Error Correction of Beamsplitter-Generated Entangled GKP States

Abstract: To be useful, quantum computers will be required to successfully correct errors occurring at the hardware level. Bosonic codes provide a hardware-efficient option for error correction, but fault-tolerance further requires that the available gate interactions be compatible with the code. A promising bosonic code is the Gottesman-Kitaev-Preskill (GKP) code, for which a linear beamsplitter-like coupling between two bosonic modes is fault-tolerant, making this a key primitive for building larger systems. Here, using two motional modes of a trapped ion, we demonstrate the generation of entangled states of GKP qubits by interfering two qunaught states, which have a grid structure but carry no logical information, on a beamsplitter. We generate all four Bell states with an average fidelity of 69%, and subsequently demonstrate an extension of the entangled state lifetime through the use of quantum error correction. These results complete the set of Gaussian operations required for quantum computing with GKP codes and enable explorations of multi-mode bosonic encodings as well as fundamental tests of information channels.