Measurement-based feedback control is central in quantum computing and precise quantum control. Here we realize a fast and flexible field-programmable-gate-array-based feedback control in a superconducting Xmon qubit system. The latency of room-temperature electronics is custom optimized to be as short as 140 ns. Projective measurement of a signal qubit produces a feedback tag to actuate a conditional pulse gate to the qubit. In a feed-forward process, the measurement-based feedback tag is brought to a different target qubit for a conditional control. In a two-qubit experiment, the feedback and feed-forward controls are simultaneously actuated in consecutive steps. A quantum number is then generated by the signal qubit, and a random walk of the target qubit is correspondingly triggered and realized on the Bloch sphere. Our experiment provides a conceptually simple and intuitive benchmark for the feedback control in a multi-qubit system. The feedback system can be further scaled up for more complex feedback control experiments.

中文翻译：

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同时反馈和前馈控制及其在Transmon超导量子位系统中实现Bloch球上随机游走的应用

基于测量的反馈控制在量子计算和精确量子控制中至关重要。在这里，我们在超导Xmon量子位系统中实现了快速灵活的基于现场可编程门阵列的反馈控制。定制的室温电子设备的等待时间最短可短至140 ns。信号量子比特的投影测量会产生一个反馈标签，以驱动到该量子比特的条件脉冲门。在前馈过程中，将基于测量的反馈标签带到不同的目标qubit进行条件控制。在一个两比特的实验中，反馈和前馈控制在连续的步骤中同时被致动。然后由信号量子比特产生量子数，并且相应地触发并实现目标量子比特的随机游走并在布洛赫球上实现。我们的实验为多量子位系统中的反馈控制提供了概念上简单直观的基准。反馈系统可以进一步扩大规模，以进行更复杂的反馈控制实验。