Star Code: Experimental Demonstration of Autonomous Error Correction with Two-Qutrits (Part I Theory)

Large-scale future quantum computers will need quantum error correction (QEC) to protect fragile quantum information against decoherence. Autonomous quantum error correction (AQEC) is one hardware-efficient path that avoids feedback control and fast high-fidelity readout. The very small logical qubit (VSLQ) is one of the AQEC proposals requiring only two qutrits and two lossy resonators to protect against the single-photon loss, the dominating source of error [1]. We develop a new protocol, called the star code, that utilizes only two-photon beam-splitting and squeezing processes to preserve a logical qubit. The scheme's simplicity provides the potential for adoption in any linear two-qutrit coupler device. Our simulations indicate significant improvements in logical qubit lifetimes and suppression of dephasing noise. We discuss the design choices for the successful realization of the star code.

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