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arXiv:2610.11081

Quantum Simulation of a Hyperbolically Driven Quantum System with Superconducting Circuits

Han-xin Che, Yangyang Yu, Tao Zhang, Wen Zheng, Hai-Feng Yu, Xinsheng Tan, Yang Yu

quant-phSubmitted Oct 8, 2026• Announced Oct 9, 2026• 0 citations
arXivHTMLPDF

Abstract

Hyperbolic geometry hosts a plethora of exotic quantum phenomena ranging from holographic duality to novel topological phases. However, investigating these effects experimentally remains challenging 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.

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quant-pharXiv:2609.14876•Sep 15, 2026
Hyperbolic geometry hosts a plethora of exotic quantum phenomena ranging from holographic duality to novel topological phases. However, investigating these effects experimentally remains challenging 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.
We introduce a geometrical framework to construct a large class of time-dependent quantum systems in which the position of a classical particle moving autonomously on a smooth connected manifold is used to steer a quantum Hamiltonian over time. This results in quantum drives with structured temporal profiles and properties dependent on the local and global nature of the underlying choice of manifold. We show that our construction recovers the well-known classes of periodically driven and quasiperiodically driven quantum systems, but also unveils fundamentally new classes of quantum dynamics: by utilizing a compact two-dimensional hyperbolic Bolza surface and a nonorientable Klein-bottle surface, we demonstrate examples of a hyperbolically driven quantum system and a nonorientably driven quantum system respectively. Furthermore, we demonstrate that these driven systems exhibit unusual quantized dynamical responses reflecting their different underlying topologies, under the condition of being fully gapped and in the adiabatic limit, and which have interpretations as quantized crystalline electromagnetic responses in certain exotic effective tight-binding lattice models. We envision geometric quantum driving as a general framework to chart the landscape of time-dependent quantum systems and investigate the universal phase structures they exhibit, as well as a useful tool to enhance the capabilities of modern day quantum simulators.
During the past decades, the exploration of new topological material and the study of their novel physical properties have become a hot topic in condensed matter physics. However, it is hard to realize various topological materials and observe their physical properties that have been predicted theoretically due to the limitation of experimental techniques, such as fabrication, parameter control, and measurement. This situation makes quantum simulation a way alternative to simulating large quantum systems. In general, quantum simulation can be implemented by some controllable quantum systems. As a kind of all-solid state device, superconducting quantum circuit is an artificial quantum system that has great advantage in scalability, integration, and controllability, which provides an important scheme to realize the quantum simulator. In this paper, we review our recent results of quantum simulation in the space-time inversion symmetry protected topological semimetal bands, Hopf-link semimetal bands, and topological Maxwell metal bands with superconducting quantum circuits. These results show that the superconducting circuit is a promising system for simulating the quantum many-body system in condensed matter physics.
We show how quantum many-body systems on hyperbolic lattices with nearest-neighbor hopping and local interactions can be mapped onto quantum field theories in continuous negatively curved space. The underlying lattices have recently been realized experimentally with superconducting resonators and therefore allow for a table-top quantum simulation of quantum physics in curved background. Our mapping provides a computational tool to determine observables of the discrete system even for large lattices, where exact diagonalization fails. As an application and proof of principle we quantitatively reproduce the ground state energy, spectral gap, and correlation functions of the noninteracting lattice system by means of analytic formulas on the Poincaré disk, and show how conformal symmetry emerges for large lattices. This sets the stage for studying interactions and disorder on hyperbolic graphs in the future. Importantly, our analysis reveals that even relatively small discrete hyperbolic lattices emulate the continuous geometry of negatively curved space, and thus can be used to experimentally resolve fundamental open problems at the interface of interacting many-body systems, quantum field theory in curved space, and quantum gravity.
We report an experimental work on simulating the Kitaev chain of one-dimensional ppp-wave superconductivity with long-range coupling using superconducting quantum circuits. The effective Hamiltonian of this model in the momentum space is mapped onto that of a qubit driven by a tunable microwave control field. By monitoring the dynamics of the qubit, we generate intuitive yet precise visualization of topological characteristics of different quantum phases of the system. Topological invariants can be directly deduced from the experimental results, without relying on indirect extraction from measurements such as microwave spectroscopy and temporal averaging. Therefore a much enhanced efficiency of measurement can be realized compared to other methods that are often used to simulate topological phase transitions. As a consequence, a comprehensive phase diagram covering a wide range of the parameter space is obtained. Topological phase transitions and quantum multicritical points are clearly demonstrated. In particular, new topological phases emerge as a consequence of long-range coupling. The method used here can be readily generalized to simulate more complex systems on different experimental platforms.
We investigate a class of cyclic evolutions for %the cyclic evolution of driven two-level quantum systems (effective spin-1/2) with a particular focus on the geometric characteristics of the driving and their specific imprints on the quantum dynamics. By introducing the concept of geometric field curvature for any field trajectory in the parameter space we are able to unveil underlying patterns in the overall quantum behavior: the knowledge of the field curvature provides a non-standard and fresh access to the interrelation between field and spin trajectories, and the corresponding quantum phases acquired in non-adiabatic cyclic evolutions. In this context, we single out setups in which the driving field curvature can be employed to demonstrate a pure geometric control of the quantum phases. Furthermore, the driving field curvature can be naturally exploited to introduce the geometrical torque and derive a general expression for the total quantum phase acquired in a cycle. Remarkably, such relation allows to access the mechanisms controlling the changeover of the quantum phase across a topological transition and to disentangle the role of the spin and field topological windings. As for implementations, we discuss a series of physical systems and platforms to demonstrate how the geometric control of the quantum phases can be realized for pendular field drivings. This includes setups based on superconducting islands coupled to a Josephson junction and inversion asymmetric nanochannels with suitably tailored geometric shapes.
Hyperbolic band theory (HBT) has recently unveiled a wealth of exotic physical phenomena in negatively curved spaces. Concurrently, the quantum metric has emerged as a fundamental tensor governing quantum geometry and topological phases. In this Letter, we bridge these two frontiers by investigating the quantum metric in HBT. Because conventional Euclidean metric extraction protocols fundamentally fail in these non-commutative geometries, we introduce holonomy shaking, a novel, experimentally viable technique utilizing periodic lattice driving to dynamically extract the metric. Using the {8,3} regular hyperbolic and kagome-like lattices as concrete examples, we demonstrate the high-fidelity dynamical extraction of the quantum metric. Our results establish a robust blueprint for probing hyperbolic quantum geometries, paving the way for the discovery of exotic topological phenomena in hyperbolic quantum matter.