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

TL;DR

This paper introduces the $2T$-qutrit, a novel two-mode bosonic quantum code based on the binary tetrahedral group, which offers potential robustness and new algebraic properties for quantum information processing.

Contribution

It presents the first study of a two-mode bosonic qutrit code based on the binary tetrahedral group, expanding the class of bosonic quantum codes with new algebraic and robustness features.

Findings

The $2T$-qutrit encodes information in 24 coherent states linked to the binary tetrahedral group.

The code inherits algebraic properties from the group $2T$, which may enhance robustness.

Initial stabilizers and logical operators for this code are identified.

Abstract

Quantum computers often manipulate physical qubits encoded on two-level quantum systems. Bosonic qubit codes depart from this idea by encoding information in a well-chosen subspace of an infinite-dimensional Fock space. This larger physical space provides a natural protection against experimental 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 resulting $2T$-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.