Performing SU(d) operations and rudimentary algorithms in a superconducting transmon qudit for d=3 and d=4

  1. Pei Liu,
  2. Ruixia Wang,
  3. Jing-Ning Zhang,
  4. Yingshan Zhang,
  5. Xiaoxia Cai,
  6. Huikai Xu,
  7. Zhiyuan Li,
  8. Jiaxiu Han,
  9. Xuegang Li,
  10. Guangming Xue,
  11. Weiyang Liu,
  12. Li You,
  13. Yirong Jin,
  14. and Haifeng Yu
Quantum computation architecture based on d-level systems, or qudits, has attracted considerable attention recently due to their enlarged Hilbert space. Extensive theoretical and experimental studies have addressed aspects of algorithms and benchmarking techniques for qudit-based quantum computation and quantum information processing. Here, we report a physical realization of qudit with upto 4 embedded levels in a superconducting transmon, demonstrating high-fidelity initialization, manipulation, and simultaneous multi-level readout. In addition to constructing SU(d) operations and benchmarking protocols for quantum state tomography, quantum process tomography, and randomized benchmarking etc, we experimentally carry out these operations for d=3 and d=4. Moreover, we perform prototypical quantum algorithms and observe outcomes consistent with expectations. Our work will hopefully stimulate further research interest in developing manipulation protocols and efficient applications for quantum processors with qudits.
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