Optimal encoding of two dissipative interacting qubits

TL;DR

This paper explores optimal encoding strategies for a logical qubit in a two-qubit system interacting with an Ohmic bath, demonstrating enhanced robustness by exploiting decoherence-free subspaces and numerical methods.

Contribution

It introduces a numerical approach to optimize logical qubit encoding in dissipative two-qubit systems, extending analysis to strong coupling regimes and identifying the most robust encoding strategy.

Findings

Encoding in the direct sum of antiferromagnetic states and DFS offers maximum protection.

Numerical matrix product state methods match perturbative results and handle strong coupling.

Optimal encoding leverages both DFS and antiferromagnetic interactions for improved robustness.

Abstract

We investigate a system of two coupled qubits interacting with an Ohmic bath as a physical model for the implementation of one logical qubit. In this model, the interaction with the other qubit represents unitary noise while the Ohmic bath is responsible for finite temperature. In the presence of a one-dimensional decoherence-free subspace (DFS), we show that, while this is not sufficient to protect a qubit from decoherence, it can be exploited to encode one logical qubit with greater performance than the physical one. We show different possible strategies for the optimal encoding of a logical qubit through a numerical analysis based on matrix product states. This method reproduces faithfully the results of perturbative calculations, but it can be extended to cases of crucial interest for physical implementations, e.g., in the case of strong coupling with the bath. As a result, a logical qubit encoded in the subspace which is the direct sum of the antiferromagnetic states in Bell basis, the DFS and the one in the triplet, is the optimally robust one, as it takes advantage of both the anchoring to the DFS and the protection from the antiferromagnetic interaction. These authors contributed equally to this work, and their names are listed in alphabetical order.