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Measurement-based feedback control is central in quantum computing andprecise quantum control. Here we realize a fast and flexiblefield-programmable-gate-array-based feedback control in a superconducting Xmonqubit system. The latency of room-temperature electronics is custom optimizedto be as short as 140 ns. Projective measurement of a signal qubit produces afeedback tag to actuate a conditional pulse gate to the qubit. In afeed-forward process, the measurement-based feedback tag is brought to adifferent target qubit for a conditional control. In a two-qubit experiment,the feedback and feed-forward controls are simultaneously actuated inconsecutive steps. A quantum number is then generated by the signal qubit, anda random walk of the target qubit is correspondingly triggered and realized onthe Bloch sphere. Our experiment provides a conceptually simple and intuitivebenchmark for the feedback control in a multi-qubit system. The feedback systemcan be further scaled up for more complex feedback control experiments.

physical review applied

A simultaneous feedback and feed-forward control and its application to  realize a random walk on the Bloch sphere in a superconducting Xmon-qubit  system