Hardware efficient autonomous error correction protocol (Part I)*

Quantum error correction (QEC) would be indispensable when scaling up qubits for building a full-fledged quantum computer. Autonomous quantum error correction (AQEC) is a hardware-efficient way to realize QEC without fast digital feedback control. The Very Small Logical Qubit (VSLQ) is one of the AQEC protocols which requires two qutrits and two lossy resonators for protection against relaxation errors [1]. We propose a new scheme to implement the VSLQ Hamiltonian, which we call the star code, that requires only two-photon processes. The star code can be implemented using any linear coupler that can parametrically drive qutrit-qutrit red and blue sidebands, making the code more flexible and easier to realize than the original design. Our simulations show a significant improvement in logical qubit lifetimes and suppression of dephasing noise. We also discuss other constraints that must be addressed while designing the device for successful implementation.

[1] Kapit et al., Phys. Rev. Lett. 116, 150501