Passive Quantum Error Correction on Bosonic Qubit at Breakeven

Quantum Error Correction is an important step in making a useful quantum computer. To run complicated algorithms that actually provide an advantage over classical computers it is essential that we not only suppress the errors by reducing the physical qubit imperfections but also correct for the errors as they occur. Within many architectures being used for error correction in quantum computing, the bosonic qubits in superconducting cavities have earned a reputation to be easier to work with since they can be made robust to surface quality and are biased to having error channels that can be corrected efficiently without huge hardware overhead. In our previous paper [1] by engineering a driven dissipative process we autonomously corrected for the single photon loss error on the bosonic qubit. That however had a limitation from ancilla, such as, the spurious excitations during the four-wave mixing (FWM) pumping that resulted in the logical qubit lifetime not reaching breakeven. In this work we improved the scheme to use intrinsically stronger fourth order terms of hybridized cavity-transmon system to do single photon loss correction, i.e., we use the f-state of the transmon in the FWM. This allows us to use a weaker FWM pumps while increasing the speed of correction by twice, thus also reduces the adverse effects of the strong pumping drives on the ancilla. We were able to correct the logical qubit and get a process fidelity lifetime which is 5 times the uncorrected logical qubit and also reach the breakeven point.