Controllable non-Hermitian topology in a dynamically protected cat qubit

TL;DR

This paper explores the non-Hermitian spectral topology of dissipatively stabilized cat qubits, revealing controllable higher-order exceptional points and a topological invariant, with implications for quantum information processing.

Contribution

It uncovers controllable higher-order Liouvillian exceptional points in a cat-qubit system, linking dissipative stabilization, phase control, and non-Hermitian topology.

Findings

Identification of second- and third-order Liouvillian exceptional points (LEP2s and LEP3s).

Demonstration that the phase of two-photon drive controls the exceptional points.

Master-equation simulations show high-fidelity confinement to the logical subspace.

Abstract

Dissipatively stabilized cat qubits are promising for fault-tolerant quantum information processing, yet their non-Hermitian (NH) spectral topology remains largely unexplored. We uncover rich Liouvillian exceptional structures in a cat-qubit mode stabilized by two-photon drive (TPD) and engineered two-photon loss, in the presence of single-photon drive (SPD) and single-photon loss. In the parameter space spanned by SPD strength and detuning, we identify both second- and third-order Liouvillian exceptional points (LEP2s and LEP3s). Remarkably, we show that the phase $\theta$ of TPD provides coherent control over these exceptional points: the LEP3 diverges and vanishes at $\theta=\pi/2$, while remaining stable and tunable elsewhere. We introduce a topological invariant based on the winding number of a resultant vector, which robustly identifies LEP3s with unit topological charge. Full master-equation simulations confirm that the system dynamics remains confined to the logical subspace with near-unity fidelity. Our results bridge dissipative stabilization, phase-coherent control, and NH topology, demonstrating controllable higher-order LEPs in open quantum systems.