Multidimensional dark space and its underlying symmetries: towards dissipation-protected qubits

TL;DR

This paper introduces a symmetry-based framework for engineering degenerate dark spaces in quantum systems, enabling decoherence protection and robust quantum information storage inspired by topological states like Laughlin states.

Contribution

It proposes a novel symmetry-driven method to create degenerate dark states in open quantum systems, enhancing decoherence resistance and quantum information protection.

Findings

Constructed a model protocol inspired by fractional quantum Hall effect.

Demonstrated the long-time steady state exhibits topological characteristics.

Showed the approach enables decoherence-protected quantum information storage.

Abstract

Quantum systems are always subject to interactions with an environment, typically resulting in decoherence and distortion of quantum correlations. It has been recently shown that a controlled interaction with the environment may actually help to create a state, dubbed as {\em ``dark''}, which is immune to decoherence. To encode quantum information in the dark states, they need to span a space with a dimensionality larger than one, so different orthogonal states act as a computational basis. We devise a symmetry-based conceptual framework to engineer such degenerate dark spaces (DDS), protected from decoherence by the environment. We illustrate this construction with a model protocol, inspired by the fractional quantum Hall effect, where the DDS basis is isomorphic to a set of degenerate Laughlin states. The long-time steady state of our driven-dissipative model exhibits thus all the characteristics of degenerate vacua of a unitary topological system. This approach offers new possibilities for storing, protecting and manipulating quantum information in open systems.