Decoherence-free quantum information in the presence of dynamical evolution

TL;DR

This paper investigates how to preserve decoherence-free quantum information in systems with complex Hamiltonian dynamics, proposing optimal encodings and analyzing small systems like three and four qubits.

Contribution

It introduces an encoding strategy for decoherence-free quantum information under arbitrary system Hamiltonians, especially in small qubit systems, with practical examples.

Findings

Optimal encoding in the ~(2/9) N excitation subspace.

Protection against arbitrary bath-induced Hamiltonians.

Explicit encoding for four qubits in the two-excitation subspace.

Abstract

We analyze decoherence-free (DF) quantum information in the presence of an arbitrary non-nearest-neighbor bath-induced system Hamiltonian using a Markovian master equation. We show that the most appropriate encoding for N qubits is probably contained within the ~(2/9) N excitation subspace. We give a timescale over which one would expect to apply other methods to correct for the system Hamiltonian. In order to remain applicable to experiment, we then focus on small systems, and present examples of DF quantum information for three and four qubits. We give an encoding for four qubits that, while quantum information remains in the two-excitation subspace, protects against an arbitrary bath-induced system Hamiltonian. Although our results are general to any system of qubits that satisfies our assumptions, throughout the paper we use dipole-coupled qubits as an example physical system.