Boson-Assisted Quantum Error-Correcting Codes*

Quantum error-correcting codes (QECC), which detect and correct errors that occur during quantum computations, are a crucial avenue for scaling up quantum computing. Originally, these codes encoded information using spin-½ physical qubits, but they were later extended to apply to bosonic systems as well [1-2]. In this study, we present a hybrid QECC that leverages both spin and bosonic degrees of freedom in systems combining both spins and bosons. We investigate the application of these codes in trapped-ion quantum processors and discuss their fault-tolerant implementation. 

[1] R. Calderbank and P. Shor (1996). "Good quantum error-correcting codes exist". Physical Review A. 54 (2): 1098-1105; P. W. Shor, "Fault-tolerant quantum computation," Proceedings of 37th Conference on Foundations of Computer Science, Burlington, VT, USA, 1996, pp. 56-65.

[2] D. Gottesman, A. Kitaev, and J. Preskill, “Encoding a qubit in an oscillator”, Physical Review A 64, (2001).