Quantum state stability against decoherence

Jincheng Zhang

Quantum systems often exhibit complex and unpredictable behavior, particularly concerning quantum entanglement and decoherence. Traditional models frequently fail to capture the nuanced effects of this phenomenon, leading to inaccurate predictions of system evolution and stability. This paper introduces a novel non-linear decoherence modeling framework, designed to address these limitations by explicitly incorporating non-linear interactions within the decoherence process. We propose a dynamic, multi-scale model that utilizes a tensor-based approach to represent quantum states and their evolution, incorporating a self-stabilizing feedback loop to mitigate decoherence. The framework's core mechanism involves characterizing the decoherence process as a complex, non-linear interaction between the quantum system and its environment, where the strength of this interaction is dynamically adjusted based on the system's state. We demonstrate the framework's efficacy through a series of simulations, showing improved predictions of quantum system stability and evolution compared to existing models.

Nima Arkani-hamed A, John E. Sipe

Luis Roa, A. Krügel

We have found, for a specific model of interaction, an expression which allows us to estimate the time scale order of magnitude for which the decoherence instability of a quantum state is onset. We study the stability of the coherence of a pure state for a three level quantum system under the effect of an interaction with a set of boson systems and driven by two Raman classical fields. Evaluating the order of magnitude of the decoherence time scale and assuming the boson systems to be in thermal states, we find for a symmetric V -system a set of three states stable against decoherence and, for a symmetric cascade-system we find a bidimensional subspace whose states are stable against the considered decoherence mechanism.

Piotr Marecki

Francisco Revson F. Pereira, Stefano Mancini, Giuliano G. La Guardia

The Lindblad master equation describes the evolution of a large variety of open quantum systems. An important property of some open quantum systems is the existence of decoherence-free subspaces. A quantum state from a decoherence-free subspace will evolve unitarily. However, there is no procedural and optimal method for constructing a decoherence-free subspace. In this paper, we develop tools for constructing decoherence-free stabilizer codes for open quantum systems governed by the Lindblad master equation. This is done by pursuing an extension of the stabilizer formalism beyond the celebrated group structure of Pauli error operators. We then show how to utilize decoherence-free stabilizer codes in quantum metrology in order to attain the Heisenberg limit scaling with low computational complexity.

Andrea López-Incera