We develop an analytic theory for the recently demonstrated Josephson Junction laser (Science 355, p. 939, 2017). By working in the time-domain representation (rather than the frequency-domain)a single non-linear equation is obtained for the dynamics of the device, which is fully solvable in some regimes of operation. The nonlinear drive is seen to lead to mode-locked output, with a period set by the round-trip time of the resonant cavity.
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 majorchallenges 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 long-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.