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 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.

翻译：林德布拉德主方程描述了大量开放量子系统的演化。此类系统的一个关键性质是存在无消相干子空间。来自无消相干子空间的量子态将进行幺正演化。然而，目前尚缺乏系统性且最优的方法来构造无消相干子空间。本文针对服从林德布拉德主方程的开放量子系统，开发了构造无消相干稳定子码的工具。这一成果是通过将稳定子形式主义扩展到超越经典泡利误差算子群结构而实现的。我们进一步展示了如何将无消相干稳定子码应用于量子计量学，从而以低计算复杂度实现海森堡极限标度。