  The Gottesman-Kitaev-Preskill encoding of a qubit in a harmonic oscillator is
a promising building block towards fault-tolerant quantum computation.
Recently, this encoding was experimentally demonstrated for the first time in
trapped-ion and superconducting circuit systems. However, these systems lack
some of the Gaussian operations which are critical to efficiently manipulate
the encoded qubits. In particular, homodyne detection, which is the preferred
method for readout of the encoded qubit, is not readily available, heavily
limiting the readout fidelity. Here, we present an alternative read-out
strategy designed for qubit-coupled systems. Our method can improve the readout
fidelity with several orders of magnitude for such systems and, surprisingly,
even surpass the fidelity of homodyne detection in the low squeezing regime.
