Hyperbolic geometry hosts a plethora of exotic quantum phenomena ranging from holographic duality to novel topological phases. However, investigating these effects experimentally remainschallenging due to the Euclidean constraints of natural crystalline materials. While recent synthetic lattices have achieved static realizations, they often lack the dynamical tunability required to explore the full geometric landscape. Here, we overcome these limitations by implementing a quantum simulation of hyperbolic geometry within the parameter space of a superconducting quantum circuit. We construct a Hyperbolically Driven Quantum System (HDQS) by mapping the hyperbolic properties onto the dynamically controllable Hamiltonian parameters. By probing the systems‘ response under geometric quantum driving, we elucidate how the intrinsic geometry of the parameter space dictates observable physical quantities. Furthermore, we extend the theoretical framework to realize ensemble simulation. This generalization enables us to harness the fast coherent control of superconducting qubits to capture essential geometric characteristics, establishing a versatile platform for exploring quantum dynamics on hyperbolic manifolds.
The transmon, a fabrication-friendly superconducting qubit, remains a leading candidate for scalable quantum computing. Recent advances in tunable couplers have accelerated progresstoward high-performance quantum processors. However, extending coherent interactions beyond millimeter scales to enhance quantum connectivity presents a critical challenge. Here, we introduce a hybrid-mode coupler exploiting resonator-transmon hybridization to simultaneously engineer the two lowest-frequency mode, enabling high-contrast coupling between centimeter-scale transmons. For a 1-cm coupler, our framework predicts flux-tunable XX and ZZ coupling strengths reaching 23 MHz and 100 MHz, with modulation contrasts exceeding 102 and 104, respectively, demonstrating quantitative agreement with an effective two-channel model. This work provides an efficient pathway to mitigate the inherent connectivity constraints imposed by short-range interactions, enabling transmon-based architectures compatible with hardware-efficient quantum tasks.
In recent years, the tunable coupling scheme has become the mainstream scheme for designing superconducting quan tum circuits. By working in the dispersive regime, the ZZ coupling andhigh-energy level leakage can be effectively suppressed and realize a high fidelity quantum gate. We propose a tunable fluxonium-transmon-transmon (FTT) cou pling scheme. In our system, the coupler is a frequency tunable transmon qubit. Both qubits and coupler are capacitively coupled. The asymmetric structure composed of fluxonium and transmon will optimize the frequency space and form a high fidelity two-qubit quantum gate. By decoupling, the effective coupling strength can be easily adjusted to close to the net coupling between qubits. We numerical simulation the master equation to reduce the quantum noise to zero. We study the performance of this scheme by simulating the general single-qubit X{\pi}/2 gate and two-qubit (iSWAP) gate. In the bias point of the qubits, we achieve a single qubit gate with 99.99% fidelity and a two-qubit gate with 99.95% fidelity. By adjusting the nonlinear Kerr coefficient of fluxonium to an appropriate value, we can achieve a multi-body entanglement state. We consider the correlation between the two qubits and the coupler, and the magnetic flux passing through one qubit has an effect on the other qubit and the coupler. Finally, we analyze the quantum correlation of the two-body entanglement state.