Long-lived topological time-crystalline order on a quantum processor

  1. Liang Xiang,
  2. Wenjie Jiang,
  3. Zehang Bao,
  4. Zixuan Song,
  5. Shibo Xu,
  6. Ke Wang,
  7. Jiachen Chen,
  8. Feitong Jin,
  9. Xuhao Zhu,
  10. Zitian Zhu,
  11. Fanhao Shen,
  12. Ning Wang,
  13. Chuanyu Zhang,
  14. Yaozu Wu,
  15. Yiren Zou,
  16. Jiarun Zhong,
  17. Zhengyi Cui,
  18. Aosai Zhang,
  19. Ziqi Tan,
  20. Tingting Li,
  21. Yu Gao,
  22. Jinfeng Deng,
  23. Xu Zhang,
  24. Hang Dong,
  25. Pengfei Zhang,
  26. Si Jiang,
  27. Weikang Li,
  28. Zhide Lu,
  29. Zheng-Zhi Sun,
  30. Hekang Li,
  31. Zhen Wang,
  32. Chao Song,
  33. Qiujiang Guo,
  34. Fangli Liu,
  35. Zhe-Xuan Gong,
  36. Alexey V. Gorshkov,
  37. Norman Y. Yao,
  38. Thomas Iadecola,
  39. Francisco Machado,
  40. H. Wang,
  41. and Dong-Ling Deng
Topologically ordered phases of matter elude Landau’s symmetry-breaking theory, featuring a variety of intriguing properties such as long-range entanglement and intrinsic robustness
against local perturbations. Their extension to periodically driven systems gives rise to exotic new phenomena that are forbidden in thermal equilibrium. Here, we report the observation of signatures of such a phenomenon — a prethermal topologically ordered time crystal — with programmable superconducting qubits arranged on a square lattice. By periodically driving the superconducting qubits with a surface-code Hamiltonian, we observe discrete time-translation symmetry breaking dynamics that is only manifested in the subharmonic temporal response of nonlocal logical operators. We further connect the observed dynamics to the underlying topological order by measuring a nonzero topological entanglement entropy and studying its subsequent dynamics. Our results demonstrate the potential to explore exotic topologically ordered nonequilibrium phases of matter with noisy intermediate-scale quantum processors.

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.