Disorder-tunable entanglement at infinite temperature.

Emerging quantum technologies hold the promise of unravelling difficult problems ranging from condensed matter to high-energy physics while, at the same time, motivating the search for unprecedented phenomena in their setting. Here, we use a custom-built superconducting qubit ladder to realize non-thermalizing states with rich entanglement structures in the middle of the energy spectrum. Despite effectively forming an "infinite" temperature ensemble, these states robustly encode quantum information far from equilibrium, as we demonstrate by measuring the fidelity and entanglement entropy in the quench dynamics of the ladder. Our approach harnesses the recently proposed type of non-ergodic behavior known as "rainbow scar," which allows us to obtain analytically exact eigenfunctions whose ergodicity-breaking properties can be conveniently controlled by randomizing the couplings of the model without affecting their energy. The on-demand tunability of quantum correlations via disorder allows for in situ control over ergodicity breaking, and it provides a knob for designing exotic many-body states that defy thermalization.

Observation of a Superradiant Phase Transition with Emergent Cat States.

Superradiant phase transitions (SPTs) are important for understanding light-matter interactions at the quantum level, and play a central role in criticality-enhanced quantum sensing. So far, SPTs have been observed in driven-dissipative systems, but the emergent light fields did not show any nonclassical characteristic due to the presence of strong dissipation. Here we report an experimental demonstration of the SPT featuring the emergence of a highly nonclassical photonic field, realized with a resonator coupled to a superconducting qubit, implementing the quantum Rabi model. We fully characterize the light-matter state by Wigner matrix tomography. The measured matrix elements exhibit quantum interference intrinsic of a photonic mesoscopic superposition, and reveal light-matter entanglement.

Quantum Control of a Single Magnon in a Macroscopic Spin System.

Nonclassical quantum states are the pivotal features of a quantum system that differs from its classical counterpart. However, the generation and coherent control of quantum states in a macroscopic spin system remain an outstanding challenge. Here we experimentally demonstrate the quantum control of a single magnon in a macroscopic spin system (i.e., 1 mm-diameter yttrium-iron-garnet sphere) coupled to a superconducting qubit via a microwave cavity. By tuning the qubit frequency in situ via the Autler-Townes effect, we manipulate this single magnon to generate its nonclassical quantum states, including the single-magnon state and the superposition of single-magnon state and vacuum (zero magnon) state. Moreover, we confirm the deterministic generation of these nonclassical states by Wigner tomography. Our experiment offers the first reported deterministic generation of the nonclassical quantum states in a macroscopic spin system and paves a way to explore its promising applications in quantum engineering.

Observation of entanglement transition of pseudo-random mixed states.

Random quantum states serve as a powerful tool in various scientific fields, including quantum supremacy and black hole physics. It has been theoretically predicted that entanglement transitions may happen for different partitions of multipartite random quantum states; however, the experimental observation of these transitions is still absent. Here, we experimentally demonstrate the entanglement transitions witnessed by negativity on a fully connected superconducting processor. We apply parallel entangling operations, that significantly decrease the depth of the pseudo-random circuits, to generate pseudo-random pure states of up to 15 qubits. By quantum state tomography of the reduced density matrix of six qubits, we measure the negativity spectra. Then, by changing the sizes of the environment and subsystems, we observe the entanglement transitions that are directly identified by logarithmic entanglement negativities based on the negativity spectra. In addition, we characterize the randomness of our circuits by measuring the distance between the distribution of output bit-string probabilities and the Porter-Thomas distribution. Our results show that superconducting processors with all-to-all connectivity constitute a promising platform for generating random states and understanding the entanglement structure of multipartite quantum systems.

Exceptional Entanglement Phenomena: Non-Hermiticity Meeting Nonclassicality.

Non-Hermitian (NH) extension of quantum-mechanical Hamiltonians represents one of the most significant advancements in physics. During the past two decades, numerous captivating NH phenomena have been revealed and demonstrated, but all of which can appear in both quantum and classical systems. This leads to the fundamental question: what NH signature presents a radical departure from classical physics? The solution of this problem is indispensable for exploring genuine NH quantum mechanics, but remains experimentally untouched so far. Here, we resolve this basic issue by unveiling distinct exceptional entanglement phenomena, exemplified by an entanglement transition, occurring at the exceptional point of NH interacting quantum systems. We illustrate and demonstrate such purely quantum-mechanical NH effects with a naturally dissipative light-matter system, engineered in a circuit quantum electrodynamics architecture. Our results lay the foundation for studies of genuinely quantum-mechanical NH physics, signified by exceptional-point-enabled entanglement behaviors.

Observing the quantum topology of light.

Topological photonics provides a powerful platform to explore topological physics beyond traditional electronic materials and shows promising applications in light transport and lasers. Classical degrees of freedom are routinely used to construct topological light modes in real or synthetic dimensions. Beyond the classical topology, the inherent quantum nature of light provides a wealth of fundamentally distinct topological states. Here we implement experiments on topological states of quantized light in a superconducting circuit, with which one- and two-dimensional Fock-state lattices are constructed. We realize rich topological physics including topological zero-energy states of the Su-Schrieffer-Heeger model, strain-induced pseudo-Landau levels, valley Hall effect, and Haldane chiral edge currents. Our study extends the topological states of light to the quantum regime, bridging topological phases of condensed-matter physics with circuit quantum electrodynamics, and offers a freedom in controlling the quantum states of multiple resonators.

Variational Quantum Computation of Molecular Linear Response Properties on a Superconducting Quantum Processor.

Simulating response properties of molecules is crucial for interpreting experimental spectroscopies and accelerating materials design. However, it remains a long-standing computational challenge for electronic structure methods on classical computers. While quantum computers hold the promise of solving this problem more efficiently in the long run, existing quantum algorithms requiring deep quantum circuits are infeasible for near-term noisy quantum processors. Herein, we introduce a pragmatic variational quantum response (VQR) algorithm for response properties, which circumvents the need for deep quantum circuits. Using this algorithm, we report the first simulation of linear response properties of molecules including dynamic polarizabilities and absorption spectra on a superconducting quantum processor. Our results indicate that a large class of important dynamical properties, such as Green's functions, are within the reach of near-term quantum hardware using this algorithm in combination with suitable error mitigation techniques.

Digital quantum simulation of Floquet symmetry-protected topological phases.

Quantum many-body systems away from equilibrium host a rich variety of exotic phenomena that are forbidden by equilibrium thermodynamics. A prominent example is that of discrete time crystals1-8, in which time-translational symmetry is spontaneously broken in periodically driven systems. Pioneering experiments have observed signatures of time crystalline phases with trapped ions9,10, solid-state spin systems11-15, ultracold atoms16,17 and superconducting qubits18-20. Here we report the observation of a distinct type of non-equilibrium state of matter, Floquet symmetry-protected topological phases, which are implemented through digital quantum simulation with an array of programmable superconducting qubits. We observe robust long-lived temporal correlations and subharmonic temporal response for the edge spins over up to 40 driving cycles using a circuit of depth exceeding 240 and acting on 26 qubits. We demonstrate that the subharmonic response is independent of the initial state, and experimentally map out a phase boundary between the Floquet symmetry-protected topological and thermal phases. Our results establish a versatile digital simulation approach to exploring exotic non-equilibrium phases of matter with current noisy intermediate-scale quantum processors21.

Metrological Characterization of Non-Gaussian Entangled States of Superconducting Qubits.

Multipartite entangled states are significant resources for both quantum information processing and quantum metrology. In particular, non-Gaussian entangled states are predicted to achieve a higher sensitivity of precision measurements than Gaussian states. On the basis of metrological sensitivity, the conventional linear Ramsey squeezing parameter (RSP) efficiently characterizes the Gaussian entangled atomic states but fails for much wider classes of highly sensitive non-Gaussian states. These complex non-Gaussian entangled states can be classified by the nonlinear squeezing parameter (NLSP), as a generalization of the RSP with respect to nonlinear observables and identified via the Fisher information. However, the NLSP has never been measured experimentally. Using a 19-qubit programmable superconducting processor, we report the characterization of multiparticle entangled states generated during its nonlinear dynamics. First, selecting ten qubits, we measure the RSP and the NLSP by single-shot readouts of collective spin operators in several different directions. Then, by extracting the Fisher information of the time-evolved state of all 19 qubits, we observe a large metrological gain of 9.89_{-0.29}^{+0.28} dB over the standard quantum limit, indicating a high level of multiparticle entanglement for quantum-enhanced phase sensitivity. Benefiting from high-fidelity full controls and addressable single-shot readouts, the superconducting processor with interconnected qubits provides an ideal platform for engineering and benchmarking non-Gaussian entangled states that are useful for quantum-enhanced metrology.

Synthesizing Five-Body Interaction in a Superconducting Quantum Circuit.

Synthesizing many-body interaction Hamiltonians is a central task in quantum simulation. However, it is challenging to synthesize Hamiltonians that have more than two spins in a single term. Here we synthesize m-body spin-exchange Hamiltonians with m up to 5 in a superconducting quantum circuit by simultaneously exciting multiple independent qubits with time-energy correlated photons generated from a qudit. The dynamic evolution of the m-body interaction is governed by the Rabi oscillation between two m-spin states, in which the states of each spin are different. We demonstrate the scalability of our approach by comparing the influence of noises on the three-, four- and five-body interaction and building a many-body Mach-Zehnder interferometer which potentially has a Heisenberg-limit sensitivity. This study paves a way for quantum simulation involving many-body interaction Hamiltonians such as lattice gauge theories in quantum circuits.

Experimental quantum adversarial learning with programmable superconducting qubits.

Quantum computing promises to enhance machine learning and artificial intelligence. However, recent theoretical works show that, similar to traditional classifiers based on deep classical neural networks, quantum classifiers would suffer from adversarial perturbations as well. Here we report an experimental demonstration of quantum adversarial learning with programmable superconducting qubits. We train quantum classifiers, which are built on variational quantum circuits consisting of ten transmon qubits featuring average lifetimes of 150 µs, and average fidelities of simultaneous single- and two-qubit gates above 99.94% and 99.4%, respectively, with both real-life images (for example, medical magnetic resonance imaging scans) and quantum data. We demonstrate that these well-trained classifiers (with testing accuracy up to 99%) can be practically deceived by small adversarial perturbations, whereas an adversarial training process would substantially enhance their robustness to such perturbations.

Stark Many-Body Localization on a Superconducting Quantum Processor.

Quantum emulators, owing to their large degree of tunability and control, allow the observation of fine aspects of closed quantum many-body systems, as either the regime where thermalization takes place or when it is halted by the presence of disorder. The latter, dubbed many-body localization (MBL) phenomenon, describes the nonergodic behavior that is dynamically identified by the preservation of local information and slow entanglement growth. Here, we provide a precise observation of this same phenomenology in the case where the quenched on-site energy landscape is not disordered, but rather linearly varied, emulating the Stark MBL. To this end, we construct a quantum device composed of 29 functional superconducting qubits, faithfully reproducing the relaxation dynamics of a nonintegrable spin model. At large Stark potentials, local observables display periodic Bloch oscillations, a manifesting characteristic of the fragmentation of the Hilbert space in sectors that conserve dipole moments. The flexible programmability of our quantum emulator highlights its potential in helping the understanding of nontrivial quantum many-body problems, in direct complement to simulations in classical computers.

Rapid and unconditional parametric reset protocol for tunable superconducting qubits.

Qubit initialization is a critical task in quantum computation and communication. Extensive efforts have been made to achieve this with high speed, efficiency and scalability. However, previous approaches have either been measurement-based and required fast feedback, suffered from crosstalk or required sophisticated calibration. Here, we report a fast and high-fidelity reset scheme, avoiding the issues above without any additional chip architecture. By modulating the flux through a transmon qubit, we realize a swap between the qubit and its readout resonator that suppresses the excited state population to 0.08% ± 0.08% within 34 ns (284 ns if photon depletion of the resonator is required). Furthermore, our approach (i) can achieve effective second excited state depletion, (ii) has negligible effects on neighboring qubits, and (iii) offers a way to entangle the qubit with an itinerant single photon, useful in quantum communication applications.

Scalable Evaluation of Quantum-Circuit Error Loss Using Clifford Sampling.

A major challenge in developing quantum computing technologies is to accomplish high precision tasks by utilizing multiplex optimization approaches, on both the physical system and algorithm levels. Loss functions assessing the overall performance of quantum circuits can provide the foundation for many optimization techniques. In this Letter, we use the quadratic error loss and the final-state fidelity loss to characterize quantum circuits. We find that the distribution of computation error is approximately Gaussian, which in turn justifies the quadratic error loss. It is shown that these loss functions can be efficiently evaluated in a scalable way by sampling from Clifford-dominated circuits. We demonstrate the results by numerically simulating 10-qubit noisy quantum circuits with various error models as well as executing 4-qubit circuits with up to ten layers of 2-qubit gates on a superconducting quantum processor. Our results pave the way toward the optimization-based quantum device and algorithm design in the intermediate-scale quantum regime.

Two-Dimensional Superconductivity at the LaAlO_{3}/KTaO_{3}(110) Heterointerface.

We report on the observation of a T_{c}∼0.9 K superconductivity at the interface between LaAlO_{3} film and the 5d transition metal oxide KTaO_{3}(110) single crystal. The interface shows a large anisotropy of the upper critical field, and its superconducting transition is consistent with a Berezinskii-Kosterlitz-Thouless transition. Both facts suggest that the superconductivity is two-dimensional (2D) in nature. The carrier density measured at 5 K is ∼7×10^{13} cm^{-2}. The superconducting layer thickness and coherence length are estimated to be ∼8 and ∼30 nm, respectively. Our result provides a new platform for the study of 2D superconductivity at oxide interfaces.

Simultaneous Excitation of Two Noninteracting Atoms with Time-Frequency Correlated Photon Pairs in a Superconducting Circuit.

We report the first observation of simultaneous excitation of two noninteracting atoms by a pair of time-frequency correlated photons in a superconducting circuit. The strong coupling regime of this process enables the synthesis of a three-body interaction Hamiltonian, which allows the generation of the tripartite Greenberger-Horne-Zeilinger state in a single step with a fidelity as high as 0.95. We further demonstrate the inhibition of the simultaneous two-atom excitation by continuously measuring whether the first photon is emitted. This work provides a new route in synthesizing many-body interaction Hamiltonian and coherent control of entanglement.

Probing dynamical phase transitions with a superconducting quantum simulator.

Nonequilibrium quantum many-body systems, which are difficult to study via classical computation, have attracted wide interest. Quantum simulation can provide insights into these problems. Here, using a programmable quantum simulator with 16 all-to-all connected superconducting qubits, we investigate the dynamical phase transition in the Lipkin-Meshkov-Glick model with a quenched transverse field. Clear signatures of dynamical phase transitions, merging different concepts of dynamical criticality, are observed by measuring the nonequilibrium order parameter, nonlocal correlations, and the Loschmidt echo. Moreover, near the dynamical critical point, we obtain a spin squeezing of -7.0 ± 0.8 dB, showing multipartite entanglement, useful for measurements with precision fivefold beyond the standard quantum limit. On the basis of the capability of entangling qubits simultaneously and the accurate single-shot readout of multiqubit states, this superconducting quantum simulator can be used to study other problems in nonequilibrium quantum many-body systems, such as thermalization, many-body localization, and emergent phenomena in periodically driven systems.

Controllable Switching between Superradiant and Subradiant States in a 10-qubit Superconducting Circuit.

Superradiance and subradiance concerning enhanced and inhibited collective radiation of an ensemble of atoms have been a central topic in quantum optics. However, precise generation and control of these states remain challenging. Here we deterministically generate up to 10-qubit superradiant and 8-qubit subradiant states, each containing a single excitation, in a superconducting quantum circuit with multiple qubits interconnected by a cavity resonator. The sqrt[N]-scaling enhancement of the coupling strength between the superradiant states and the cavity is validated. By applying an appropriate phase gate on each qubit, we are able to switch the single collective excitation between superradiant and subradiant states. While the subradiant states containing a single excitation are forbidden from emitting photons, we demonstrate that they can still absorb photons from the resonator. However, for an even number of qubits, a singlet state with half of the qubits being excited can neither emit nor absorb photons, which is verified with 4 qubits. This study is a step forward in coherent control of collective radiation and has promising applications in quantum information processing.

Deterministic Entanglement Swapping in a Superconducting Circuit.

Entanglement swapping, the process to entangle two particles without coupling them in any way, is one of the most striking manifestations of the quantum-mechanical nonlocal characteristic. Besides fundamental interest, this process has applications in complex entanglement manipulation and quantum communication. Here we report a high-fidelity, unconditional entanglement swapping experiment in a superconducting circuit. The measured concurrence characterizing the qubit-qubit entanglement produced by swapping is above 0.75, confirming most of the entanglement of one qubit with its partner is deterministically transferred to another qubit that has never interacted with it. We further realize delayed-choice entanglement swapping, showing whether two qubits previously behaved as in an entangled state or as in a separable state is determined by a later choice of the type of measurement on their partners. This is the first demonstration of entanglement-separability duality in a deterministic way.

Generation of multicomponent atomic Schrödinger cat states of up to 20 qubits.

Multipartite entangled states are crucial for numerous applications in quantum information science. However, the generation and verification of multipartite entanglement on fully controllable and scalable quantum platforms remains an outstanding challenge. We report the deterministic generation of an 18-qubit Greenberger-Horne-Zeilinger (GHZ) state and multicomponent atomic Schrödinger cat states of up to 20 qubits on a quantum processor, which features 20 superconducting qubits, also referred to as artificial atoms, interconnected by a bus resonator. By engineering a one-axis twisting Hamiltonian, the system of qubits, once initialized, coherently evolves to multicomponent atomic Schrödinger cat states-that is, superpositions of atomic coherent states including the GHZ state-at specific time intervals as expected. Our approach on a solid-state platform should not only stimulate interest in exploring the fundamental physics of quantum many-body systems, but also enable the development of applications in practical quantum metrology and quantum information processing.