  The Gottesman-Kitaev-Preskill (GKP) encoding of a qubit within an oscillator
provides a number of advantages when used in a fault-tolerant architecture for
quantum computing, most notably that Gaussian operations suffice to implement
all single- and two-qubit Clifford gates. The main drawback of the encoding is
that the logical states themselves are challenging to produce. Here we present
a method for generating optical GKP-encoded qubits by coupling an atomic
ensemble to a squeezed state of light. Particular outcomes of a subsequent spin
measurement of the ensemble herald successful generation of the resource state
in the optical mode. We analyze the method in terms of the resources required
(total spin and amount of squeezing) and the probability of success. We propose
a physical implementation using a Faraday-based quantum non-demolition
interaction.

Quantum Physics