Implementing microelectromechanical system (MEMS) resonators calls for detailed microscopic understanding of the devices, such as energy dissipation channels, spurious modes, and imperfections from microfabrication. Here, we report the nanoscale imaging of a freestanding super-high-frequency (3 – 30 GHz) lateral overtone bulk acoustic resonator with unprecedented spatial resolution and displacement sensitivity. Using transmission-mode microwave impedance microscopy, we have visualized mode profiles of individual overtones and analyzed higher-order transverse spurious modes and anchor loss. The integrated TMIM signals are in good agreement with the stored mechanical energy in the resonator. Quantitative analysis with finite-element modeling shows that the noise floor is equivalent to an in-plane displacement of 10 fm/√Hz at room temperatures, which can be further improved under cryogenic environments. Our work contributes to the design and characterization of MEMS resonators with better performance for telecommunication, sensing, and quantum information science applications.

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We present a holographic quantum simulation algorithm to variationally prepare thermal states of d-dimensional interacting quantum many-body systems, using only enough hardware qubits to represent a (d-1)-dimensional cross-section. This technique implements the thermal state by approximately unraveling the quantum matrix-product density operator (qMPDO) into a stochastic mixture of quantum matrix product states (sto-qMPS). The parameters of the quantum circuits generating the qMPS and of the probability distribution generating the stochastic mixture are determined through a variational optimization procedure. We demonstrate a small-scale proof of principle demonstration of this technique on Quantinuum's trapped-ion quantum processor to simulate thermal properties of correlated spin-chains over a wide temperature range using only a single pair of hardware qubits. Then, through classical simulations, we explore the representational power of two versions of sto-qMPS ansatzes for larger and deeper circuits and establish empirical relationships between the circuit resources and the accuracy of the variational free-energy.

We report the implementation of a dilution refrigerator-based scanning microwave impedance microscope with a base temperature of ∼100 mK. The vibration noise of our apparatus with tuning-fork feedback control is as low as 1 nm. Using this setup, we have demonstrated the imaging of quantum anomalous Hall states in magnetically (Cr and V) doped (Bi, Sb)2Te3 thin films grown on mica substrates. Both the conductive edge modes and topological phase transitions near the coercive fields of Cr- and V-doped layers are visualized in the field-dependent results. Our study establishes the experimental platform for investigating nanoscale quantum phenomena at ultralow temperatures.