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High-order topological phases of matter refer to the systems of $n$-dimensional bulk with the topology of $m$-th order, exhibiting $(n-m)$-dimensional boundary modes and can be characterized by topological pumping. Here, we experimentally demonstrate two types of second-order topological pumps, forming four 0-dimensional corner localized states on a 4$\times$4 square lattice array of 16 superconducting qubits. The initial ground state of the system for half-filling, as a product of four identical entangled 4-qubit states, is prepared using an adiabatic scheme. During the pumping procedure, we adiabatically modulate the superlattice Bose-Hubbard Hamiltonian by precisely controlling both the hopping strengths and on-site potentials. At the half pumping period, the system evolves to a corner-localized state in a quadrupole configuration. The robustness of the second-order topological pump is also investigated by introducing different on-site disorder. Our work studies the topological properties of high-order topological phases from the dynamical transport picture using superconducting qubits, which would inspire further research on high-order topological phases.

Correlated errors can significantly impact the quantum error correction, which challenges the assumption that errors occur in different qubits independently in both space and time. Superconducting qubits have been found to suffer correlated errors across multiple qubits, which could be attributable to ionizing radiations and cosmic rays. Nevertheless, the direct evidence and a quantitative understanding of this relationship are currently lacking. In this work, we propose to continuously monitor multi-qubit simultaneous charge-parity jumps to detect correlated errors and find that occur more frequently than multi-qubit simultaneous bit flips. Then, we propose to position two cosmic-ray muon detectors directly beneath the sample box in a dilution refrigerator and successfully observe the correlated errors in a superconducting qubit array triggered by muons. By introducing a lead shielding layer on the refrigerator, we also reveal that the majority of other correlated errors are primarily induced by gamma rays. Furthermore, we find the superconducting film with a higher recombination rate of quasiparticles used in the qubits is helpful in reducing the duration of correlated errors. Our results provide experimental evidence of the impact of gamma rays and muons on superconducting quantum computation and offer practical insights into mitigation strategies for quantum error correction. In addition, we observe the average occurrence rate of muon-induced correlated errors in our processor is approximately 0.40 min$^{-1}$cm$^{-2}$, which is comparable to the muon event rate detected by the muon detector with 0.506 min$^{-1}$cm$^{-2}$. This demonstrates the potential applications of superconducting qubit arrays as low-energy threshold sensors in the field of high-energy physics., Comment: 7 pages and 5 figures for the main text, 20 pages and 20 figures for the supplementary materials