Random walk on the Bloch sphere realized by a simultaneous feedback and feed-forward control in a superconducting Xmon qubit system

  1. Liang Xiang,
  2. Zhiwen Zong,
  3. Zhenhai Sun,
  4. Ze Zhan,
  5. Ying Fei,
  6. Zhangjingzi Dong,
  7. Chongxin Run,
  8. Zhilong Jia,
  9. Peng Duan,
  10. Jianlan Wu,
  11. Yi Yin,
  12. and Guoping Guo
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 control can also be further explored to study complex stochastic quantum control.
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