Symmetry and decoherence-free subspaces in quantum neural networks

TL;DR

This paper investigates how symmetry in quantum dot arrays can lead to decoherence-free subspaces, showing that symmetric states can remain unaffected by environmental interactions, which is promising for quantum information stability.

Contribution

It demonstrates that symmetric states in quantum dot arrays can form decoherence-free subspaces, providing insights into preserving quantum coherence in multi-qubit systems.

Findings

Symmetric states in two-qubit systems lead to decoherence-free subspaces.

In three-qubit systems, symmetric quartet states also exhibit decoherence-free behavior.

Numerical solutions of the von Neumann equation reveal the role of symmetry in quantum state evolution.

Abstract

Evolution of quantum states of array of quantum dots is analyzed by means of numerical solution of the von Neumann equation. For two qubit system with dipole-dipole interaction and common phonon bath the evolution of the symmetric state $\frac{\uparrow\downarrow+\downarrow\uparrow}{\sqrt{2}}$ leads to the mixture of the triplet states, leaving the singlet decoupled. For three qubit system ($D_{1/2}^{\otimes3}=D_{3/2}+2D_{1/2}$) with common phonon bath we observed similar effects within the quartet state $D_{3/2}$ if all qubits were symmetrically connected.