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.

Enhanced quantum state transfer by circumventing quantum chaotic behavior.

The ability to realize high-fidelity quantum communication is one of the many facets required to build generic quantum computing devices. In addition to quantum processing, sensing, and storage, transferring the resulting quantum states demands a careful design that finds no parallel in classical communication. Existing experimental demonstrations of quantum information transfer in solid-state quantum systems are largely confined to small chains with few qubits, often relying upon non-generic schemes. Here, by using a superconducting quantum circuit featuring thirty-six tunable qubits, accompanied by general optimization procedures deeply rooted in overcoming quantum chaotic behavior, we demonstrate a scalable protocol for transferring few-particle quantum states in a two-dimensional quantum network. These include single-qubit excitation, two-qubit entangled states, and two excitations for which many-body effects are present. Our approach, combined with the quantum circuit's versatility, paves the way to short-distance quantum communication for connecting distributed quantum processors or registers, even if hampered by inherent imperfections in actual quantum devices.

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.

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.

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.