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Hawking radiation is one of the quantum features of a black hole that can be understood as a quantum tunneling across the event horizon of the black hole, but it is quite difficult to directly observe the Hawking radiation of an astrophysical black hole. Here, we report a fermionic lattice-model-type realization of an analogue black hole by using a chain of 10 superconducting transmon qubits with interactions mediated by 9 transmon-type tunable couplers. The quantum walks of quasi-particle in the curved spacetime reflect the gravitational effect near the black hole, resulting in the behaviour of stimulated Hawking radiation, which is verified by the state tomography measurement of all 7 qubits outside the horizon. In addition, the dynamics of entanglement in the curved spacetime is directly measured. Our results would stimulate more interests to explore the related features of black holes using the programmable superconducting processor with tunable couplers. Recently, the theory of Hawking radiation of a black hole has been tested in several analogue platforms. Shi et al. report a fermionic-lattice model realization of an analogue black hole using a chain of superconducting transmon qubits with tuneable couplers and show the stimulated Hawking radiation.

The Bloch oscillation (BO) and Wannier-Stark localization (WSL) are fundamental concepts about metal-insulator transitions in condensed matter physics. These phenomena have also been observed in semiconductor superlattices and simulated in platforms such as photonic waveguide arrays and cold atoms. Here, we report experimental investigation of BOs and WSL simulated with a 5-qubit programmable superconducting processor, of which the effective Hamiltonian is an isotropic XY spin chain. When applying a linear potential to the system by properly tuning all individual qubits, we observe that the propagation of a single spin on the chain is suppressed. It tends to oscillate near the neighborhood of their initial positions, which demonstrates the characteristics of BOs and WSL. We verify that the WSL length is inversely correlated to the potential gradient. Benefiting from the precise single-shot simultaneous readout of all qubits in our experiments, we can also investigate the thermal transport, which requires the joint measurement of more than one qubits. The experimental results show that, as an essential characteristic for BOs and WSL, the thermal transport is also blocked under a linear potential. Our experiment would be scalable to more superconducting qubits for simulating various of out-of-equilibrium problems in quantum many-body systems.

The existence of zero-dimensional superradiant quantum phase transitions seems inconsistent with conventional statistical physics. This work clarifies this apparent inconsistency. We demonstrate the corresponding effective field theories and finite-temperature properties of light-matter interacting systems, and show how this zero-dimensional quantum phase transition occurs. We first focus on the Rabi model, which is a minimum model that hosts a superradiant quantum phase transition. With the path integral method, we derive the imaginary-time action of the photon degrees of freedom. We also define a dynamical critical exponent as the rescaling between the temperature and the photon frequency, and perform dimensional analysis to the effective action. The dynamical critical exponent shows that the effective theory of the Rabi model is a free scalar field, where a true second-order quantum phase transition emerges. These results are also verified by numerical simulations of imaginary-time correlation functions of the order parameter. Furthermore, we also generalize this method to the Dicke model. Our results make the zero-dimensional superradiant quantum phase transition compatible with conventional statistical physics, and pave the way to understand it in the perspective of effective field theories.

We investigate the multipartite entanglement for a slow quantum quench crossing a critical point. We consider the quantum Ising model and the Lipkin-Meshkov-Glick model, which are local and full-connected quantum systems, respectively. The multipartite entanglement is quantified by quantum Fisher information with the generator defined as the operator of the ferromagnetic order parameter. The quench dynamics begins with a ground state in a paramagnetic phase, and then the transverse field is driven slowly to cross a quantum critical point, and ends with a zero transverse field. For the quantum Ising model, based on methods of matrix product states, we calculate the quantum Fisher information density of the final state. Numerical results of both linear and nonlinear quenches show that the quantum Fisher information density of the final state scales as a power law of the quench rate, which overall conforms to the prediction of the Kibble-Zurek mechanism with a small correction. We show that this correction results from the long-range behaviors. We also calculate the quantum Fisher information density in the Lipkin-Meshkov-Glick model. The results show that the scaling of quantum Fisher information in this full-connected system conforms to the Kibble-Zurek mechanism better, since the long-range physics cannot be defined in this nonlocal system. Our results reveal that the multipartite entanglement provides an alternative viewpoint to understand the dynamics of quantum phase transitions, specifically, the nontrivial long-range physics.

We investigate the meson excitations (particle-antiparticle bound states) in quantum many-body scars of a 1D \\(\\mathbb{Z}_2\\) lattice gauge theory coupled to a dynamical spin-\\(\\frac{1}{2}\\) chain as a matter field. By introducing a string representation of the physical Hilbert space, we express a scar state \\(\\ket {\\Psi_{n,l}}\\) as a superposition of all string bases with an identical string number \\(n\\) and a total length \\(l\\). For the small-\\(l\\) scar state \\(\\ket {\\Psi_{n,l}}\\), the gauge-invariant spin exchange correlation function of the matter field hosts an exponential decay as the distance increases, indicating the existence of stable mesons. However, for large \\(l\\), the correlation function exhibits a power-law decay, signaling the emergence of nonmesonic excitations. Furthermore, we show that this mesonic-nonmesonic crossover can be detected by the quench dynamics, starting from two low-entangled initial states, respectively, which are experimentally feasible in quantum simulators. Our results expand the physics of quantum many-body scars in lattice gauge theories and reveal that the nonmesonic state can also manifest ergodicity breaking.

We focus on the many-body eigenstates across a localization-delocalization phase transition. To characterize the robustness of the eigenstates, we introduce the eigenstate overlaps \\(\\mathcal{O}\\) with respect to the different boundary conditions. In the ergodic phase, the average of eigenstate overlaps \\(\\bar{\\mathcal{O}}\\) is exponential decay with the increase of the system size indicating the fragility of its eigenstates, and this can be considered as an eigenstate-version butterfly effect of the chaotic systems. For localized systems, \\(\\bar{\\mathcal{O}}\\) is almost size-independent showing the strong robustness of the eigenstates and the broken of eigenstate thermalization hypothesis. In addition, we find that the response of eigenstates to the change of boundary conditions in many-body localized systems is identified with the single-particle wave functions in Anderson localized systems. This indicates that the eigenstates of the many-body localized systems, as the many-body wave functions, may be independent of each other. We demonstrate that this is consistent with the existence of a large number of quasilocal integrals of motion in the many-body localized phase. Our results provide a new method to study localized and delocalized systems from the perspective of eigenstates.

Recently, quantum simulation of low-dimensional lattice gauge theories (LGTs) has attracted many interests, which may improve our understanding of strongly correlated quantum many-body systems. Here, we propose an implementation to approximate \\(\\mathbb{Z}_2\\) LGT on superconducting quantum circuits, where the effective theory is a mixture of a LGT and a gauge-broken term. Using matrix product state based methods, both the ground state properties and quench dynamics are systematically investigated. With an increase of the transverse (electric) field, the system displays a quantum phase transition from a disordered phase to a translational symmetry breaking phase. In the ordered phase, an approximate Gauss law of the \\(\\mathbb{Z}_2\\) LGT emerges in the ground state. Moreover, to shed light on the experiments, we also study the quench dynamics, where there is a dynamical signature of the spontaneous translational symmetry breaking. The spreading of the single particle of matter degree is diffusive under the weak transverse field, while it is ballistic with small velocity for the strong field. Furthermore, due to the emergent Gauss law under the strong transverse field, the matter degree can also exhibit confinement dynamics which leads to a strong suppression of the nearest-neighbor hopping. Our results pave the way for simulating the LGT on superconducting circuits, including the quantum phase transition and quench dynamics.

Quantum simulation in experiments of many-body systems may bring new phenomena which are not well studied theoretically. Motivated by a recent work of quantum simulation on a superconducting ladder circuit, we investigate the rung-pair localization of the Bose-Hubbard ladder model without quenched disorder. Our results show that, in the hard-core limit, there exists a rung-pair localization both at the edges and in the bulk. Using center-of-mass frame, the two-particle system can be mapped to an effective single-particle system with an approximate sub-lattice symmetry. Under the condition of hard-core limit, the effective system is forced to have a defect at the left edge leading to a zero-energy flat band, which is the origin of the rung-pair localization. We also study the multi-particle dynamics of the Bose-Hubbard ladder model, which is beyond the singleparticle picture. In this case, we find that the localization can still survive despite of the existence of interaction between the pairs. Moreover, the numerical results show that the entanglement entropy exhibits a long-time logarithmic growth and the saturated values satisfy a volume law. This phenomenon implies that the interaction plays an important role during the dynamics, although it cannot break the localization. Our results reveal another interesting type of disorder-free localization related to a zero-energy flat band, which is induced by on-site interaction and specific lattice symmetry.

Solving finite-temperature properties of quantum many-body systems is generally challenging to classical computers due to their high computational complexities. In this article, we present experiments to demonstrate a hybrid quantum-classical simulation of thermal quantum states. By combining a classical probabilistic model and a 5-qubit programmable superconducting quantum processor, we prepare Gibbs states and excited states of Heisenberg XY and XXZ models with high fidelity and compute thermal properties including the variational free energy, energy, and entropy with a small statistical error. Our approach combines the advantage of classical probabilistic models for sampling and quantum co-processors for unitary transformations. We show that the approach is scalable in the number of qubits, and has a self-verifiable feature, revealing its potentials in solving large-scale quantum statistical mechanics problems on near-term intermediate-scale quantum computers.

Hawking radiation is one of the quantum features of a black hole that can be understood as a quantum tunneling across the event horizon of the black hole, but it is quite difficult to directly observe the Hawking radiation of an astrophysical black hole. Here, we report a fermionic lattice-model-type realization of an analogue black hole by using a chain of 10 superconducting transmon qubits with interactions mediated by 9 transmon-type tunable couplers. The quantum walks of quasi-particle in the curved spacetime reflect the gravitational effect near the black hole, resulting in the behaviour of stimulated Hawking radiation, which is verified by the state tomography measurement of all 7 qubits outside the horizon. In addition, the dynamics of entanglement in the curved spacetime is directly measured. Our results would stimulate more interests to explore the related features of black holes using the programmable superconducting processor with tunable couplers.