To realize fault-tolerant quantum computing, it is necessary to store quantum information in logical qubits with error correction functions, realized by distributing a logical state among multiple physical qubits or by encoding it in the Hilbert space of a high-dimensional system. Quantum gate operations between these error-correctable logical qubits, which are essential for implementation of any practical quantum computational task, have not been experimentally demonstrated yet. Here we demonstrate a geometric method for realizing controlled-phase gates between two logical qubits encoded in photonic fields stored in cavities. The gates are realized by dispersively coupling an ancillary superconducting qubit to these cavities and driving it to make a cyclic evolution depending on the joint photonic state of the cavities, which produces a conditional geometric phase. We first realize phase gates for photonic qubits with the logical basis states encoded in two quasiorthogonal coherent states, which have important implications for continuous-variable-based quantum computation. Then we use this geometric method to implement a controlled-phase gate between two binomially encoded logical qubits, which have an error-correctable function.

中文翻译：

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演示两个可纠错光子量子位之间的相控门

为了实现容错量子计算，必须将具有量子纠错功能的量子信息存储在逻辑纠错码中，该纠错功能是通过在多个物理纠错码之间分配逻辑状态或在高维系统的希尔伯特空间中对其进行编码来实现的。这些纠错逻辑量子位之间的量子门操作，对于任何实际的量子计算任务的实现都是必不可少的，尚未通过实验证明。在这里，我们演示了一种几何方法，用于实现在存储在腔中的光子场中编码的两个逻辑量子位之间的控制相门。这些门是通过将辅助超导量子比特分散耦合到这些腔体并根据腔体的联合光子状态驱动其进行循环演化来实现的，产生条件几何相位。我们首先实现具有两个基本正交相干态编码的逻辑基态的光子量子位的相位门，这对基于连续变量的量子计算具有重要意义。然后，我们使用这种几何方法来实现两个二项式编码逻辑量子位之间的控制相位门，这些逻辑量子位具有纠错功能。