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In large-scale quantum networks, distributing the multi-particle entangled state among selected nodes is crucial for realizing long-distance and complicated quantum communication. Quantum repeaters provides an efficient method to generate entanglement between distant nodes. However, it is difficult to extend quantum repeater protocols to high-dimensional quantum states in existing experiments. Here we develop a series of scheme for generating high-dimensional entangled states via quantum walks with multiple coins or single coin by quantum repeaters, including $d$-dimensional Bell states, multi-particle high dimensional GHZ states etc.. Furthermore, we give entanglement distribution schemes on arbitrary quantum networks according to the above theoretical framework. As applications, we construct quantum fractal networks and multiparty quantum secret sharing protocols based on $d$-dimensional GHZ states. In the end, we give the experiment implementing of various 2-party or 3-party entanglement generation schemes based on repeaters. Our work can serve as a building block for constructing larger and more complex quantum networks.

Simulating response properties of molecules is crucial for interpreting experimental spectroscopies and accelerating materials design. However, it remains a long-standing computational challenge for electronic structure methods on classical computers. While quantum computers hold the promise to solve this problem more efficiently in the long run, existing quantum algorithms requiring deep quantum circuits are infeasible for near-term noisy quantum processors. Here, we introduce a pragmatic variational quantum response (VQR) algorithm for response properties, which circumvents the need for deep quantum circuits. Using this algorithm, we report the first simulation of linear response properties of molecules including dynamic polarizabilities and absorption spectra on a superconducting quantum processor. Our results indicate that a large class of important dynamical properties such as Green's functions are within the reach of near-term quantum hardware using this algorithm in combination with suitable error mitigation techniques., Comment: 22 pages, 4 figures

Utilizing quantum computer to investigate quantum chemistry is an important research field nowadays. In addition to the ground-state problems that have been widely studied, the determination of excited-states plays a crucial role in the prediction and modeling of chemical reactions and other physical processes. Here, we propose a non-variational full circuit-based quantum algorithm for obtaining the excited-state spectrum of a quantum chemistry Hamiltonian. Compared with previous classical-quantum hybrid variational algorithms, our method eliminates the classical optimization process, reduces the resource cost caused by the interaction between different systems, and achieves faster convergence rate and stronger robustness against noise without barren plateau. The parameter updating for determining the next energy-level is naturally dependent on the energy measurement outputs of the previous energy-level and can be realized by only modifying the state preparation process of ancillary system, introducing little additional resource overhead. Numerical simulations of the algorithm with hydrogen, LiH, H2O and NH3 molecules are presented. Furthermore, we offer an experimental demonstration of the algorithm on a superconducting quantum computing platform, and the results show a good agreement with theoretical expectations. The algorithm can be widely applied to various Hamiltonian spectrum determination problems on the fault-tolerant quantum computers., Comment: accepted for publication in Quantum