Encoding qubits in multimode grid states - Part 2

Bosonic error-correction codes are emerging as an attractive and hardware-efficient alternative to qubit-based encodings. In particular, the Gottesman-Kitaev-Preskill (GKP) grid codes have generated interest due to predicted long logical lifetimes and the fact that Clifford operations can be implemented using Gaussian circuits. Moreover, they have recently been implemented in microwave cavities and in the motion of trapped ions. However, one recurring challenge with practical implementations of bosonic codes, including the GKP code, is that errors in the ancilla used for quantum control of the oscillator modes propagate as logical errors, limiting the information lifetime. In this talk, we show how this limitation can be overcome using multimode GKP codes. First, we will introduce general qubit ancilla-based error-correction circuits to stabilize the code space of multimode grid codes. Then, we show that stabilizing the code space of a two-mode hypercubic code, ancilla errors mostly propagate as correctable errors. Our new error-correction circuits promise the extension of the logical lifetime orders of magnitude beyond the ancilla lifetime.