Improved readout of qubit-coupled Gottesman-Kitaev-Preskill states

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.