  Both discrete and continuous systems can be used to encode quantum
information. Most quantum computation schemes propose encoding qubits in
two-level systems, such as a two-level atom or an electron spin. Others exploit
the use of an infinite-dimensional system, such as a harmonic oscillator. In
"Encoding a qubit in an oscillator" [Phys. Rev. A 64 012310 (2001)], Gottesman,
Kitaev, and Preskill (GKP) combined these approaches when they proposed a
fault-tolerant quantum computation scheme in which a qubit is encoded in the
continuous position and momentum degrees of freedom of an oscillator. One
advantage of this scheme is that it can be performed by use of relatively
simple linear optical devices, squeezing, and homodyne detection. However, we
lack a practical method to prepare the initial GKP states. Here we propose the
generation of an approximate GKP state by using superpositions of optical
coherent states (sometimes called "Schr\"odinger cat states"), squeezing,
linear optical devices, and homodyne detection.
