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Highly robust logical qubit encoding in an ensemble of V-symmetrical qutrits

Luis Octavio Castaños-Cervantes1,2,*, Manuel Calixto3,4,†, and Julio Guerrero4,5,‡

  • *Contact author: luis.castanos@tec.mx
  • †Contact author: calixto@ugr.es
  • ‡Contact author: jguerrer@ujaen.es
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Phys. Rev. Research 8, 033169 – Published 10 August, 2026

DOI: https://doi.org/10.1103/9g4j-7r69

Abstract

We propose using even and odd Schrödinger cat states formed from coherent states of U(3) of an ensemble of qutrits with a symmetrical V configuration (a qubit-disguised qutrit) to encode a logical qubit. These carefully engineered logical qubit states are parameter-independent stationary states of the effective master equation governing the evolution of the ensemble and, consequently, constitute dark states that are invulnerable to dissipation and correlated collective dephasing. In particular, the logical qubit states are immune to single-qutrit decay (the analogous of single-photon loss process for qutrits) and simultaneous decay and driving of two qutrits (the analogous of two-photon loss and driving processes for qutrits). In addition, we show how to implement the single-qubit quantum NOT gate and the Hadamard gate followed by either the phase gate or the phase and Z gates. We study analytically the case of two qutrits and conclude that the logical qubit states exhibit parity-sensitive inhomogeneous broadening and local correlated dephasing: The even logical state is completely immune to these processes, while the odd one is vulnerable. Nevertheless, in the presence of these interactions one can also define two odd states with mixed permutation symmetry (with fully distinguishable qutrits) that are immune to both inhomogeneous broadening and local correlated dephasing. We show that these results can be extended to an arbitrary number of qutrits. We also present how the logical qubit states can be defined for qutrits with an asymmetrical V configuration and that they preserve their robustness properties. The effective master equation is deduced from a physical system composed of two parametrically coupled cavities with one of them interacting dispersively with an ensemble of three-level atoms (the qutrits). A proof that the logical qubit is also part of a stationary solution of the physical system under the considered approximations is given. In principle, this physical system can be implemented by means of two coplanar waveguide resonators, a superconducting quantum interference device parametrically coupling them, and a cloud of alkali atoms close to one of the resonators.

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Phys. Rev. Research 8, 033169– Published 10 August, 2026
  • Received 17 December 2025
  • Accepted 13 July 2026
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