Self correcting GKP qubits

Harnessing dissipation for error correction, known as dissipative error correction (DEC), offers an alternative approach to quantum computing that may resolve important scalability challenges of conventional approaches, such as, e.g., transmon-based surface codes. Rather than readout/control, DEC leverages the laws of thermodynamics for removal of noise induced entropy, thereby reducing, or eliminating, the need for overhead qubits and monitoring/control. Despite its potential, DEC has long remained an elusive goal. Here I show that DEC is realized in a generic class of models based on the GKP encoding, which can be naturally realized in circuit-QED devices. The GKP encoding encodes a qubit in the Fock space of a single bosonic mode, such as a mode in an electromagnetic resonator. I show that coupling the generic class of phase-space local observables (finite-order polynomials of mode quadratures) to thermodynamic baths will cause the system to spontaneously relax into the GKP code subspace. The relaxation generates quantum error correction, by dissipatively removing noise-induced entropy without affecting encoded information. This makes the qubit exponentially long-lived, even in the presence of generic noise. I discuss various routes to experimental realization and estimate expected performances.