The 2T-qutrit, a two-mode bosonic qutrit

Quantum computers often manipulate physical qubits encoded on two -level quantum systems. Bosonic qubit codes depart from this idea by en-coding information in a well-chosen subspace of an infinite-dimensional Fock space. This larger physical space provides a natural protection against exper-imental imperfections and allows bosonic codes to circumvent no-go results that apply to states constrained by a 2-dimensional Hilbert space. A bosonic qubit is usually defined in a single bosonic mode but it makes sense to look for multimode versions that could exhibit better performance.In this work, building on the observation that the cat code lives in the span of coherent states indexed by a finite subgroup of the complex numbers, we consider a two-mode generalisation living in the span of 24 coherent states indexed by the binary tetrahedral group 2T of the quaternions. The result-ing 2T-qutrit naturally inherits the algebraic properties of the group 2T and appears to be quite robust in the low-loss regime. We initiate its study and identify stabilisers as well as some logical operators for this bosonic code.

Automated summary

Quantum computers manipulate physical qubits encoded on two-level quantum systems, but bosonic qubit codes encode information in a well-chosen subspace of an infinite-dimensional Fock space, allowing them to circumvent certain limitations. This study introduces a two-mode generalization of the cat code, which lives in the span of 24 coherent states and demonstrates robustness in the low-loss regime. The properties of the binary tetrahedral group 2T are inherited by the resulting 2T-qutrit.