Recently, the Cloud Quantum Computing Platform Group and the Superconducting Quantum Computing Group of Beijing Academy of Quantum Information Sciences (BAQIS), collaborated with the Institute of Physics, Chinese Academy of Sciences (IOP, CAS), and South China University of Technology (SCUT), among other institutions, experimentally demonstrated high-order topological pumping for the first time, utilizing 16 qubits from a 2D 62-qubit tunable-coupling superconducting quantum processor with a geometry of square lattice. This demonstration exhibited the dynamic properties of higher-order topological phases, laying the foundation for further research into the dynamics of topological pumping and various higher-order topological phases. On October 1, 2024, the corresponding studies were published in Physical Review Letters entitled ‘High-Order Topological Pumping on a Superconducting Quantum Processor’.

Topological phases of matter are an important research direction in condensed matter physics, characterized by the bulk-edge correspondence. Higher-order topological systems exhibit similar properties. In general, high-order topological phases of matter refer to the systems of n-dimensional bulk with the topological of m-th order, exhibiting (n-m)-dimensional edge modes and can be characterized by topological pumping. Although there are various works that reported the simulation of topological phases of matter using other platforms with the development of quantum control technologies, the demonstration of high-order topological pumping quantum simulation remains a challenge. Among other quantum computing systems, the superconducting quantum processor offers the advantages of stability, high scalability, and strong versatility, making it an ideal platform for simulating high-order topological pumping.

Firstly, the Superconducting Quantum Computing Group of BAQIS designed and prepared the high-quality processor integrated with 62 qubits and 105 couplers, forming a 2D square lattice (Figure 1 A1-A2). A subset of 4×4 qubits and 24 couplers are used to simulate the topological properties of high-order topological phases. Subsequently, the research team proposed a scheme for preparing the initial quantum state through an adiabatic evolution approach and then demonstrated the topological pumping experiment with an initial state fidelity of 94.9% (2×2 qubit unit cell, Figure1 B1-B2). Based on different schemes, i.e. the diagonal and non-diagonal transports, the corner localized states clearly appeared at four distinct corners. After applying different types of pulse sequences to 16 qubits and 24 couplers simultaneously, the research team measured all qubits with 6000 single-shot readouts for recording the dynamic evolutions of diagonal topological pump. Starting from an initial state with uniformly distributed occupation, particles are gradually transported along the diagonal direction to the corresponding corners, in which the corner localized states appear (Figure 1C). Another non-diagonal pumping was also shown in Figure 1D. Notably, this pumping process was topologically protected, and the variation of the transported particle number is related to the Chern number. Moreover, the research team investigated a robust plateau on diagonal pumping with on-site potential disorder, which confirmed the robust topological protection of transported particle number (Figure 1E). Theoretically, the Chern number of the system exhibits quantized steps (1 or -1), and experimentally, the change in the number of particles transported by the diagonal pumping scheme reached 0.964, showing a high degree of consistency with the theoretical prediction.

These dynamical behaviors revealed a notable characteristic of higher-order topological phases, namely that a two-dimensional topological phase can give rise to zero-dimensional corner states under second-order topological pumping. The robust plateau protected by topology, as demonstrated by the research team, further validated the topological nature of the constructed experimental system. This word provided a solid experimental foundation for further investigating more intrinsic topological properties of higher-order topological phases, such as entanglement entropy and long-range correlations.

The first authors of this work are Chenglin Deng (PhD from IOP, CAS), Yu Liu (PhD from IOP, CAS), and Yu-Ran Zhang (Professor of SCUT). The corresponding authors are Heng Fan (researcher of IOP, CAS and jointly appointed researcher of BAQIS), Kai Xu (associate researcher of IOP, CAS) and Haifeng Yu (researcher of BAQIS). Additional contributors include Dongning Zheng (researcher of IOP, CAS), Zhongcheng Xiang (deputy chief engineer of  IOP, CAS), Guangming Xue (associate researcher, BQAIS), Xuegang Li (associate researcher, BAQIS), and Kaixuan Huang (assistant researcher, BAQIS), as well as Tao Liu, professor of SCUT, and Jieci Wang, professor at Hunan Normal University. This work was supported by the National Natural Science Foundation of China, the Beijing Natural Science Foundation, the Natural Science Foundation of Guangdong Province, the Innovation Program for Quantum Science and Technology, the Beijing Nova Program, and the Scientific Instrument Developing Project of Chinese Academy of Sciences

Link：http://link.aps.org/supplemental/10.1103/PhysRevLett.133.140402

Figure 1. Quantum processor, initial ground state preparation and experimental results. (A1-A2) A Schematic diagram of a 2D quantum chip with 62 qubits, showing the 16 qubits and 24 couplers used for the simulation. (B1-B2) The density matrix of the quantum state tomography during adiabatic evolution and the variations of fidelity over evolution time. (C) The dynamic results of diagonal pumping. (D) The dynamic results of non-diagonal pumping. (E) The robust plateau protected by topology observed experimentally after applying on-site disorder.