that fully characterize the reachable states in the space
comprising walker and coin, and providing a method to efficiently compute the
corresponding set of coin parameters. We assess the feasibility of our proposal
by identifying a linear optics experiment based on photonic orbital angular
momentum technology.
