The decoherence effect caused by the coupling between the system and the environment undoubtedly leads to the errors in efficient implementations of two (or three) qubit logical gates in quantum information processing. Fortunately, decoherence-free subspace (DFS) introduced can effectively decrease the influence of decoherence effect. In this paper, we propose some schemes for setting up a family of quantum control gates, including controlled-NOT (CNOT), Toffoli, and Fredkin gates for two or three logical qubits by means of cross-Kerr nonlinearities in DFS. These three logical gates require neither complicated quantum computational circuits nor auxiliary photons (or entangled states). The success probabilities of three logical gates are approximate 1 by performing the corresponding classical feed-forward operations based on the different measuring results of the X-homodyne detectors, and their fidelities are robust against the photon loss with the current technology. The proposed logical gates rely on only simple linear-optics elements, available single-qubit operations, and mature measurement methods, making our proposed gates be feasible and efficient in practical applications.

中文翻译：

---

无退相干子空间中基于克尔效应的量子逻辑门

系统与环境耦合引起的退相干效应无疑会导致量子信息处理中两个（或三个）量子位逻辑门的高效实现出现错误。幸运的是，引入的无退相干子空间（DFS）可以有效降低退相干效应的影响。在本文中，我们提出了一些通过 DFS 中的跨克尔非线性建立一系列量子控制门的方案，包括用于两个或三个逻辑量子位的受控非 (CNOT)、Toffoli 和 Fredkin 门。这三个逻辑门既不需要复杂的量子计算电路，也不需要辅助光子（或纠缠态）。根据X零差探测器的不同测量结果执行相应的经典前馈操作，三个逻辑门的成功概率近似为1，并且它们的保真度对于当前技术的光子损失具有鲁棒性。所提出的逻辑门仅依赖于简单的线性光学元件、可用的单量子位操作和成熟的测量方法，使得我们提出的逻辑门在实际应用中可行且高效。