Coherent control of quantum states is at the heart of implementing solid-state quantum processors and testing quantum mechanics at the macroscopic level. Despite significant progress made in recent years in controlling single- and bi-partite quantum systems, coherent control of quantum wave function in multipartite systems involving artificial solid-state qubits has been hampered due to the relatively short decoherence time and lack of precise control methods. Here we report the creation and coherent manipulation of quantum states in a tripartite quantum system, which is formed by a superconducting qubit coupled to two microscopic two-level systems (TLSs). The avoided crossings in the system's energy-level spectrum due to the qubit–TLS interaction act as tunable quantum beam splitters of wave functions. Our result shows that the Landau–Zener–Stückelberg interference has great potential in precise control of the quantum states in the tripartite system.

No abstract

Berry curvature is an imaginary component of the quantum geometric tensor (QGT) and is well studied in many branches of modern physics; however, the quantum metric as a real component of the QGT is less explored. Here, by using tunable superconducting circuits, we experimentally demonstrate two methods to directly measure the quantum metric tensor for characterizing the geometry and topology of underlying quantum states in parameter space. The first method is to probe the transition probability after a sudden quench, and the second one is to detect the excitation rate under weak periodic driving. Furthermore, based on quantum-metric and Berry-curvature measurements, we explore a topological phase transition in a simulated time-reversal-symmetric system, which is characterized by the Euler characteristic number instead of the Chern number. The work opens up a unique approach to explore the topology of quantum states with the QGT.