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A long-standing challenge in quantum computing is developing technologies to overcome the inevitable noise in qubits. To enable meaningful applications in the early stages of fault-tolerant quantum computing, devising methods to suppress post-correction logical failures is becoming increasingly crucial. In this work, we propose and experimentally demonstrate the application of zero-noise extrapolation, a practical quantum error mitigation technique, to error correction circuits on state-of-the-art superconducting processors. By amplifying the noise on physical qubits, the circuits yield outcomes that exhibit a predictable dependence on noise strength, following a polynomial function determined by the code distance. This property enables the effective application of polynomial extrapolation to mitigate logical errors. Our experiments demonstrate a universal reduction in logical errors across various quantum circuits, including fault-tolerant circuits of repetition and surface codes. We observe a favorable performance in multi-round error correction circuits, indicating that this method remains effective when the circuit depth increases. These results advance the frontier of quantum error suppression technologies, opening a practical way to achieve reliable quantum computing in the early fault-tolerant era.

Symmetry-protected topological phases cannot be described by any local order parameter and are beyond the conventional symmetry-breaking paradigm for understanding quantum matter. They are characterized by topological boundary states robust against perturbations that respect the protecting symmetry. In a clean system without disorder, these edge modes typically only occur for the ground states of systems with a bulk energy gap and would not survive at finite temperatures due to mobile thermal excitations. Here, we report the observation of a distinct type of topological edge modes, which are protected by emergent symmetries and persist even up to infinite temperature, with an array of 100 programmable superconducting qubits. In particular, through digital quantum simulation of the dynamics of a one-dimensional disorder-free "cluster" Hamiltonian, we observe robust long-lived topological edge modes over up to 30 cycles at a wide range of temperatures. By monitoring the propagation of thermal excitations, we show that despite the free mobility of these excitations, their interactions with the edge modes are substantially suppressed in the dimerized regime due to an emergent U(1)$\times$U(1) symmetry, resulting in an unusually prolonged lifetime of the topological edge modes even at infinite temperature. In addition, we exploit these topological edge modes as logical qubits and prepare a logical Bell state, which exhibits persistent coherence in the dimerized and off-resonant regime, despite the system being disorder-free and far from its ground state. Our results establish a viable digital simulation approach to experimentally exploring a variety of finite-temperature topological phases and demonstrate a potential route to construct long-lived robust boundary qubits that survive to infinite temperature in disorder-free systems.

The discovery of nontrivial topology in quantum critical states has introduced a new paradigm for classifying quantum phase transitions and challenges the conventional belief that topological phases are typically associated with a bulk energy gap. However, realizing and characterizing such topologically nontrivial quantum critical states with large particle numbers remains an outstanding experimental challenge in statistical and condensed matter physics. Programmable quantum processors can directly prepare and manipulate exotic quantum many-body states, offering a powerful path for exploring the physics behind these states. Here, we present an experimental exploration of the critical cluster Ising model by preparing its low-lying critical states on a superconducting processor with up to $100$ qubits. We develop an efficient method to probe the boundary $g$-function based on prepared low-energy states, which allows us to uniquely identify the nontrivial topology of the critical systems under study. Furthermore, by adapting the entanglement Hamiltonian tomography technique, we recognize two-fold topological degeneracy in the entanglement spectrum under periodic boundary condition, experimentally verifying the universal bulk-boundary correspondence in topological critical systems. Our results demonstrate the low-lying critical states as useful quantum resources for investigating the interplay between topology and quantum criticality.

Non-equilibrium quantum transport is crucial to technological advances ranging from nanoelectronics to thermal management. In essence, it deals with the coherent transfer of energy and (quasi-)particles through quantum channels between thermodynamic baths. A complete understanding of quantum transport thus requires the ability to simulate and probe macroscopic and microscopic physics on equal footing. Using a superconducting quantum processor, we demonstrate the emergence of non-equilibrium steady quantum transport by emulating the baths with qubit ladders and realising steady particle currents between the baths. We experimentally show that the currents are independent of the microscopic details of bath initialisation, and their temporal fluctuations decrease rapidly with the size of the baths, emulating those predicted by thermodynamic baths. The above characteristics are experimental evidence of pure-state statistical mechanics and prethermalisation in non-equilibrium many-body quantum systems. Furthermore, by utilising precise controls and measurements with single-site resolution, we demonstrate the capability to tune steady currents by manipulating the macroscopic properties of the baths, including filling and spectral properties. Our investigation paves the way for a new generation of experimental exploration of non-equilibrium quantum transport in strongly correlated quantum matter., Comment: 7 pages, 4 figures

Fabric-based pneumatic exosuits have a broad application prospect due to their good human-machine interaction performance, but their structural design paradigm has not yet been finalized and requires in-depth research. This paper proposes the concepts of zone inflation and volume transfer for the design of a fabric-based pneumatic exosuit with both efficiency and wearability. The meaning of zone inflation is to divide the inflation area of pneumatic exosuit into inflation-deflation zone and inflation-holding zone which can reduce the consumption of compressed air and improve efficiency. Volume transfer, a strategic distribution method of inflatable regions inside the garment, can effectively enhance the wearability of the exosuit. Using inexpensive thermoplastic polyurethane film and clothing fabric, the exosuit is made by heat pressing and sewing. The exosuit has a response time of 0.5s, a stress area of 1500mm2, and a profile of only 32mm, which can be hidden inside common clothing. A mathematical model is developed to predict the output torque of the exosuit with an error of 3.6%. Mechanical experiments show that the exosuit outputs a torque of 9.1Nm at a pressure of 100kPa. Surface electromyography experiments show that the exosuit can provide users with a boost from sitting to standing, with an average reduction in electromyography signals of 14.95%. The exosuit designed using these methods synthesizes efficiency and wearability and is expected to be an ideal paradigm for fabric-based pneumatic exosuits.

Quantum computers may outperform classical computers on machine learning tasks. In recent years, a variety of quantum algorithms promising unparalleled potential to enhance, speed up, or innovate machine learning have been proposed. Yet, quantum learning systems, similar to their classical counterparts, may likewise suffer from the catastrophic forgetting problem, where training a model with new tasks would result in a dramatic performance drop for the previously learned ones. This problem is widely believed to be a crucial obstacle to achieving continual learning of multiple sequential tasks. Here, we report an experimental demonstration of quantum continual learning on a fully programmable superconducting processor. In particular, we sequentially train a quantum classifier with three tasks, two about identifying real-life images and the other on classifying quantum states, and demonstrate its catastrophic forgetting through experimentally observed rapid performance drops for prior tasks. To overcome this dilemma, we exploit the elastic weight consolidation strategy and show that the quantum classifier can incrementally learn and retain knowledge across the three distinct tasks, with an average prediction accuracy exceeding 92.3%. In addition, for sequential tasks involving quantum-engineered data, we demonstrate that the quantum classifier can achieve a better continual learning performance than a commonly used classical feedforward network with a comparable number of variational parameters. Our results establish a viable strategy for empowering quantum learning systems with desirable adaptability to multiple sequential tasks, marking an important primary experimental step towards the long-term goal of achieving quantum artificial general intelligence., Comment: 21 pages, 14 figures

Tracking the time evolution of a quantum state allows one to verify the thermalization rate or the propagation speed of correlations in generic quantum systems. Inspired by the energy-time uncertainty principle, bounds have been demonstrated on the maximal speed at which a quantum state can change, resulting in immediate and practical tasks. Based on a programmable superconducting quantum processor, we test the dynamics of various emulated quantum mechanical systems encompassing single- and many-body states. We show that one can test the known quantum speed limits and that modifying a single Hamiltonian parameter allows the observation of the crossover of the different bounds on the dynamics. We also unveil the observation of minimal quantum speed limits in addition to more common maximal ones, i.e., the lowest rate of change of a unitarily evolved quantum state. Our results establish a comprehensive experimental characterization of quantum speed limits and pave the way for their subsequent study in engineered non-unitary conditions., Comment: 9 pages,4 figures + supplementary information

Bell nonlocality is an intrinsic feature of quantum mechanics, which can be certified via the violation of Bell inequalities. It is therefore a fundamental question to certify Bell nonlocality from experimental data. Here, we present an optimization scheme to improve nonlocality certification by exploring flexible mappings between Bell inequalities and Hamiltonians corresponding to the Bell operators. We show that several Hamiltonian models can be mapped to new inequalities with improved classical bounds than the original one, enabling a more robust detection of nonlocality. From the other direction, we investigate the mapping from fixed Bell inequalities to Hamiltonians, aiming to maximize quantum violations while considering experimental imperfections. As a practical demonstration, we apply this method to an XXZ-like honeycomb-lattice model utilizing over 70 superconducting qubits. The successful application of this technique, as well as combining the two directions to form an optimization loop, may open new avenues for developing more practical and noise-resilient nonlocality certification techniques and enable broader experimental explorations., Comment: 11 pages, 5 figures, 1 table

Quantum nonlocality describes a stronger form of quantum correlation than that of entanglement. It refutes Einstein's belief of local realism and is among the most distinctive and enigmatic features of quantum mechanics. It is a crucial resource for achieving quantum advantages in a variety of practical applications, ranging from cryptography and certified random number generation via self-testing to machine learning. Nevertheless, the detection of nonlocality, especially in quantum many-body systems, is notoriously challenging. Here, we report an experimental certification of genuine multipartite Bell correlations, which signal nonlocality in quantum many-body systems, up to 24 qubits with a fully programmable superconducting quantum processor. In particular, we employ energy as a Bell correlation witness and variationally decrease the energy of a many-body system across a hierarchy of thresholds, below which an increasing Bell correlation depth can be certified from experimental data. As an illustrating example, we variationally prepare the low-energy state of a two-dimensional honeycomb model with 73 qubits and certify its Bell correlations by measuring an energy that surpasses the corresponding classical bound with up to 48 standard deviations. In addition, we variationally prepare a sequence of low-energy states and certify their genuine multipartite Bell correlations up to 24 qubits via energies measured efficiently by parity oscillation and multiple quantum coherence techniques. Our results establish a viable approach for preparing and certifying multipartite Bell correlations, which provide not only a finer benchmark beyond entanglement for quantum devices, but also a valuable guide towards exploiting multipartite Bell correlation in a wide spectrum of practical applications., Comment: 11 pages,6 figures + 14 pages, 6 figures

Node classification is a fundamental task, but obtaining node classification labels can be challenging and expensive in many real-world scenarios. Transfer learning has emerged as a promising solution to address this challenge by leveraging knowledge from source domains to enhance learning in a target domain. Existing transfer learning methods for node classification primarily focus on integrating Graph Convolutional Networks (GCNs) with various transfer learning techniques. While these approaches have shown promising results, they often suffer from a lack of theoretical guarantees, restrictive conditions, and high sensitivity to hyperparameter choices. To overcome these limitations, we propose a Graph Convolutional Multinomial Logistic Regression (GCR) model and a transfer learning method based on the GCR model, called Trans-GCR. We provide theoretical guarantees of the estimate obtained under GCR model in high-dimensional settings. Moreover, Trans-GCR demonstrates superior empirical performance, has a low computational cost, and requires fewer hyperparameters than existing methods.

Recent advancements of intermediate-scale quantum processors have triggered tremendous interest in the exploration of practical quantum advantage. The simulation of fluid dynamics, a highly challenging problem in classical physics but vital for practical applications, emerges as a good candidate for showing quantum utility. Here, we report an experiment on the digital simulation of unsteady flows, which consists of quantum encoding, evolution, and detection of flow states, with a superconducting quantum processor. The quantum algorithm is based on the Hamiltonian simulation using the hydrodynamic formulation of the Schr\"odinger equation. With the median fidelities of 99.97% and 99.67% for parallel single- and two-qubit gates respectively, we simulate the dynamics of a two-dimensional (2D) compressible diverging flow and a 2D decaying vortex with ten qubits. The experimental results well capture the temporal evolution of averaged density and momentum profiles, and qualitatively reproduce spatial flow fields with moderate noises. This work demonstrates the potential of quantum computing in simulating more complex flows, such as turbulence, for practical applications.

Non-Abelian topological orders offer an intriguing path towards fault-tolerant quantum computation, where information can be encoded and manipulated in a topologically protected manner immune to arbitrary local noises and perturbations. However, realizing non-Abelian topologically ordered states is notoriously challenging in both condensed matter and programmable quantum systems, and it was not until recently that signatures of non-Abelian statistics were observed through digital quantum simulation approaches. Despite these exciting progresses, none of them has demonstrated the appropriate type of topological orders and associated non-Abelian anyons whose braidings alone support universal quantum computation. Here, we report the realization of non-Abelian topologically ordered states of the Fibonacci string-net model and demonstrate braidings of Fibonacci anyons featuring universal computational power, with a superconducting quantum processor. We exploit efficient quantum circuits to prepare the desired states and verify their nontrivial topological nature by measuring the topological entanglement entropy. In addition, we create two pairs of Fibonacci anyons and demonstrate their fusion rule and non-Abelian braiding statistics by applying unitary gates on the underlying physical qubits. Our results establish a versatile digital approach to exploring exotic non-Abelian topological states and their associated braiding statistics with current noisy intermediate-scale quantum processors.

The spectral form factor (SFF) captures universal spectral fluctuations as signatures of quantum chaos, and has been instrumental in advancing multiple frontiers of physics including the studies of black holes and quantum many-body systems. However, the measurement of SFF in many-body systems is challenging due to the difficulty in resolving level spacings that become exponentially small with increasing system size. Here we experimentally measure the SFF to probe the presence or absence of chaos in quantum many-body systems using a superconducting quantum processor with a randomized measurement protocol. For a Floquet chaotic system, we observe signatures of spectral rigidity of random matrix theory in SFF given by the ramp-plateau behavior. For a Hamiltonian system, we utilize SFF to distinguish the quantum many-body chaotic phase and the prethermal many-body localization. We observe the dip-ramp-plateau behavior of random matrix theory in the chaotic phase, and contrast the scaling of the plateau time in system size between the many-body chaotic and localized phases. Furthermore, we probe the eigenstate statistics by measuring a generalization of the SFF, known as the partial SFF, and observe distinct behaviors in the purities of the reduced density matrix in the two phases. This work unveils a new way of extracting the universal signatures of many-body quantum chaos in quantum devices by probing the correlations in eigenenergies and eigenstates., Comment: 12 pages, 9 figures

In the realm of shared memory systems, the challenge of reader-writer synchronization is closely coupled with the potential for readers to access outdated updates. Read-Copy-Update (RCU) is a synchronization primitive that allows for concurrent and non-blocking read access to fresh data. This is achieved through the creation of updated data copies, with each prior version retained until all associated read-locks are released. Given the principle that frequent updating keeps information fresh, the concern is whether we accumulate an infinite number of update copies, leading to excessively large memory usage. This paper analyzes trade-offs between memory usage and update age within real-time status updating systems, focusing specifically on RCU. The analysis demonstrates that with finite read time and read request rate, the average number of updates within the system remains bounded., Comment: Submitted to IEEE INFOCOM Age and Semantics of Information (ASoI) Workshop 2024

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 large-scale 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 and also 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., Comment: 10 pages, 4 figures (main text); 14 pages, 20 figures (supplementary materials)

Greenberger-Horne-Zeilinger (GHZ) states, also known as two-component Schr\"{o}dinger cats, play vital roles in the foundation of quantum physics and, more attractively, in future quantum technologies such as fault-tolerant quantum computation. Enlargement in size and coherent control of GHZ states are both crucial for harnessing entanglement in advanced computational tasks with practical advantages, which unfortunately pose tremendous challenges as GHZ states are vulnerable to noise. Here we propose a general strategy for creating, preserving, and manipulating large-scale GHZ entanglement, and demonstrate a series of experiments underlined by high-fidelity digital quantum circuits. For initialization, we employ a scalable protocol to create genuinely entangled GHZ states with up to 60 qubits, almost doubling the previous size record. For protection, we take a new perspective on discrete time crystals (DTCs), originally for exploring exotic nonequilibrium quantum matters, and embed a GHZ state into the eigenstates of a tailor-made cat scar DTC to extend its lifetime. For manipulation, we switch the DTC eigenstates with in-situ quantum gates to modify the effectiveness of the GHZ protection. Our findings establish a viable path towards coherent operations on large-scale entanglement, and further highlight superconducting processors as a promising platform to explore nonequilibrium quantum matters and emerging applications., Comment: 7 pages, 4 figures + supplementary information

The fabric-based pneumatic exosuit is now a hot research topic because it is lighter and softer than traditional exoskeletons. Existing research focused more on the mechanical properties of the exosuit (e.g., torque and speed), but less on its wearability (e.g., appearance and comfort). This work presents a new design concept for fabric-based pneumatic exosuits Volume Transfer, which means transferring the volume of pneumatic actuators beyond the garments profile to the inside. This allows for a concealed appearance and a larger stress area while maintaining adequate torques. In order to verify this concept, we develop a fabric-based pneumatic exosuit for knee extension assistance. Its profile is only 26mm and its stress area wraps around almost half of the leg. We use a mathematical model and simulation to determine the parameters of the exosuit, avoiding multiple iterations of the prototype. Experiment results show that the exosuit can generate a torque of 7.6Nm at a pressure of 90kPa and produce a significant reduction in the electromyography activity of the knee extensor muscles. We believe that Volume Transfer could be utilized prevalently in future fabric-based pneumatic exosuit designs to achieve a significant improvement in wearability.

Emerging quantum technologies hold the promise of unraveling 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 utilize 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., Comment: 11+15 pages

Time-critical cyber-physical applications demand the timely delivery of information. In this work, we employ a high-speed packet processing testbed to quantitatively analyze a packet forwarding application running on a shared memory multi-processor architecture, where efficient synchronization of concurrent access to a Forwarding Information Base is essential for low-latency and timely delivery of information. While modern packet processing frameworks are optimized for maximum packet throughput, their ability to support timely delivery remains an open question. Here we focus on the age of information performance issues induced by throughput-focused packet processing frameworks. Our results underscore the importance of careful selection of offered load parameters and concurrency constructs in such frameworks., Comment: To be published in IEEE INFOCOM 2023 - IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS)

We examine status updating systems in which time-stamped status updates are stored/written in shared-memory. Specifically, we compare Read-Copy-Update (RCU) and Readers-Writer lock (RWL) as shared-memory synchronization primitives on the update freshness. To demonstrate the tension between readers and writers accessing shared-memory, we consider a network scenario with a pair of coupled updating processes. Location updates of a mobile terminal are written to a shared-memory Forwarder Information Base (FIB) at a network forwarder. An application server sends ``app updates'' to the mobile terminal via the forwarder. Arriving app updates at forwarder are addressed (by reading the FIB) and forwarded to the mobile terminal. If a FIB read returns an outdated address, the misaddressed app update is lost in transit. We redesign these reader and writer processes using preemption mechanisms that improve the timeliness of updates. We present a Stochastic Hybrid System (SHS) framework to analyze location and app update age processes and show how these two age processes are coupled through synchronization primitives. Our analysis shows that using a lock-based primitive (RWL) can serve fresher app updates to the mobile terminal at higher location update rates while lock-less (RCU) mechanism favors timely delivery of app updates at lower location update rates., Comment: Comment 1: Published in INFOCOM 2023 Comment 2: Fixed Typos

Shor's algorithm has seriously challenged information security based on public key cryptosystems. However, to break the widely used RSA-2048 scheme, one needs millions of physical qubits, which is far beyond current technical capabilities. Here, we report a universal quantum algorithm for integer factorization by combining the classical lattice reduction with a quantum approximate optimization algorithm (QAOA). The number of qubits required is O(logN/loglog N), which is sublinear in the bit length of the integer $N$, making it the most qubit-saving factorization algorithm to date. We demonstrate the algorithm experimentally by factoring integers up to 48 bits with 10 superconducting qubits, the largest integer factored on a quantum device. We estimate that a quantum circuit with 372 physical qubits and a depth of thousands is necessary to challenge RSA-2048 using our algorithm. Our study shows great promise in expediting the application of current noisy quantum computers, and paves the way to factor large integers of realistic cryptographic significance., Comment: 32 pages, 12 figures

Non-Abelian anyons are exotic quasiparticle excitations hosted by certain topological phases of matter. They break the fermion-boson dichotomy and obey non-Abelian braiding statistics: their interchanges yield unitary operations, rather than merely a phase factor, in a space spanned by topologically degenerate wavefunctions. They are the building blocks of topological quantum computing. However, experimental observation of non-Abelian anyons and their characterizing braiding statistics is notoriously challenging and has remained elusive hitherto, in spite of various theoretical proposals. Here, we report an experimental quantum digital simulation of projective non-Abelian anyons and their braiding statistics with up to 68 programmable superconducting qubits arranged on a two-dimensional lattice. By implementing the ground states of the toric-code model with twists through quantum circuits, we demonstrate that twists exchange electric and magnetic charges and behave as a particular type of non-Abelian anyons, i.e., the Ising anyons. In particular, we show experimentally that these twists follow the fusion rules and non-Abelian braiding statistics of the Ising type, and can be explored to encode topological logical qubits. Furthermore, we demonstrate how to implement both single- and two-qubit logic gates through applying a sequence of elementary Pauli gates on the underlying physical qubits. Our results demonstrate a versatile quantum digital approach for simulating non-Abelian anyons, offering a new lens into the study of such peculiar quasiparticles.

Quantum many-body simulation provides a straightforward way to understand fundamental physics and connect with quantum information applications. However, suffering from exponentially growing Hilbert space size, characterization in terms of few-body probes in real space is often insufficient to tackle challenging problems such as quantum critical behavior and many-body localization (MBL) in higher dimensions. Here, we experimentally employ a new paradigm on a superconducting quantum processor, exploring such elusive questions from a Fock space view: mapping the many-body system onto an unconventional Anderson model on a complex Fock space network of many-body states. By observing the wave packet propagating in Fock space and the emergence of a statistical ergodic ensemble, we reveal a fresh picture for characterizing representative many-body dynamics: thermalization, localization, and scarring. In addition, we observe a quantum critical regime of anomalously enhanced wave packet width and deduce a critical point from the maximum wave packet fluctuations, which lend support for the two-dimensional MBL transition in finite-sized systems. Our work unveils a new perspective of exploring many-body physics in Fock space, demonstrating its practical applications on contentious MBL aspects such as criticality and dimensionality. Moreover, the entire protocol is universal and scalable, paving the way to finally solve a broader range of controversial many-body problems on future larger quantum devices., Comment: 8 pages, 4 figures + supplementary information

Quantum computing promises to enhance machine learning and artificial intelligence. Different quantum algorithms have been proposed to improve a wide spectrum of machine learning tasks. Yet, recent theoretical works show that, similar to traditional classifiers based on deep classical neural networks, quantum classifiers would suffer from the vulnerability problem: adding tiny carefully-crafted perturbations to the legitimate original data samples would facilitate incorrect predictions at a notably high confidence level. This will pose serious problems for future quantum machine learning applications in safety and security-critical scenarios. Here, we report the first experimental demonstration of quantum adversarial learning with programmable superconducting qubits. We train quantum classifiers, which are built upon variational quantum circuits consisting of ten transmon qubits featuring average lifetimes of 150 $\mu$s, and average fidelities of simultaneous single- and two-qubit gates above 99.94% and 99.4% respectively, with both real-life images (e.g., 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 significantly enhance their robustness to such perturbations. Our results reveal experimentally a crucial vulnerability aspect of quantum learning systems under adversarial scenarios and demonstrate an effective defense strategy against adversarial attacks, which provide a valuable guide for quantum artificial intelligence applications with both near-term and future quantum devices., Comment: 26 pages, 17 figures, 8 algorithms

Quantum many-body scarring (QMBS) -- a recently discovered form of weak ergodicity breaking in strongly-interacting quantum systems -- presents opportunities for mitigating thermalization-induced decoherence in quantum information processsing. However, the existing experimental realizations of QMBS are based on kinetically-constrained systems where an emergent dynamical symmetry "shields" such states from the thermalizing bulk of the spectrum. Here, we experimentally realize a distinct kind of QMBS phenomena by approximately decoupling a part of the many-body Hilbert space in the computational basis. Utilizing a programmable superconducting processor with 30 qubits and tunable couplings, we realize Hilbert space scarring in a non-constrained model in different geometries, including a linear chain as well as a quasi-one-dimensional comb geometry. By performing full quantum state tomography on 4-qubit subsystems, we provide strong evidence for QMBS states by measuring qubit population dynamics, quantum fidelity and entanglement entropy following a quench from initial product states. Our experimental findings broaden the realm of QMBS mechanisms and pave the way to exploiting correlations in QMBS states for applications in quantum information technology.

We report the observation of a symmetry-protected topological time crystal, which is implemented with an array of programmable superconducting qubits. Unlike the time crystals reported in previous experiments, where spontaneous breaking of the discrete time translational symmetry occurs for local observables throughout the whole system, the topological time crystal observed in our experiment breaks the time translational symmetry only at the boundaries and has trivial dynamics in the bulk. More concretely, we observe robust long-lived temporal correlations and sub-harmonic temporal response for the edge spins up to 40 driving cycles. We demonstrate that the sub-harmonic response is independent of whether the initial states are random product states or symmetry-protected topological states, and experimentally map out the phase boundary between the time crystalline and thermal phases. Our work paves the way to exploring peculiar non-equilibrium phases of matter emerged from the interplay between topology and localization as well as periodic driving, with current noisy intermediate-scale quantum processors., Comment: 8 pages main text, and 11 pages for supplementary materials

Background and objective: The stepped wedge cluster randomized trial is a study design increasingly used for public health intervention evaluations. Most previous literature focuses on power calculations for this particular type of cluster randomized trials for continuous outcomes, along with an approximation to this approach for binary outcomes. Although not accurate for binary outcomes, it has been widely used. To improve the approximation for binary outcomes, two new methods for stepped wedge designs (SWDs) of binary outcomes have recently been published. However, these new methods have not been implemented in publicly available software. The objective of this paper is to present power calculation software for SWDs in various settings for both continuous and binary outcomes. Methods: We have developed a SAS macro %swdpwr and an R package swdpwr for power calculation in SWDs. Different scenarios including cross-sectional and cohort designs, binary and continuous outcomes, marginal and conditional models, three link functions, with and without time effects are accommodated in this software. Results: swdpwr provides an efficient tool to support investigators in the design and analysis of stepped wedge cluster randomized trails. swdpwr addresses the implementation gap between newly proposed methodology and their application to obtain more accurate power calculations in SWDs. Conclusions: This user-friendly software makes the new methods more accessible and incorporates as many variations as currently available, which were not supported in other related packages. swdpwr is implemented under two platforms: SAS and R, satisfying the needs of investigators from various backgrounds., Comment: 29 pages, 4 figures

Information dissemination applications (video, news, social media, etc.) with large number of receivers need to be efficient but also have limited loss tolerance. The new Information-Centric Networks (ICN) paradigm offers an alternative approach for reliably delivering data by naming content and exploiting data available at any intermediate point (e.g., caches). However, receivers are often heterogeneous, with widely varying receive rates. When using existing ICN congestion control mechanisms with in-sequence delivery, a particularly thorny problem of receivers going out-of-sync results in inefficiency and unfairness with heterogeneous receivers. We argue that separating reliability from congestion control leads to more scalable, efficient and fair data dissemination, and propose SAID, a Control Protocol for Scalable and Adaptive Information Dissemination in ICN. To maximize the amount of data transmitted at the first attempt, receivers request any next packet (ANP) of a flow instead of next-in-sequence packet, independent of the provider's transmit rate. This allows providers to transmit at an application-efficient rate, without being limited by the slower receivers. SAID ensures reliable delivery to all receivers eventually, by cooperative repair, while preserving privacy without unduly trusting other receivers., Comment: 12 pages