Implementing quantum error correction has been difficult in practice. Techniques from engineering, computer science, coding theory, experimental and theoretical physics have been blended together to tackle this problem. Traditionally, quantum error correcting codes mostly focus on dealing with phenomenological Pauli errors primarily due to their theoretical convenience. But this approach neglects physical types of noise, which are more realistically modelled
with physically motivated noise models. This work focuses on a specific encoding in quantum computing called the Gottesman-Kitaev Preskill (GKP) codes. Firstly we study the basic properties and quantum estimation capabilities of a closely related state that is symmetric in phase space called the grid sensor state, motivating
the GKP code as a good candidate for physical qubit level error correction in quantum optics. The grid codes aim to correct for errors before they build up to become Pauli errors. Then, we propose a quantum error correction protocol for continuous-variable finite-energy, approximate GKP states undergoing small Gaussian random displacement errors, based on the scheme of
Glancy and Knill [Phys. Rev. A 73, 012325 (2006)]. We show that combining multiple rounds of error-syndrome extraction with Bayesian estimation offers enhanced protection of GKP-encoded qubits over comparible single-round approaches. Furthermore, we show that the
expected total displacement error incurred in multiple rounds of error followed by syndrome
extraction is bounded by 2√π. Finally, we show that by recompiling the syndrome-extraction circuits, all the squeezing operations can be subsumed into auxiliary state preparation, reducing them to beamsplitter transformations and quadrature measurements.Open Acces
