Hyperbolic Floquet Quantum Error Correcting Codes

Large-scale universal quantum computation requires protecting quantum information against quantum noise which can be performed using quantum error-correcting codes. Recently, Hastings and Haah [1] introduced a fault-tolerant dynamical subsystem code on a honeycomb lattice using two-qubit check measurements. Despite having zero logical qubits when viewed as a static subsystem code, the sequence of two-qubit measurements protects two dynamical logical qubits. On the other hand, hyperbolic surface codes are known as a generalization of toric code on a negatively curved manifold. Since the genus of such manifolds increases with the system size, it has been demonstrated that these codes possess a constant encoding rate. In this work, we introduce hyperbolic Floquet codes, where two-qubit check operators are measured in a periodic sequence. Using this measurement scheme, first, we show that the number of dynamically protected logical qubits grows with the system size. Next, we numerically demonstrate the existence of a threshold for the error rate of physical qubits that our code can protect against. Finally, we propose a planar version of these codes with open boundary conditions which are experimentally more feasible to be realized using current platforms.

[1] Hastings, M. B., and Jeongwan H., "Dynamically generated logical qubits" Quantum 5 (2021): 564