Quantify the Non-Markovian Process with Intermediate Projections in a Superconducting Processor

  1. Liang Xiang,
  2. Zhiwen Zong,
  3. Ze Zhan,
  4. Ying Fei,
  5. Chongxin Run,
  6. Yaozu Wu,
  7. Wenyan Jin,
  8. Cong Xiao,
  9. Zhilong Jia,
  10. Peng Duan,
  11. Jianlan Wu,
  12. Yi Yin,
  13. and Guoping Guo
The physical system is commonly considered memoryless to simplify its dynamics, which is called a Markov assumption. However, memory effect is a fundamental phenomenon in the universe.
In the quantum regime, this effect is roughly attributed to the correlated noise. With quantum measurements often collapsing the quantum state, it is hard to characterize non-Markovianity of quantum dynamics. Based on the recently developed framework by Pollock et al., we design a 2-step quantum process, where one qubit is the system and another ancilla serves as its environment. In a superconducting processor, the restricted quantum process tensor is determined using a set of sequential projective measurements, and the result is then used to predict the output state of the process. When the environment has memory, we have achieved very high fidelity in predicting the final state of the system (99.86%±1.1‰). We further take a closer look at the cause of the memory effect and quantify the non-Markovianity of the quantum process conditioned on the historical operations.

Optimization of Controlled-Z Gate with Data-Driven Gradient Ascent Pulse Engineering in a Superconducting Qubit System

  1. Zhiwen Zong,
  2. Zhenhai Sun,
  3. Zhangjingzi Dong,
  4. Chongxin Run,
  5. Liang Xiang,
  6. Ze Zhan,
  7. Qianlong Wang,
  8. Ying Fei,
  9. Yaozu Wu,
  10. Wenyan Jin,
  11. Cong Xiao,
  12. Zhilong Jia,
  13. Peng Duan,
  14. Jianlan Wu,
  15. Yi Yin,
  16. and Guoping Guo
The experimental optimization of a two-qubit controlled-Z (CZ) gate is realized following two different data-driven gradient ascent pulse engineering (GRAPE) protocols in the aim of
optimizing the gate operator and the output quantum state, respectively. For both GRAPE protocols, the key computation of gradients utilizes mixed information of the input Z-control pulse and the experimental measurement. With an imperfect initial pulse in a flattop waveform, our experimental implementation shows that the CZ gate is quickly improved and the gate fidelities subject to the two optimized pulses are around 99%. Our experimental study confirms the applicability of the data-driven GRAPE protocols in the problem of the gate optimization.

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.