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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

Topological photonics provides a novel platform to explore topological physics beyond traditional electronic materials and stimulates promising applications in topologically protected light transport and lasers. Classical degrees of freedom such as polarizations and wavevectors are routinely used to synthesize topological light modes. Beyond the classical regime, inherent quantum nature of light gives birth to a wealth of fundamentally distinct topological states, which offer topological protection in quantum information processing. Here we implement such experiments on topological states of quantized light in a superconducting circuit, on which three resonators are tunably coupled to a gmon qubit. We construct one and two-dimensional Fock-state lattices where topological transport of zero-energy states, strain induced pseudo-Landau levels, valley Hall effect and Haldane chiral edge currents are demonstrated. Our study extends the topological states of light to the quantum regime, bridges topological phases of condensed matter physics with circuit quantum electrodynamics, and offers a new freedom in controlling the quantum states of multiple resonators., Comment: 9 pages, 6 figures

In the management of lung nodules, we are desirable to predict nodule evolution in terms of its diameter variation on Computed Tomography (CT) scans and then provide a follow-up recommendation according to the predicted result of the growing trend of the nodule. In order to improve the performance of growth trend prediction for lung nodules, it is vital to compare the changes of the same nodule in consecutive CT scans. Motivated by this, we screened out 4,666 subjects with more than two consecutive CT scans from the National Lung Screening Trial (NLST) dataset to organize a temporal dataset called NLSTt. In specific, we first detect and pair regions of interest (ROIs) covering the same nodule based on registered CT scans. After that, we predict the texture category and diameter size of the nodules through models. Last, we annotate the evolution class of each nodule according to its changes in diameter. Based on the built NLSTt dataset, we propose a siamese encoder to simultaneously exploit the discriminative features of 3D ROIs detected from consecutive CT scans. Then we novelly design a spatial-temporal mixer (STM) to leverage the interval changes of the same nodule in sequential 3D ROIs and capture spatial dependencies of nodule regions and the current 3D ROI. According to the clinical diagnosis routine, we employ hierarchical loss to pay more attention to growing nodules. The extensive experiments on our organized dataset demonstrate the advantage of our proposed method. We also conduct experiments on an in-house dataset to evaluate the clinical utility of our method by comparing it against skilled clinicians., Comment: MICCAI 2022

The ability to morph flat sheets into complex 3D shapes is extremely useful for fast manufacturing and saving materials while also allowing volumetrically efficient storage and shipment and a functional use. Direct 4D printing is a compelling method to morph complex 3D shapes out of as-printed 2D plates. However, most direct 4D printing methods require multi-material systems involving costly machines. Moreover, most works have used an open-cell design for shape shifting by encoding a collection of 1D rib deformations, which cannot remain structurally stable. Here, we demonstrate the direct 4D printing of an isotropic single-material system to morph 2D continuous bilayer plates into doubly curved and multimodal 3D complex shapes whose geometry can also be locked after deployment. We develop an inverse-design algorithm that integrates extrusion-based 3D printing of a single-material system to directly morph a raw printed sheet into complex 3D geometries such as a doubly curved surface with shape locking. Furthermore, our inverse-design tool encodes the localized shape-memory anisotropy during the process, providing the processing conditions for a target 3D morphed geometry. Our approach could be used for conventional extrusion-based 3D printing for various applications including biomedical devices, deployable structures, smart textiles, and pop-up Kirigami structures.

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.

Solving the wave equation numerically constitutes the majority of the computational cost for applications like seismic imaging and full waveform inversion. An alternative approach is to solve the frequency domain Helmholtz equation, since it offers a reduction in dimensionality as it can be solved per frequency. However, computational challenges with the classical Helmholtz solvers such as the need to invert a large stiffness matrix can make these approaches computationally infeasible for large 3D models or for modeling high frequencies. Moreover, these methods do not have a mechanism to transfer information gained from solving one problem to the next. This becomes a bottleneck for applications like full waveform inversion where repeated modeling is necessary. Therefore, recently a new approach based on the emerging paradigm of physics informed neural networks (PINNs) has been proposed to solve the Helmholtz equation. The method has shown promise in addressing several challenging associated with the conventional algorithms, including flexibility to model additional physics and the use of transfer learning to speed up computations. However, the approach still needs further developments to be fully practicable. Foremost amongst the challenges is the slow convergence speed and reduced accuracy, especially in presence of sharp heterogeneities in the velocity model. Therefore, with an eye on exploring how improved convergence can be obtained for the PINN Helmholtz solvers, we study different activation functions routinely used in the PINN literature, in addition to the swish activation function - a variant of ReLU that has shown improved performance on a number of data science problems. Through a comparative study, we find that swish yields superior performance compared to the other activation functions routinely used in the PINN literature.