Passive correction of quantum logical errors in a driven, dissipative system: A blueprint for an analog quantum code fabric

A physical realization of self-correcting quantum code would be profoundly useful for constructing a quantum computer. In this theoretical work, we provide a partial solution to major challenges preventing self-correcting quantum code from being engineered in realistic devices. We consider a variant of Kitaev's toric code coupled to propagating bosons, which induce a ranged interaction between anyonic defects. By coupling the primary quantum system to an engineered dissipation source through resonant energy transfer, we demonstrate a "rate barrier" which leads to a potentially enormous increase in the system's quantum-state lifetime through purely passive quantum error correction, even when coupled to an infinite-temperature bath. While our mechanism is not scalable to infinitely large systems, the maximum effective size can be very large, and it is fully compatible with active error-correction schemes. Our model uses only on-site and nearest-neighbor interactions and could be implemented in superconducting qubits. We sketch one such implementation at the end of this work.