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

TL;DR

This paper introduces a method to encode a logical qubit in an ensemble of V-symmetrical qutrits using Schrödinger cat states, achieving robustness against dissipation and certain decay processes, with potential physical implementations.

Contribution

It proposes a novel logical qubit encoding in qutrit ensembles with engineered dark states that are immune to specific decoherence mechanisms.

Findings

Logical qubit states are stationary and parameter-independent.

States are immune to single qutrit decay and certain collective decay processes.

Analytical study of two-qutrit system shows immunity to inhomogeneous broadening and dephasing.

Abstract

We propose using even and odd Sch\"odinger 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 and 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 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 odd one is vulnerable. Nevertheless, in the presence of these interactions one can also define another odd state with mixed permutation symmetry that is immune to both inhomogeneous broadening and local correlated dephasing. We suggest that these results can be extrapolated to an arbitrary number of qutrits. 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). In principle this physical system can be implemented by means of two coplanar waveguide resonators, a SQUID parametrically coupling them, and a cloud of alkali atoms close to one of the resonators.