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Nonlinear partial differential equations (PDEs) are crucial for modeling complex fluid dynamics and are foundational to many computational fluid dynamics (CFD) applications. However, solving these nonlinear PDEs is challenging due to the vast computational resources they demand, highlighting the pressing need for more efficient computational methods. Quantum computing offers a promising but technically challenging approach to solving nonlinear PDEs. Recently, Liao proposed a framework that leverages quantum computing to accelerate the solution of nonlinear PDEs based on the homotopy analysis method (HAM), a semi-analytical technique that transforms nonlinear PDEs into a series of linear PDEs. However, the no-cloning theorem in quantum computing poses a major limitation, where directly applying quantum simulation to each HAM step results in exponential complexity growth with the HAM truncation order. This study introduces a "secondary linearization" approach that maps the whole HAM process into a system of linear PDEs, allowing for a one-time solution using established quantum PDE solvers. Our method preserves the exponential speedup of quantum linear PDE solvers while ensuring that computational complexity increases only polynomially with the HAM truncation order. We demonstrate the efficacy of our approach by applying it to the Burgers' equation and the Korteweg-de Vries (KdV) equation. Our approach provides a novel pathway for transforming nonlinear PDEs into linear PDEs, with potential applications to fluid dynamics. This work thus lays the foundation for developing quantum algorithms capable of solving the Navier-Stokes equations, ultimately offering a promising route to accelerate their solutions using quantum computing., Comment: 22 pages, 4 figures

Across finite temperatures and fields, a quantum critical point (QCP) can extend to a quantum critical regime (QCR), characterized by prominent quantum fluctuations and universal scalings. The QCR is essential for comprehending many-body systems and correlated quantum materials, attracting intensive research interest over the past decades. In this study, we identify a distinct quantum supercritical regime (QSR) that also originates from the QCP but is driven by a symmetry-breaking field $h$, which couples to the order parameter. The QSR has crossover lines following $T \propto h^{\frac{z\nu}{\beta+\gamma}}$, where $\beta, \gamma, z, \nu$ are the critical exponents. Amongst other intriguing phenomena in QSR, the magnetocaloric effect (MCE) exhibits a universally diverging magnetic Gr\"uneisen ratio as $\Gamma_h \equiv \frac{1}{T} (\frac{\partial T}{\partial h})_{S} \propto T^{-\frac{\beta+\gamma}{z\nu}}$. This constitutes a boost in the universal MCE, when compared to that of QCR, as even a small field $h$ can induce a dramatic temperature variation. Experimental realizations involving quantum Ising and Heisenberg magnets are discussed. These systems offer an ideal platform for investigating quantum supercriticality and also hold significant potential as advanced refrigerants., Comment: 5 pages, 4 figures

In recent years, quantum computation has been rapidly advancing, driving a technological revolution with significant potential across various sectors, particularly in finance. Despite this, the insurance industry, an essential tool for mitigating unforeseen risks and losses, has received limited attention. This paper provides an initial exploration into the realm of quantum computational insurance and actuarial science. After introducing key insurance models and challenges, we examine quantum algorithms designed to address complex insurance issues. Our study includes experimental and numerical demonstrations of quantum applications in non-life insurance, life insurance, and reinsurance. Additionally, we explore the timeline for quantum insurance, the development of quantum-enhanced insurance products, and the challenges posed by quantum computational advancements., Comment: 10 pages, 5 figures

Large-scale quantum computation requires to be performed in the fault-tolerant manner. One crucial challenge of fault-tolerant quantum computing (FTQC) is reducing the overhead of implementing logical gates. Recently work proposed correlated decoding and ``algorithmic fault tolerance" to achieve constant-time logical gates that enables universal quantum computation. However, for circuits involving mid-circuit measurements and feedback, the previous scheme for constant-time logical gates is incompatible with window-based decoding, which is a scalable approach for handling large-scale circuits. In this work, we propose an architecture that employs delayed fixup circuits and window-based correlated decoding, realizing scalable constant-time logical gates. This design significantly reduces both the frequency and duration of decoding, while maintaining support for constant-time and universal logical gates across a broad class of quantum codes. More importantly, by spatial parallelism of windows, this architecture well adapts to time-optimal FTQC, making it particularly useful for large-scale quantum computation. Using Shor's algorithm as an example, we explore the application of our architecture and reveals the promising potential of using constant-time logical gates to perform large-scale quantum computation with acceptable overhead on physical systems like ion traps., Comment: 12 pages, 9 figures

Traditional magnetic sub-Kelvin cooling relies on the nearly free local moments in hydrate paramagnetic salts, whose utility is hampered by the dilute magnetic ions and low thermal conductivity. Here we propose to use instead fractional excitations inherent to quantum spin liquids (QSLs) as an alternative, which are sensitive to external fields and can induce a very distinctive magnetocaloric effect. With state-of-the-art tensor-network approach, we compute low-temperature properties of Kitaev honeycomb model. For the ferromagnetic case, strong demagnetization cooling effect is observed due to the nearly free $Z_2$ vortices via spin fractionalization, described by a paramagnetic equation of state with a renormalized Curie constant. For the antiferromagnetic Kitaev case, we uncover an intermediate-field gapless QSL phase with very large spin entropy, possibly due to the emergence of spinon Fermi surface. Potential realization of topological excitation cooling in Kitaev materials is also discussed, which may offer a promising pathway to circumvent existing limitations in the paramagnetic hydrates., Comment: 10 pages, 4 figures; supplementary materials; to appear in Nat. Commun. (2024)

Quantum computational fluid dynamics (QCFD) offers a promising alternative to classical computational fluid dynamics (CFD) by leveraging quantum algorithms for higher efficiency. This paper introduces a comprehensive QCFD method, including an iterative method "Iterative-QLS" that suppresses error in quantum linear solver, and a subspace method to scale the solution to a larger size. We implement our method on a superconducting quantum computer, demonstrating successful simulations of steady Poiseuille flow and unsteady acoustic wave propagation. The Poiseuille flow simulation achieved a relative error of less than $0.2\%$, and the unsteady acoustic wave simulation solved a 5043-dimensional matrix. We emphasize the utilization of the quantum-classical hybrid approach in applications of near-term quantum computers. By adapting to quantum hardware constraints and offering scalable solutions for large-scale CFD problems, our method paves the way for practical applications of near-term quantum computers in computational science., Comment: 31 pages, 10 figures

Quantum machine learning has demonstrated significant potential in solving practical problems, particularly in statistics-focused areas such as data science and finance. However, challenges remain in preparing and learning statistical models on a quantum processor due to issues with trainability and interpretability. In this letter, we utilize the maximum entropy principle to design a statistics-informed parameterized quantum circuit (SI-PQC) for efficiently preparing and training of quantum computational statistical models, including arbitrary distributions and their weighted mixtures. The SI-PQC features a static structure with trainable parameters, enabling in-depth optimized circuit compilation, exponential reductions in resource and time consumption, and improved trainability and interpretability for learning quantum states and classical model parameters simultaneously. As an efficient subroutine for preparing and learning in various quantum algorithms, the SI-PQC addresses the input bottleneck and facilitates the injection of prior knowledge., Comment: 19 pages, 5 figures

The rapid development of quantum computers has enabled demonstrations of quantum advantages on various tasks. However, real quantum systems are always dissipative due to their inevitable interaction with the environment, and the resulting non-unitary dynamics make quantum simulation challenging with only unitary quantum gates. In this work, we present an innovative and scalable method to simulate open quantum systems using quantum computers. We define an adjoint density matrix as a counterpart of the true density matrix, which reduces to a mixed-unitary quantum channel and thus can be effectively sampled using quantum computers. This method has several benefits, including no need for auxiliary qubits and noteworthy scalability. Moreover, accurate long-time simulation can also be achieved as the adjoint density matrix and the true dissipated one converge to the same state. Finally, we present deployments of this theory in the dissipative quantum $XY$ model for the evolution of correlation and entropy with short-time dynamics and the disordered Heisenberg model for many-body localization with long-time dynamics. This work promotes the study of real-world many-body dynamics with quantum computers, highlighting the potential to demonstrate practical quantum advantages., Comment: 13 pages, 6 figures

Motivated by widespread dominance hierarchy, growth of group sizes, and feedback mechanisms in social species, we are devoted to exploring the scalable second-order consensus of hierarchical groups. More specifically, a hierarchical group consists of a collection of agents with double-integrator dynamics on a directed acyclic graph with additional reverse edges, which characterize feedback mechanisms across hierarchical layers. As the group size grows and the reverse edges appear, we investigate whether the absolute velocity protocol and the relative velocity protocol can preserve the system consensus property without tuning the control gains. It is rigorously proved that the absolute velocity protocol is able to achieve completely scalable second-order consensus but the relative velocity protocol cannot. This result theoretically reveals how the scalable coordination behavior in hierarchical groups is determined by local interaction rules. Moreover, we develop a hierarchical structure in order to achieve scalable second-order consensus for networks of any size and with any number of reverse edges., Comment: 9 pages, 1 figure

Low-dimensional quantum magnets, particularly those with strong spin frustration, are characterized by their notable spin fluctuations. Nuclear magnetic resonance (NMR) serves as a sensitive probe of low-energy fluctuations that offers valuable insight into rich magnetic phases and emergent phenomena in quantum magnets. Although experimentally accessible, the numerical simulation of NMR relaxation rates, specifically the spin-lattice relaxation rate $1/T_1$, remains a significant challenge. Analytical continuation based on Monte Carlo calculations are hampered by the notorious negative sign for frustrated systems, and the real-time simulations incur significant costs to capture low-energy fluctuations. Here we propose computing the relaxation rate using thermal tensor networks (TTNs), which provides a streamlined approach by calculating its imaginary-time proxy. We showcase the accuracy and versatility of our methodology by applying it to one-dimensional spin chains and two-dimensional lattices, where we find that the critical exponents $\eta$ and $z\nu$ can be extracted from the low-temperature scalings of the simulated $1/T_1$ near quantum critical points. Our results also provide insights into the low-dimensional and frustrated magnetic materials, elucidating universal scaling behaviors in the Ising chain compound CoNb$_2$O$_6$ and revealing the renormalized classical behaviors in the triangular-lattice antiferromagnet Ba$_8$CoNb$_6$O$_{24}$. We apply the approach to effective model of the family of frustrated magnets AYbCh$_2$ (A = Na, K, Cs, and Ch = O, S, Se), and find dramatic changes from spin ordered to the proposed quantum spin liquid phase. Overall, with high reliability and accuracy, the TTN methodology offers a systematic strategy for studying the intricate dynamics observed across a broad spectrum of quantum magnets and related fields., Comment: 15 pages, 12 figures

Quantum integrability emerging near a quantum critical point (QCP) is manifested by exotic excitation spectrum that is organized by the associated algebraic structure. A well known example is the emergent $E_8$ integrability near the QCP of a transverse field Ising chain (TFIC), which was long predicted theoretically and initially proposed to be realized in the quasi-one-dimensional (q1D) quantum magnet CoNb$_2$O$_6$. However, later measurements on the spin excitation spectrum of this material revealed a series of satellite peaks that cannot be described by the $E_8$ Lie algebra. Motivated by these experimental progresses, we hereby revisit the spin excitations of CoNb$_2$O$_6$ by combining numerical calculation and analytical analysis. We show that, as effects of strong interchain fluctuations, the spectrum of the system near the 1D QCP is characterized by the $D_{8}^{(1)}$ Lie algebra with robust topological soliton excitation. We further show that the $D_{8}^{(1)}$ spectrum can be realized in a broad class of interacting quantum systems. Our results advance the exploration of integrability and manipulation of topological excitations in quantum critical systems., Comment: 6 pages, 3 figures - Supplementary Material 5 pages

The field of quantum deep learning presents significant opportunities for advancing computational capabilities, yet it faces a major obstacle in the form of the "information loss problem" due to the inherent limitations of the necessary quantum tomography in scaling quantum deep neural networks. This paper introduces an end-to-end Quantum Vision Transformer (QViT), which incorporates an innovative quantum residual connection technique, to overcome these challenges and therefore optimize quantum computing processes in deep learning. Our thorough complexity analysis of the QViT reveals a theoretically exponential and empirically polynomial speedup, showcasing the model's efficiency and potential in quantum computing applications. We conducted extensive numerical tests on modern, large-scale transformers and datasets, establishing the QViT as a pioneering advancement in applying quantum deep neural networks in practical scenarios. Our work provides a comprehensive quantum deep learning paradigm, which not only demonstrates the versatility of current quantum linear algebra algorithms but also promises to enhance future research and development in quantum deep learning., Comment: 24pages, 10 figures

Emergent Ising$_h^2$ integrability is anticipated in a quantum Ising ladder composed of two weakly coupled, critical transverse field Ising chains. This integrable system is remarkable for including eight types of massive relativistic particles, with their scattering matrix and spectrum characterized by the $\mathcal{D}_8^{(1)}$ Lie algebra. In this article we delve into the zero-temperature spin dynamics of this integrable quantum Ising ladder. By computing the dynamical structure factors from analytical form factor approach, we clearly identify dispersive single-particle excitations of (anti-) soliton and breathers as well as their multi-particle continua in the spin dynamical spectrum. We show that the selection rule to the form factor, which is inherent in the intrinsic charge-parity $\mathcal{C}$ of the Ising$_h^2$ particles as well as the local spin operators, causes a significant result that $\mathcal{C}$-odd particles, termed as dark particles, cannot be directly excited from the ground state through any local or quasi-local operations. Furthermore, the lightest dark particle is proposed to be generated and controlled through resonant absorption-resonant emission processes. The long lifetime of dark particle suggests its potential as a stable qubit for advancing quantum information technology., Comment: 5 pages, 4 figures - Supplementary Material 9 pages

Fractional magnetisation plateaus, in which the magnetisation is pinned at a fraction of its saturated value within a range of external magnetic field, are spectacular macroscopic manifestations of the collective quantum behaviours. One prominent example of the plateau phase is found in spin-1/2 triangular-lattice antiferromagnets featuring strong geometrical frustration, and is often interpreted as quantum-fluctuation-stabilised state in magnetic field via the "order-by-disorder" mechanism. Here, we observe an unprecedented 1/3 magnetisation plateau between 5.2 and 7.4 T at 2 K in a spin-1 antiferromagnet Na$_3$Ni$_2$BiO$_6$ with a honeycomb lattice, where conventionally no geometrical frustration is anticipated. By carrying out elastic neutron scattering measurements, we propose the spin structure of the plateau phase to be an unusual partial spin-flop ferrimagnetic order, transitioning from the zigzag antiferromagnetic order in zero field. Our theoretical calculations show that the plateau phase is stabilised by the bond-anisotropic Kitaev interaction. These results provide a new paradigm for the exploration of rich quantum phases in frustrated magnets and exotic Kitaev physics in high-spin systems., Comment: Submitted version, 10 pages, 5 figures. Final version has been published in Nature Physics

Memory corruption attacks (MCAs) refer to malicious behaviors of system intruders that modify the contents of a memory location to disrupt the normal operation of computing systems, causing leakage of sensitive data or perturbations to ongoing processes. Unlike general-purpose systems, unmanned systems cannot deploy complete security protection schemes, due to their limitations in size, cost and performance. MCAs in unmanned systems are particularly difficult to defend against. Furthermore, MCAs have diverse and unpredictable attack interfaces in unmanned systems, severely impacting digital and physical sectors. In this paper, we first generalize, model and taxonomize MCAs found in unmanned systems currently, laying the foundation for designing a portable and general defense approach. According to different attack mechanisms, we found that MCAs are mainly categorized into two types--return2libc and return2shellcode. To tackle return2libc attacks, we model the erratic operation of unmanned systems with cycles and then propose a cycle-task-oriented memory protection (CToMP) approach to protect control flows from tampering. To defend against return2shellcode attacks, we introduce a secure process stack with a randomized memory address by leveraging the memory pool to prevent Shellcode from being executed. Moreover, we discuss the mechanism by which CToMP resists the ROP attack, a novel variant of return2libc attacks. Finally, we implement CToMP on CUAV V5+ with Ardupilot and Crazyflie. The evaluation and security analysis results demonstrate that the proposed approach CToMP is resilient to various MCAs in unmanned systems with low footprints and system overhead., Comment: This paper has been accepted by SCIENCE CHINA Information Sciences

Phase transitions in condensed matter are often linked to exotic emergent properties. We study the fully frustrated bilayer Heisenberg antiferromagnet to demonstrate that an applied magnetic field creates a novel emergent criticality. The quantum phase diagram contains four states, the DS (singlets on every interlayer dimer bond), DTAF (all triplets with antiferromagnetic order), TC (a singlet-triplet checkerboard) and FM (saturated ferromagnet). The thermal phase diagram is dominated by a wall of discontinuities extending from the zero-field DTAF-DS transition to a quantum critical endpoint where the field drives the DTAF and TC into the FM. This first-order wall is terminated at finite temperatures by a line of critical points, where the Berezinskii-Kosterlitz-Thouless (BKT) transition of the DTAF and the thermal Ising transition of the TC also terminate. We demonstrate by quantum Monte Carlo simulations that the BKT transition does not change the Ising nature of the DTAF-DS critical line. By contrast, the combination of symmetries merging on the multicritical DTAF-TC line leads to a 4-state Potts universality not contained in the microscopic Hamiltonian, which we associate with the Ashkin-Teller model. Our results represent a systematic step in understanding emergent phenomena in quantum magnetic materials including the ``Shastry-Sutherland compound'' SrCu$_2$(BO$_3$)$_2$., Comment: 10+8 pages, 5+7 figures

Quantum Random Access Memory (QRAM) is a critical component for enabling data queries in superposition, which is the cornerstone of quantum algorithms. Among various QRAM architectures, the bucket-brigade model stands out due to its noise resilience. This paper presents a hardware-efficient native gate set {iSCZ, C-iSCZ} for implementing bucket-brigade QRAM on superconducting platforms. The experimental feasibility of the proposed gate set is demonstrated, showing high fidelity and reduced complexity. By leveraging the complementary control property in QRAM, our approach directly substitutes the conventional {SWAP, CSWAP} gates with the new gate set, eliminating decomposition overhead and significantly reducing circuit depth and gate count., Comment: 19 pages, 15 figures

The nature of the 1/9-magnetization plateau of the spin-1/2 kagome Heisenberg antiferromagnet remains controversial due to the exotic physical properties and high complexity induced by the geometrical frustration. Instead of a Z3 quantum spin liquid revealed on a cylinder, we show on an infinite-size lattice that the 1/9 plateau can be described by a valence bond crystal (VBC) that breaks spatial translational invariance. Consistent results are achieved by two accurate tensor network methods, namely the full-update infinite projected-entangled pair states and the projected-entangled simplex states. The VBC exhibits an hourglass pattern with $\sqrt{3}\times\sqrt{3}$ spatial symmetry, demonstrated by magnetizations, bond energies, and three-body correlators. The spatial inversion symmetry in the $\sqrt{3}\times\sqrt{3}$ VBC is instantly broken with the presence of the difference between the coupling strengths in the up and down triangles, suggesting the existence of gapless excitations. The gapless nature of the 1/9 plateau is further indicated by the scaling behaviors of the entanglement entropy and the correlation length, which indicate a c=1 conformal field theory., Comment: 6 pages, 5 figures, Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevB.107.L220401

The increasing focus on long-term time series prediction across various fields has been significantly strengthened by advancements in quantum computation. In this paper, we introduce a data-driven method designed for long-term time series prediction with quantum dynamical embedding (QDE). This approach enables a trainable embedding of the data space into an extended state space, allowing for the recursive retrieval of time series information. Based on its independence of time series length, this method achieves depth-efficient quantum circuits that are crucial for near-term quantum computers. Numerical simulations demonstrate the model's improved performance in prediction accuracy and resource efficiency over existing methods, as well as its effective denoising capabilities. We implement this model on the Origin ''Wukong'' superconducting quantum processor with a learnable error-cancellation layer (LECL) for error mitigation, further validating the practical applicability of our approach on near-term quantum devices. Furthermore, the theoretical analysis of the QDE's dynamical properties and its universality enhances its potential for time series prediction. This study establishes a significant step towards the processing of long-term time series on near-term quantum computers, integrating data-driven learning with discrete dynamical embedding for enhanced forecasting capabilities., Comment: 20 pages, 12 figures

Program implementation and simulation are essential for research in the field of quantum algorithms. However, complex and large-scale quantum algorithms can pose challenges for existing quantum programming languages and simulators. Here, we present a scalable program implementation of the quantum walk on a sparse matrix and the quantum linear solver based on the quantum walk. Our implementation is based on a practical scenario in which the sparse matrix is stored in the compressed-sparse-column format in quantum random access memory. All necessary modules are implemented unitarily and are ensured to be decomposed at the quantum gate level, including implementing a quantum binary search and a modification of the original algorithm. The program is validated using a highly efficient quantum circuit simulator which is based on the register level and sparse state representation. With only a single core, we simulate the quantum walk on a 16384-dimensional matrix with 582 qubits in 1.1 minutes per step, as well as a quantum linear solver up to 1024 dimensions and 212245 steps in 70 hours. Our work narrows the gap between the simulation of a quantum algorithm and its classical counterparts, where the asymptotic complexity of our quantum linear solver simulation approximates a classical linear solver. These program implementation and simulation techniques have the potential to expand the boundary of numerical research for large-scale quantum algorithms, with implications for the development of error-correction-era quantum computing solutions., Comment: 17 pages, 11 figures

Quantum Random Access Memory (QRAM) is a critical component for loading classical data into quantum computers. While constructing a practical QRAM presents several challenges, including the impracticality of an infinitely large QRAM size and a fully error-correction implementation, it is essential to consider a practical case where the QRAM has a limited size. In this work, we focus on the access of larger data sizes without keeping on increasing the size of the QRAM. Firstly, we address the challenge of word length, as real-world datasets typically have larger word lengths than the single-bit data that most previous studies have focused on. We propose a novel protocol for loading data with larger word lengths $k$ without increasing the number of QRAM levels $n$. By exploiting the parallelism in the data query process, our protocol achieves a time complexity of $O(n+k)$ and improves error scaling performance compared to existing approaches. Secondly, we provide a data-loading method for general-sized data access tasks when the number of data items exceeds $2^n$, which outperforms the existing hybrid QRAM+QROM architecture. Our method contributes to the development of time and error-optimized data access protocols for QRAM devices, reducing the qubit count and error requirements for QRAM implementation, and making it easier to construct practical QRAM devices with a limited number of physical qubits., Comment: 19 pages, 7 figures. Changes in v2: Some minor revisions, and extend the Supplementary Information

Inspired by recent experimental measurements [Guo \textit{et al.}, Phys. Rev. Lett.~\textbf{124}, 206602 (2020); Jim\'enez \textit{et al.}, Nature \textbf{592}, 370 (2021)] on frustrated quantum magnet SrCu$_2$(BO$_3$)$_2$ under combined pressure and magnetic fields, we study the related spin-$1/2$ Shastry-Sutherland (SS) model using state-of-the-art tensor network methods. By calculating thermodynamics, correlations and susceptibilities, we find, in zero magnetic field, not only a line of first-order plaquette-singlet (PS) to dimer-singlet phase transition ending with a critical point, but also signatures of the ordered PS transition with its critical endpoint terminating on this first-order line. Moreover, we uncover prominent magnetic barocaloric responses, a novel type of quantum correlation induced cooling effect, in the strongly fluctuating supercritical regime. Under finite fields, we identify a quantum phase transition from the PS phase to the spin supersolid phase that breaks simultaneously lattice translational and spin rotational symmetries. The present findings on the SS model are accessible in current experiments and would shed new light on exotic critical and supercritical phenomena in archetypal frustrated quantum magnets., Comment: Close to the published version. 7 pages, 4 figures (SM 9 pages, 12 figures)

By performing experiment and model studies on a triangular-lattice dipolar magnet KBaGd(BO$_3$)$_2$ (KBGB), we find the highly frustrated magnet with a planar anisotropy hosts a strongly fluctuating dipolar spin liquid (DSL), which originates from the intriguing interplay between dipolar and Heisenberg interactions. The DSL constitutes an extended regime in the field-temperature phase diagram, which gets lowered in temperature as field increases and eventually ends with an unconventional quantum critical point (QCP) at $B_c\simeq 0.75$~T. Based on dipolar Heisenberg model calculations, we identify the DSL as a Berezinskii-Kosterlitz-Thouless (BKT) phase with emergent U(1) symmetry. Due to the tremendous entropy accumulation that can be related to the strong BKT and quantum fluctuations, unprecedented magnetic cooling effects are observed in the DSL regime and particularly near the QCP, making KBGB a superior dipolar coolant to commercial Gd-based refrigerants. We establish the phase diagram for triangular-lattice dipolar quantum magnets where emergent symmetry plays an essential role, and provide a basis and opens an avenue for their applications in sub-Kelvin refrigeration., Comment: 7 pages and 4 figures in main text, 5 pages and 4 figures in Supplementary Materials

The continuous time stochastic process is a mainstream mathematical instrument modeling the random world with a wide range of applications involving finance, statistics, physics, and time series analysis, while the simulation and analysis of the continuous time stochastic process is a challenging problem for classical computers. In this work, a general framework is established to prepare the path of a continuous time stochastic process in a quantum computer efficiently. The storage and computation resource is exponentially reduced on the key parameter of holding time, as the qubit number and the circuit depth are both optimized via our compressed state preparation method. The desired information, including the path-dependent and history-sensitive information that is essential for financial problems, can be extracted efficiently from the compressed sampling path, and admits a further quadratic speed-up. Moreover, this extraction method is more sensitive to those discontinuous jumps capturing extreme market events. Two applications of option pricing in Merton jump diffusion model and ruin probability computing in the collective risk model are given., Comment: 37 pages, 15 figures

Human limb motion tracking and recognition plays an important role in medical rehabilitation training, lower limb assistance, prosthetics design for amputees, feedback control for assistive robots, etc. Lightweight wearable sensors, including inertial sensors, surface electromyography sensors, and flexible strain/pressure, are promising to become the next-generation human motion capture devices. Herein, we present a wireless wearable device consisting of a sixteen-channel flexible sponge-based pressure sensor array to recognize various human lower limb motions by detecting contours on the human skin caused by calf gastrocnemius muscle actions. Each sensing element is a round porous structure of thin carbon nanotube/polydimethylsiloxane nanocomposites with a diameter of 4 mm and thickness of about 400 {\mu}m. Ten human subjects were recruited to perform ten different lower limb motions while wearing the developed device. The motion classification result with the support vector machine method shows a macro-recall of about 97.3% for all ten motions tested. This work demonstrates a portable wearable muscle activity detection device with a lower limb motion recognition application, which can be potentially used in assistive robot control, healthcare, sports monitoring, etc., Comment: 17 pages, 6 figures

The deconfined quantum critical point (DQCP) represents a paradigm shift in quantum matter studies, presenting a "beyond Landau" scenario for order--order transitions. Its experimental realization, however, has remained elusive. Using high-pressure $^{11}$B NMR measurements on the quantum magnet SrCu$_2$(BO$_3$)$_2$, we here demonstrate a magnetic-field induced plaquette-singlet to antiferromagnetic transition above 1.8 GPa at a remarkably low temperature, $T_{\rm c}\simeq 0.07$ K. First-order signatures of the transition weaken with increasing pressure, and we observe quantum critical scaling at the highest pressure, 2.4 GPa. Supported by model calculations, we suggest that these observations can be explained by a proximate DQCP inducing critical quantum fluctuations and emergent O(3) symmetry of the order parameters. Our findings take the DQCP from a theoretical concept to a concrete experimental platform.

We study the critical scaling and dynamical signatures of fractionalized excitations at two different deconfined quantum critical points (DQCPs) in an $S = 1/2$ spin chain by using the time evolution of infinite matrix product states. The scaling of the correlation functions and the dispersion of the conserved current correlations explicitly show the emergence of enhanced continuous symmetries at these DQCPs. The dynamical structure factors in several different channels reveal the development of deconfined fractionalized excitations at the DQCPs. Furthermore, we find an effective spin-charge separation at the DQCP between the ferromagnetic (FM) and valence bond solid (VBS) phases, and identify two continua associated to different types of fractionalized excitations at the DQCP between the $X$-direction and $Z$-direction FM phases. Our findings not only provide direct evidence for the DQCP in one dimension but also shed light on exploring the DQCP in higher dimensions.

We show an $\rm O(4)$ symmetry emerges at a deconfined quantum tricritical point of a valence bond solid and two ferromagnetic phases in an $S = 1/2$ frustrated spin chain by combining analytical analysis and numerical calculations with the time evolution of infinite matrix product states. With this symmetry, the valence-bond solid and the three magnetic order parameters form an $\rm O(4)$ pseudovector in the infrared limit, and can continuously rotate into each other. We numerically determine the location of the quantum tricritical point and study the scaling of the correlation functions of the $\rm O(4)$ vector components and associated conserved currents. The critical behaviors of these correlation functions are all in accord with field theoretical results. The emergent $\rm O(4)$ symmetry at the tricritical point is justified by the integer value of the scaling dimension of the emergent Noether conserved currents. Our findings not only give direct evidence of such a high emergent symmetry at an one-dimensional valence bond solid to magnetic transition but also shed light on exploring emergent symmetries in higher dimensions., Comment: submitted to: Journal of Physics A: Mathematical and Theoretical

We study the ground state phase diagram of the Shastry-Sutherland model by using the variational optimization of the infinite tensor network states, and find a weakly first-order transition between the plaquette and the antiferromagnetic states. The full plaquette state strongly competes with the empty plaquette ground state, with an energy difference less than $10^{-4}J$. We show a staggered ring exchange interaction that preserves the Shastry-Sutherland lattice symmetry can stabilize the full plaquette ground state. In light of this, we propose the triple point where the full plaquette, empty plaquette, and antiferromagnetic phases meet as a deconfined quantum critical point., Comment: 5.5+2 pages, 4+3 figures

Mobile and IoT applications have greatly enriched our daily life by providing convenient and intelligent services. However, these smart applications have been a prime target of adversaries for stealing sensitive data. It poses a crucial threat to users' identity security, financial security, or even life security. Research communities and industries have proposed many Information Flow Control (IFC) techniques for data leakage detection and prevention, including secure modeling, type system, static analysis, dynamic analysis, \textit{etc}. According to the application's development life cycle, although most attacks are conducted during the application's execution phase, data leakage vulnerabilities have been introduced since the design phase. With a focus on lifecycle protection, this survey reviews the recent representative works adopted in different phases. We propose an information flow based defensive chain, which provides a new framework to systematically understand various IFC techniques for data leakage detection and prevention in Mobile and IoT applications. In line with the phases of the application life cycle, each reviewed work is comprehensively studied in terms of technique, performance, and limitation. Research challenges and future directions are also pointed out by consideration of the integrity of the defensive chain., Comment: 36 pages, 6 figures, 6 tables

Quantitative trading is an integral part of financial markets with high calculation speed requirements, while no quantum algorithms have been introduced into this field yet. We propose quantum algorithms for high-frequency statistical arbitrage trading in this work by utilizing variable time condition number estimation and quantum linear regression.The algorithm complexity has been reduced from the classical benchmark O(N^2d) to O(sqrt(d)(kappa)^2(log(1/epsilon))^2 )). It shows quantum advantage, where N is the length of trading data, and d is the number of stocks, kappa is the condition number and epsilon is the desired precision. Moreover, two tool algorithms for condition number estimation and cointegration test are developed.

In social sciences, there is currently no consensus on the mechanism for cultural evolution. The evolution of first names of newborn babies offers a remarkable example for the researches in the field. Here we perform statistical analyses on over 100 years of data in the United States. We focus in particular on how the frequency-rank distribution and inequality of baby names change over time. We propose a stochastic model where name choice is determined by personalized preference and social influence. Remarkably, variations on the strength of personalized preference can account satisfactorily for the observed empirical features. Therefore, we claim that personalization drives cultural evolution, at least in the example of baby names.

When a micro cantilever with a nano-scale tip is manipulated on a substrate with atomic-scale roughness, the periodic lateral frictional force and stochastic fluctuations may induce stick-slip motion of the cantilever tip, which greatly decreases the precision of the nano manipulation. This unwanted motion cannot be reduced by open-loop control especially when there exist parameter uncertainties in the system model, and thus needs to introduce feedback control. However, real-time feedback cannot be realized by the existing virtual reality virtual feedback techniques based on the position sensing capacity of the atomic force microscopy (AFM). To solve this problem, we propose a new method to design real-time feedback control based on the force sensing approach to compensate for the disturbances and thus reduce the stick-slip motion of the cantilever tip. Theoretical analysis and numerical simulations show that the controlled motion of the cantilever tip tracks the desired trajectory with much higher precision. Further investigation shows that our proposal is robust under various parameter uncertainties. Our study opens up new perspectives of real-time nano manipulation., Comment: 8 pages, 10 figures

In this paper, we investigate the economic mobility in some money transfer models which have been applied into the research on wealth distribution. We demonstrate the mobility by recording the time series of agents' ranks and observing their volatility. We also compare the mobility quantitatively by employing an index, "the per capita aggregate change in log-income", raised by economists. Like the shape of distribution, the character of mobility is also decided by the trading rule in these transfer models. It is worth noting that even though different models have the same type of distribution, their mobility characters may be quite different., Comment: 17 pages, 4 figures, 2nd version

In this paper the dependence of wealth distribution and the velocity of money on the required reserve ratio is examined based on a random transfer model of money and computer simulations. A fractional reserve banking system is introduced to the model where money creation can be achieved by bank loans and the monetary aggregate is determined by the monetary base and the required reserve ratio. It is shown that monetary wealth follows asymmetric Laplace distribution and latency time of money follows exponential distribution. The expression of monetary wealth distribution and that of the velocity of money in terms of the required reserve ratio are presented in a good agreement with simulation results., Comment: 21 pages, 8 figures

Recently, in order to explore the mechanism behind wealth or income distribution, several models have been proposed by applying principles of statistical mechanics. These models share some characteristics, such as consisting of a group of individual agents, a pile of money and a specific trading rule. Whatever the trading rule is, the most noteworthy fact is that money is always transferred from one agent to another in the transferring process. So we call them money transfer models. Besides explaining income and wealth distributions, money transfer models can also be applied to other disciplines. In this paper we summarize these areas as statistical distribution, economic mobility, transfer rate and money creation. First, money distribution (or income distribution) can be exhibited by recording the money stock (flow). Second, the economic mobility can be shown by tracing the change in wealth or income over time for each agent. Third, the transfer rate of money and its determinants can be analyzed by tracing the transferring process of each one unit of money. Finally, money creation process can also be investigated by permitting agents go into debts. Some future extensions to these models are anticipated to be structural improvement and generalized mathematical analysis., Comment: 5 pages, To appear in "Practical Fruits of Econophysics", Ed. H. Takayasu (Springer-Verlag Tokyo), Proc. 3rd Nikkei Econophysics Symposium, Tokyo, Nov 2004

The effects of saving and spending patterns on holding time distribution of money are investigated based on the ideal gas-like models. We show the steady-state distribution obeys an exponential law when the saving factor is set uniformly, and a power law when the saving factor is set diversely. The power distribution can also be obtained by proposing a new model where the preferential spending behavior is considered. The association of the distribution with the probability of money to be exchanged has also been discussed., Comment: 9 pages, 6 figures