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Quantum error correction (QEC) will be essential to achieve the accuracy needed for quantum computers to realise their full potential. The field has seen promising progress with demonstrations of early QEC and real-time decoded experiments. As quantum computers advance towards demonstrating a universal fault-tolerant logical gate set, implementing scalable and low-latency real-time decoding will be crucial to prevent the backlog problem, avoiding an exponential slowdown and maintaining a fast logical clock rate. Here, we demonstrate low-latency feedback with a scalable FPGA decoder integrated into the control system of a superconducting quantum processor. We perform an 8-qubit stability experiment with up to $25$ decoding rounds and a mean decoding time per round below $1$ ${\mu}s$, showing that we avoid the backlog problem even on superconducting hardware with the strictest speed requirements. We observe logical error suppression as the number of decoding rounds is increased. We also implement and time a fast-feedback experiment demonstrating a decoding response time of $9.6$ ${\mu}s$ for a total of $9$ measurement rounds. The decoder throughput and latency developed in this work, combined with continued device improvements, unlock the next generation of experiments that go beyond purely keeping logical qubits alive and into demonstrating building blocks of fault-tolerant computation, such as lattice surgery and magic state teleportation., Comment: 11 pages, 4 figures, Supplementary Information

Skid-steered wheel mobile robots (SSWMRs) operate in a variety of outdoor environments exhibiting motion behaviors dominated by the effects of complex wheel-ground interactions. Characterizing these interactions is crucial both from the immediate robot autonomy perspective (for motion prediction and control) as well as a long-term predictive maintenance and diagnostics perspective. An ideal solution entails capturing precise state measurements for decisions and controls, which is considerably difficult, especially in increasingly unstructured outdoor regimes of operations for these robots. In this milieu, a framework to identify pre-determined discrete modes of operation can considerably simplify the motion model identification process. To this end, we propose an interactive multiple model (IMM) based filtering framework to probabilistically identify predefined robot operation modes that could arise due to traversal in different terrains or loss of wheel traction.

Stabilizing vertical dynamics for on-road and off-road vehicles is an important research area that has been looked at mostly from the point of view of ride comfort. The advent of autonomous vehicles now shifts the focus more towards developing stabilizing techniques from the point of view of onboard proprioceptive and exteroceptive sensors whose real-time measurements influence the performance of an autonomous vehicle. The current solutions to this problem of managing the vertical oscillations usually limit themselves to the realm of active suspension systems without much consideration to modulating the vehicle velocity, which plays an important role by the virtue of the fact that vertical and longitudinal dynamics of a ground vehicle are coupled. The task of stabilizing vertical oscillations for military ground vehicles becomes even more challenging due lack of structured environments, like city roads or highways, in off-road scenarios. Moreover, changes in structural parameters of the vehicle, such as mass (due to changes in vehicle loading), suspension stiffness and damping values can have significant effect on the controller's performance. This demands the need for developing deep learning based control policies, that can take into account an extremely large number of input features and approximate a near optimal control action. In this work, these problems are addressed by training a deep reinforcement learning agent to minimize the vertical acceleration of a scaled vehicle travelling over bumps by controlling its velocity.

Contrary to on-road autonomous navigation, off-road autonomy is complicated by various factors ranging from sensing challenges to terrain variability. In such a milieu, data-driven approaches have been commonly employed to capture intricate vehicle-environment interactions effectively. However, the success of data-driven methods depends crucially on the quality and quantity of data, which can be compromised by large variability in off-road environments. To address these concerns, we present a novel workflow to recreate the exact vehicle and its target operating conditions digitally for domain-specific data generation. This enables us to effectively model off-road vehicle dynamics from simulation data using the Koopman operator theory, and employ the obtained models for local motion planning and optimal vehicle control. The capabilities of the proposed methodology are demonstrated through an autonomous navigation problem of a 1:5 scale vehicle, where a terrain-informed planner is employed for global mission planning. Results indicate a substantial improvement in off-road navigation performance with the proposed algorithm (5.84x) and underscore the efficacy of digital twinning in terms of improving the sample efficiency (3.2x) and reducing the sim2real gap (5.2%).

Societal-scale deployment of autonomous vehicles requires them to coexist with human drivers, necessitating mutual understanding and coordination among these entities. However, purely real-world or simulation-based experiments cannot be employed to explore such complex interactions due to safety and reliability concerns, respectively. Consequently, this work presents an immersive digital twin framework to explore and experiment with the interaction dynamics between autonomous and non-autonomous traffic participants. Particularly, we employ a mixed-reality human-machine interface to allow human drivers and autonomous agents to observe and interact with each other for testing edge-case scenarios while ensuring safety at all times. To validate the versatility of the proposed framework's modular architecture, we first present a discussion on a set of user experience experiments encompassing 4 different levels of immersion with 4 distinct user interfaces. We then present a case study of uncontrolled intersection traversal to demonstrate the efficacy of the proposed framework in validating the interactions of a primary human-driven, autonomous, and connected autonomous vehicle with a secondary semi-autonomous vehicle. The proposed framework has been openly released to guide the future of autonomy-oriented digital twins and research on human-autonomy coexistence., Comment: Accepted at IEEE Conference on Telepresence (TELE) 2024

Off-road autonomy validation presents unique challenges due to the unpredictable and dynamic nature of off-road environments. Traditional methods focusing on sequentially sweeping across the parameter space for variability analysis struggle to comprehensively assess the performance and safety of off-road autonomous systems within the imposed time constraints. This paper proposes leveraging scalable digital twin simulations within high-performance computing (HPC) clusters to address this challenge. By harnessing the computational power of HPC clusters, our approach aims to provide a scalable and efficient means to validate off-road autonomy algorithms, enabling rapid iteration and testing of autonomy algorithms under various conditions. We demonstrate the effectiveness of our framework through performance evaluations of the HPC cluster in terms of simulation parallelization and present the systematic variability analysis of a candidate off-road autonomy algorithm to identify potential vulnerabilities in the autonomy stack's perception, planning and control modules., Comment: Accepted at Ground Vehicle Systems Engineering and Technology Symposium (GVSETS) 2024. Distribution Statement A. Approved for public release; distribution is unlimited. OPSEC #8451. arXiv admin note: text overlap with arXiv:2402.12670, arXiv:2402.14739

Simulation of realistic classical mechanical systems is of great importance to many areas of engineering such as robotics, dynamics of rotating machinery and control theory. In this work, we develop quantum algorithms to estimate quantities of interest such as the kinetic energy in a given classical mechanical system in the presence of friction or damping as well as forcing or source terms, which makes the algorithm of practical interest. We show that for such systems, the quantum algorithm scales polynomially with the logarithm of the dimension of the system. We cast this problem in terms of Hamilton's equations of motion (equivalent to the first variation of the Lagrangian) and solve them using quantum algorithms for differential equations. We then consider the hardness of estimating the kinetic energy of a damped coupled oscillator system. We show that estimating the kinetic energy at a given time of this system to within additive precision is BQP hard when the strength of the damping term is bounded by an inverse polynomial in the number of qubits. We then consider the problem of designing optimal control of classical systems, which can be cast as the second variation of the Lagrangian. In this direction, we first consider the Riccati equation, which is a nonlinear differential equation ubiquitous in control theory. We give an efficient quantum algorithm to solve the Riccati differential equation well into the nonlinear regime. To our knowledge, this is the first example of any nonlinear differential equation that can be solved when the strength of the nonlinearity is asymptotically greater than the amount of dissipation. We then show how to use this algorithm to solve the linear quadratic regulator problem, which is an example of the Hamilton-Jacobi-Bellman equation., Comment: 52 pages

Multi-agent reinforcement learning (MARL) systems usually require significantly long training times due to their inherent complexity. Furthermore, deploying them in the real world demands a feature-rich environment along with multiple embodied agents, which may not be feasible due to budget or space limitations, not to mention energy consumption and safety issues. This work tries to address these pain points by presenting a sustainable digital twin framework capable of accelerating MARL training by selectively scaling parallelized workloads on-demand, and transferring the trained policies from simulation to reality using minimal hardware resources. The applicability of the proposed digital twin framework is highlighted through two representative use cases, which cover cooperative as well as competitive classes of MARL problems. We study the effect of agent and environment parallelization on training time and that of systematic domain randomization on zero-shot sim2real transfer across both the case studies. Results indicate up to 76.3% reduction in training time with the proposed parallelization scheme and as low as 2.9% sim2real gap using the suggested deployment method.

Automated vehicle (AV) platooning has the potential to improve the safety, operational, and energy efficiency of surface transportation systems by limiting or eliminating human involvement in the driving tasks. The theoretical validity of the AV platooning strategies has been established and practical applications are being tested under real-world conditions. The emergence of sensors, communication, and control strategies has resulted in rapid and constant evolution of AV platooning strategies. In this paper, we review the state-of-the-art knowledge in AV platooning using a five-component platooning framework, which includes vehicle model, information-receiving process, information flow topology, spacing policy, and controller and discuss the advantages and limitations of the components. Based on the discussion about existing strategies and associated limitations, potential future research directions are presented.

Autonomous vehicle platforms of varying spatial scales are employed within the research and development spectrum based on space, safety and monetary constraints. However, deploying and validating autonomy algorithms across varying operational scales presents challenges due to scale-specific dynamics, sensor integration complexities, computational constraints, regulatory considerations, environmental variability, interaction with other traffic participants and scalability concerns. In such a milieu, this work focuses on developing a unified framework for modeling and simulating digital twins of autonomous vehicle platforms across different scales and operational design domains (ODDs) to help support the streamlined development and validation of autonomy software stacks. Particularly, this work discusses the development of digital twin representations of 4 autonomous ground vehicles, which span across 3 different scales and target 3 distinct ODDs. We study the adoption of these autonomy-oriented digital twins to deploy a common autonomy software stack with an aim of end-to-end map-based navigation to achieve the ODD-specific objective(s) for each vehicle. Finally, we also discuss the flexibility of the proposed framework to support virtual, hybrid as well as physical testing with seamless sim2real transfer., Comment: Accepted at IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM) 2024

Simulation to reality (sim2real) transfer from a dynamics and controls perspective usually involves re-tuning or adapting the designed algorithms to suit real-world operating conditions, which often violates the performance guarantees established originally. This work presents a generalizable framework for achieving reliable sim2real transfer of autonomy-oriented control systems using multi-model multi-objective robust optimal control synthesis, which lends well to uncertainty handling and disturbance rejection with theoretical guarantees. Particularly, this work is centered around a novel actuation-redundant scaled autonomous vehicle called Nigel, with independent all-wheel drive and independent all-wheel steering architecture, whose enhanced configuration space bodes well for robust control applications. To this end, we present the mechatronic design, dynamics modeling, parameter identification, and robust stabilizing as well as tracking control of Nigel using the proposed framework, with exhaustive experimentation and benchmarking in simulation as well as real-world settings., Comment: Accepted in IEEE/ASME Transactions on Mechatronics (TMECH) and additionally accepted to be presented at IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM) 2024

Accurate modeling of noise in realistic quantum processors is critical for constructing fault-tolerant quantum computers. While a full simulation of actual noisy quantum circuits provides information about correlated noise among all qubits and is therefore accurate, it is, however, computationally expensive as it requires resources that grow exponentially with the number of qubits. In this paper, we propose an efficient systematic construction of approximate noise channels, where their accuracy can be enhanced by incorporating noise components with higher qubit-qubit correlation degree. To formulate such approximate channels, we first present a method, dubbed the cluster expansion approach, to decompose the Lindbladian generator of an actual Markovian noise channel into components based on interqubit correlation degree. We then generate a $k$-th order approximate noise channel by truncating the cluster expansion and incorporating noise components with correlations up to the $k$-th degree. We require that the approximate noise channels must be accurate and also "honest", i.e., the actual errors are not underestimated in our physical models. As an example application, we apply our method to model noise in a three-qubit quantum processor that stabilizes a [[2,0,0]] codeword, which is one of the four Bell states. We find that, for realistic noise strength typical for fixed-frequency superconducting qubits coupled via always-on static interactions, correlated noise beyond two-qubit correlation can significantly affect the code simulation accuracy. Since our approach provides a systematic noise characterization, it enables the potential for accurate, honest and scalable approximation to simulate large numbers of qubits from full modeling or experimental characterizations of small enough quantum subsystems, which are efficient but still retain essential noise features of the entire device., Comment: 13 pages, 8 figures

This work presents a modular and parallelizable multi-agent deep reinforcement learning framework for imbibing cooperative as well as competitive behaviors within autonomous vehicles. We introduce AutoDRIVE Ecosystem as an enabler to develop physically accurate and graphically realistic digital twins of Nigel and F1TENTH, two scaled autonomous vehicle platforms with unique qualities and capabilities, and leverage this ecosystem to train and deploy multi-agent reinforcement learning policies. We first investigate an intersection traversal problem using a set of cooperative vehicles (Nigel) that share limited state information with each other in single as well as multi-agent learning settings using a common policy approach. We then investigate an adversarial head-to-head autonomous racing problem using a different set of vehicles (F1TENTH) in a multi-agent learning setting using an individual policy approach. In either set of experiments, a decentralized learning architecture was adopted, which allowed robust training and testing of the approaches in stochastic environments, since the agents were mutually independent and exhibited asynchronous motion behavior. The problems were further aggravated by providing the agents with sparse observation spaces and requiring them to sample control commands that implicitly satisfied the imposed kinodynamic as well as safety constraints. The experimental results for both problem statements are reported in terms of quantitative metrics and qualitative remarks for training as well as deployment phases., Comment: Accepted as Multi-Agent Dynamic Games (MAD-Games) Workshop Paper at IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) 2023

The engineering community currently encounters significant challenges in the development of intelligent transportation algorithms that can be transferred from simulation to reality with minimal effort. This can be achieved by robustifying the algorithms using domain adaptation methods and/or by adopting cutting-edge tools that help support this objective seamlessly. This work presents AutoDRIVE, an openly accessible digital twin ecosystem designed to facilitate synergistic development, simulation and deployment of cyber-physical solutions pertaining to autonomous driving technology; and focuses on bridging the autonomy-oriented simulation-to-reality (sim2real) gap using the proposed ecosystem. In this paper, we extensively explore the modeling and simulation aspects of the ecosystem and substantiate its efficacy by demonstrating the successful transition of two candidate autonomy algorithms from simulation to reality to help support our claims: (i) autonomous parking using probabilistic robotics approach; (ii) behavioral cloning using deep imitation learning. The outcomes of these case studies further strengthen the credibility of AutoDRIVE as an invaluable tool for advancing the state-of-the-art in autonomous driving technology., Comment: Accepted at AACC/IFAC Modeling, Estimation and Control Conference (MECC) 2023

Clustering continues to be a significant and challenging task. Recent studies have demonstrated impressive results by applying clustering to feature representations acquired through self-supervised learning, particularly on small datasets. However, when dealing with datasets containing a large number of clusters, such as ImageNet, current methods struggle to achieve satisfactory clustering performance. In this paper, we introduce a novel method called Contrastive representation Disentanglement for Clustering (CDC) that leverages contrastive learning to directly disentangle the feature representation for clustering. In CDC, we decompose the representation into two distinct components: one component encodes categorical information under an equipartition constraint, and the other component captures instance-specific factors. To train our model, we propose a contrastive loss that effectively utilizes both components of the representation. We conduct a theoretical analysis of the proposed loss and highlight how it assigns different weights to negative samples during the process of disentangling the feature representation. Further analysis of the gradients reveals that larger weights emphasize a stronger focus on hard negative samples. As a result, the proposed loss exhibits strong expressiveness, enabling efficient disentanglement of categorical information. Through experimental evaluation on various benchmark datasets, our method demonstrates either state-of-the-art or highly competitive clustering performance. Notably, on the complete ImageNet dataset, we achieve an accuracy of 53.4%, surpassing existing methods by a substantial margin of +10.2%., Comment: 10 pages, 7 tables, 4 figures

The Vlasov equation is a nonlinear partial differential equation that provides a first-principles description of the dynamics of plasmas. Its linear limit is routinely used in plasma physics to investigate plasma oscillations and stability. In this work, we present a quantum algorithm that simulates the linearized Vlasov equation with and without collisions, in the one-dimensional, electrostatic limit. Rather than solving this equation in its native spatial and velocity phase-space, we adopt an efficient representation in the dual space yielded by a Fourier-Hermite expansion. The Fourier-Hermite representation is exponentially more compact, thus yielding a classical algorithm that can match the performance of a previously proposed quantum algorithm for this problem. This representation results in a system of linear ordinary differential equations which can be solved with well-developed quantum algorithms: Hamiltonian simulation in the collisionless case, and quantum ODE solvers in the collisional case. In particular, we demonstrate that a quadratic speedup in system size is attainable.

Modern-day autonomous vehicles are increasingly becoming complex multidisciplinary systems composed of mechanical, electrical, electronic, computing and information sub-systems. Furthermore, the individual constituent technologies employed for developing autonomous vehicles have started maturing up to a point, where it seems beneficial to start looking at the synergistic integration of these components into sub-systems, systems, and potentially, system-of-systems. Hence, this work applies the principles of mechatronics approach of system design, verification and validation for the development of autonomous vehicles. Particularly, we discuss leveraging multidisciplinary co-design practices along with virtual, hybrid and physical prototyping and testing within a concurrent engineering framework to develop and validate a scaled autonomous vehicle using the AutoDRIVE ecosystem. We also describe a case-study of autonomous parking application using a modular probabilistic framework to illustrate the benefits of the proposed approach., Comment: Accepted at IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM) 2023

Prototyping and validating hardware-software components, sub-systems and systems within the intelligent transportation system-of-systems framework requires a modular yet flexible and open-access ecosystem. This work presents our attempt towards developing such a comprehensive research and education ecosystem, called AutoDRIVE, for synergistically prototyping, simulating and deploying cyber-physical solutions pertaining to autonomous driving as well as smart city management. AutoDRIVE features both software as well as hardware-in-the-loop testing interfaces with openly accessible scaled vehicle and infrastructure components. The ecosystem is compatible with a variety of development frameworks, and supports both single and multi-agent paradigms through local as well as distributed computing. Most critically, AutoDRIVE is intended to be modularly expandable to explore emergent technologies, and this work highlights various complementary features and capabilities of the proposed ecosystem by demonstrating four such deployment use-cases: (i) autonomous parking using probabilistic robotics approach for mapping, localization, path planning and control; (ii) behavioral cloning using computer vision and deep imitation learning; (iii) intersection traversal using vehicle-to-vehicle communication and deep reinforcement learning; and (iv) smart city management using vehicle-to-infrastructure communication and internet-of-things.

Although robotics courses are well established in higher education, the courses often focus on theory and sometimes lack the systematic coverage of the techniques involved in developing, deploying, and applying software to real hardware. Additionally, most hardware platforms for robotics teaching are low-level toys aimed at younger students at middle-school levels. To address this gap, an autonomous vehicle hardware platform, called F1TENTH, is developed for teaching autonomous systems hands-on. This article describes the teaching modules and software stack for teaching at various educational levels with the theme of "racing" and competitions that replace exams. The F1TENTH vehicles offer a modular hardware platform and its related software for teaching the fundamentals of autonomous driving algorithms. From basic reactive methods to advanced planning algorithms, the teaching modules enhance students' computational thinking through autonomous driving with the F1TENTH vehicle. The F1TENTH car fills the gap between research platforms and low-end toy cars and offers hands-on experience in learning the topics in autonomous systems. Four universities have adopted the teaching modules for their semester-long undergraduate and graduate courses for multiple years. Student feedback is used to analyze the effectiveness of the F1TENTH platform. More than 80% of the students strongly agree that the hardware platform and modules greatly motivate their learning, and more than 70% of the students strongly agree that the hardware-enhanced their understanding of the subjects. The survey results show that more than 80% of the students strongly agree that the competitions motivate them for the course., Comment: 15 pages, 12 figures, 3 tables

In cable driven parallel robots (CDPRs), a single cable malfunction usually induces complete failure of the entire robot. However, the lost static workspace (due to failure) can often be recovered through reconfiguration of the cable attachment points on the frame. This capability is introduced by adding kinematic redundancies to the robot in the form of moving linear sliders that are manipulated in a real-time redundancy resolution controller. The presented work combines this controller with an online failure detection framework to develop a complete fault tolerant control scheme for automatic task recovery. This solution provides robustness by combining pose estimation of the end-effector with the failure detection through the application of an Interactive Multiple Model (IMM) algorithm relying only on end-effector information. The failure and pose estimation scheme is then tied into the redundancy resolution approach to produce a seamless automatic task (trajectory) recovery approach for cable failures.

Superresolution refers to the estimation of parameters of an image with an accuracy beyond standard classical techniques such as direct detection. In seminal work by Lu et al., a measurement to estimate the separation distance of two point sources (with a known centroid) was shown to achieve the quantum Cramer-Rao bound. This work made implicit use of reflection symmetry of the sources. Here we present a framework that uses more general symmetry in a constellation to construct a quantum measurement that achieves the quantum Cramer-Rao bound in estimation of parameters. We show how this technique can be used to estimate parameters simultaneously in symmetric point-source constellations with more than two point sources. In order to use symmetry explicitly, we make use discrete point spread functions in momentum space that maintain this symmetry. This framework allows us to use techniques from quantum computing such as Fourier transforms and linear optical circuits to implement the optimal measurement. To our knowledge, this is first work that shows for more than two point sources achievable quantum limits of estimation and modal transformations., Comment: 15 pages, 7 figures

We consider the hardness of computing additive approximations to output probabilities of random quantum circuits. We consider three random circuit families, namely, Haar random, $p=1$ QAOA, and random IQP circuits. Our results are as follows. For Haar random circuits with $m$ gates, we improve on prior results by showing $\mathsf{coC_=P}$ hardness of average-case additive approximations to an imprecision of $2^{-O(m)}$. Efficient classical simulation of such problems would imply the collapse of the polynomial hierarchy. For constant depth circuits i.e., when $m=O(n)$, this linear scaling in the exponent is within a constant of the scaling required to show hardness of sampling. Prior to our work, such a result was shown only for Boson Sampling in Bouland et al (2021). We also use recent results in polynomial interpolation to show $\mathsf{coC_=P}$ hardness under $\mathsf{BPP}$ reductions rather than $\mathsf{BPP}^{\mathsf{NP}}$ reductions. This improves the results of prior work for Haar random circuits both in terms of the error scaling and the power of reductions. Next, we consider random $p=1$ QAOA and IQP circuits and show that in the average-case, it is $\mathsf{coC_=P}$ hard to approximate the output probability to within an additive error of $2^{-O(n)}$. For $p=1$ QAOA circuits, this work constitutes the first average-case hardness result for the problem of approximating output probabilities for random QAOA circuits, which include Sherrington-Kirkpatrick and Erd\"{o}s-Renyi graphs. For IQP circuits, a consequence of our results is that approximating the Ising partition function with imaginary couplings to an additive error of $2^{-O(n)}$ is hard even in the average-case, which extends prior work on worst-case hardness of multiplicative approximation to Ising partition functions., Comment: 26 pages

The rising popularity of self-driving cars has led to the emergence of a new research field in the recent years: Autonomous racing. Researchers are developing software and hardware for high performance race vehicles which aim to operate autonomously on the edge of the vehicles limits: High speeds, high accelerations, low reaction times, highly uncertain, dynamic and adversarial environments. This paper represents the first holistic survey that covers the research in the field of autonomous racing. We focus on the field of autonomous racecars only and display the algorithms, methods and approaches that are used in the fields of perception, planning and control as well as end-to-end learning. Further, with an increasing number of autonomous racing competitions, researchers now have access to a range of high performance platforms to test and evaluate their autonomy algorithms. This survey presents a comprehensive overview of the current autonomous racing platforms emphasizing both the software-hardware co-evolution to the current stage. Finally, based on additional discussion with leading researchers in the field we conclude with a summary of open research challenges that will guide future researchers in this field., Comment: 29 pages, 12 figures, 6 tables, 242 references

We present substantially generalized and improved quantum algorithms over prior work for inhomogeneous linear and nonlinear ordinary differential equations (ODE). Specifically, we show how the norm of the matrix exponential characterizes the run time of quantum algorithms for linear ODEs opening the door to an application to a wider class of linear and nonlinear ODEs. In Berry et al., (2017), a quantum algorithm for a certain class of linear ODEs is given, where the matrix involved needs to be diagonalizable. The quantum algorithm for linear ODEs presented here extends to many classes of non-diagonalizable matrices. The algorithm here is also exponentially faster than the bounds derived in Berry et al., (2017) for certain classes of diagonalizable matrices. Our linear ODE algorithm is then applied to nonlinear differential equations using Carleman linearization (an approach taken recently by us in Liu et al., (2021)). The improvement over that result is two-fold. First, we obtain an exponentially better dependence on error. This kind of logarithmic dependence on error has also been achieved by Xue et al., (2021), but only for homogeneous nonlinear equations. Second, the present algorithm can handle any sparse, invertible matrix (that models dissipation) if it has a negative log-norm (including non-diagonalizable matrices), whereas Liu et al., (2021) and Xue et al., (2021) additionally require normality., Comment: In the latest version, the use of rescaling in the quantum algorithm for nonlinear differential equations is clarified. The conditions for lemmas 16 and 17 are stated more clearly and a new lemma is added to the appendix

Variational quantum algorithms such as the quantum approximate optimization algorithm (QAOA) are particularly attractive candidates for implementation on near-term quantum processors. As hardware realities such as error and qubit connectivity will constrain achievable circuit depth in the near future, new ways to achieve high-performance at low depth are of great interest. In this work, we present a modification to QAOA that adds additional variational parameters in the form of freedom of the rotation-axis in the $XY$-plane of the mixer Hamiltonian. Via numerical simulation, we show that this leads to a drastic performance improvement over standard QAOA at finding solutions to the MAXCUT problem on graphs of up to 7 qubits. Furthermore, we explore the Z-phase error mitigation properties of our modified ansatz, its performance under a realistic error model for a neutral atom quantum processor, and the class of problems it can solve in a single round., Comment: 8 pages, 4 figures, 3 pages and 5 figures supplementary

Quantum communications capacity using direct transmission over length-$L$ optical fiber scales as $R \sim e^{-\alpha L}$, where $\alpha$ is the fiber's loss coefficient. The rate achieved using a linear chain of quantum repeaters equipped with quantum memories, probabilistic Bell state measurements (BSMs) and switches used for spatial multiplexing, but no quantum error correction, was shown to surpass the direct-transmission capacity. However, this rate still decays exponentially with the end-to-end distance, viz., $R \sim e^{-s{\alpha L}}$, with $s < 1$. We show that the introduction of temporal multiplexing - i.e., the ability to perform BSMs among qubits at a repeater node that were successfully entangled with qubits at distinct neighboring nodes at {\em different} time steps - leads to a sub-exponential rate-vs.-distance scaling, i.e., $R \sim e^{-t\sqrt{\alpha L}}$, which is not attainable with just spatial or spectral multiplexing. We evaluate analytical upper and lower bounds to this rate, and obtain the exact rate by numerically optimizing the time-multiplexing block length and the number of repeater nodes. We further demonstrate that incorporating losses in the optical switches used to implement time multiplexing degrades the rate-vs.-distance performance, eventually falling back to exponential scaling for very lossy switches. We also examine models for quantum memory decoherence and describe optimal regimes of operation to preserve the desired boost from temporal multiplexing. Quantum memory decoherence is seen to be more detrimental to the repeater's performance over switching losses., Comment: 13 pages, 11 figures

Demonstrating a quantum computational advantage will require high-fidelity control and readout of multi-qubit systems. As system size increases, multiplexed qubit readout becomes a practical necessity to limit the growth of resource overhead. Many contemporary qubit-state discriminators presume single-qubit operating conditions or require considerable computational effort, limiting their potential extensibility. Here, we present multi-qubit readout using neural networks as state discriminators. We compare our approach to contemporary methods employed on a quantum device with five superconducting qubits and frequency-multiplexed readout. We find that fully-connected feedforward neural networks increase the qubit-state-assignment fidelity for our system. Relative to contemporary discriminators, the assignment error rate is reduced by up to 25% due to the compensation of system-dependent nonidealities such as readout crosstalk which is reduced by up to one order of magnitude. Our work demonstrates a potentially extensible building block for high-fidelity readout relevant to both near-term devices and future fault-tolerant systems., Comment: 18 Pages, 9 figures

Accelerating computational tasks with quantum resources is a widely-pursued goal that is presently limited by the challenges associated with high-fidelity control of many-body quantum systems. The paradigm of reservoir computing presents an attractive alternative, especially in the noisy intermediate-scale quantum era, since control over the internal system state and knowledge of its dynamics are not required. Instead, complex, unsupervised internal trajectories through a large state space are leveraged as a computational resource. Quantum systems offer a unique venue for reservoir computing, given the presence of interactions unavailable in analogous classical systems, and the potential for a computational space that grows exponentially with physical system size. Here, we consider a reservoir comprised of a single qudit ($d$-dimensional quantum system). We demonstrate a robust performance advantage compared to an analogous classical system accompanied by a clear improvement with Hilbert space dimension for two benchmark tasks: signal processing and short-term memory capacity. Qudit reservoirs are directly realized by current-era quantum hardware, offering immediate practical implementation, and a promising outlook for increased performance in larger systems., Comment: 6 pages, 3 figures, 6 supplementary pages, 6 supplementary figures

Knowledge distillation (KD) has become an important technique for model compression and knowledge transfer. In this work, we first perform a comprehensive analysis of the knowledge transferred by different KD methods. We demonstrate that traditional KD methods, which minimize the KL divergence of softmax outputs between networks, are related to the knowledge alignment of an individual sample only. Meanwhile, recent contrastive learning-based KD methods mainly transfer relational knowledge between different samples, namely, knowledge correlation. While it is important to transfer the full knowledge from teacher to student, we introduce the Multi-level Knowledge Distillation (MLKD) by effectively considering both knowledge alignment and correlation. MLKD is task-agnostic and model-agnostic, and can easily transfer knowledge from supervised or self-supervised pretrained teachers. We show that MLKD can improve the reliability and transferability of learned representations. Experiments demonstrate that MLKD outperforms other state-of-the-art methods on a large number of experimental settings including different (a) pretraining strategies (b) network architectures (c) datasets (d) tasks., Comment: 15 pages, 11 tables, 4 figures

Nonlinear differential equations model diverse phenomena but are notoriously difficult to solve. While there has been extensive previous work on efficient quantum algorithms for linear differential equations, the linearity of quantum mechanics has limited analogous progress for the nonlinear case. Despite this obstacle, we develop a quantum algorithm for dissipative quadratic $n$-dimensional ordinary differential equations. Assuming $R < 1$, where $R$ is a parameter characterizing the ratio of the nonlinearity and forcing to the linear dissipation, this algorithm has complexity $T^2 q~\mathrm{poly}(\log T, \log n, \log 1/\epsilon)/\epsilon$, where $T$ is the evolution time, $\epsilon$ is the allowed error, and $q$ measures decay of the solution. This is an exponential improvement over the best previous quantum algorithms, whose complexity is exponential in $T$. While exponential decay precludes efficiency, driven equations can avoid this issue despite the presence of dissipation. Our algorithm uses the method of Carleman linearization, for which we give a novel convergence theorem. This method maps a system of nonlinear differential equations to an infinite-dimensional system of linear differential equations, which we discretize, truncate, and solve using the forward Euler method and the quantum linear system algorithm. We also provide a lower bound on the worst-case complexity of quantum algorithms for general quadratic differential equations, showing that the problem is intractable for $R \ge \sqrt{2}$. Finally, we discuss potential applications, showing that the $R < 1$ condition can be satisfied in realistic epidemiological models and giving numerical evidence that the method may describe a model of fluid dynamics even for larger values of $R$., Comment: 36 pages, 1 figure. Published in PNAS

Realizing the promise of quantum information processing remains a daunting task, given the omnipresence of noise and error. Adapting noise-resilient classical computing modalities to quantum mechanics may be a viable path towards near-term applications in the noisy intermediate-scale quantum era. Here, we propose continuous variable quantum reservoir computing in a single nonlinear oscillator. Through numerical simulation of our model we demonstrate quantum-classical performance improvement, and identify its likely source: the nonlinearity of quantum measurement. Beyond quantum reservoir computing, this result may impact the interpretation of results across quantum machine learning. We study how the performance of our quantum reservoir depends on Hilbert space dimension, how it is impacted by injected noise, and briefly comment on its experimental implementation. Our results show that quantum reservoir computing in a single nonlinear oscillator is an attractive modality for quantum computing on near-term hardware., Comment: 9 pages, 5 figures

Quantum key distribution (QKD) allows for secure communications safe against attacks by quantum computers. QKD protocols are performed by sending a sizeable, but finite, number of quantum signals between the distant parties involved. Many QKD experiments however predict their achievable key rates using asymptotic formulas, which assume the transmission of an infinite number of signals, partly because QKD proofs with finite transmissions (and finite key lengths) can be difficult. Here we develop a robust numerical approach for calculating the key rates for QKD protocols in the finite-key regime in terms of two novel semi-definite programs (SDPs). The first uses the relation between smooth min-entropy and quantum relative entropy, and the second uses the relation between the smooth min-entropy and quantum fidelity. We then solve these SDPs using convex optimization solvers and obtain some of the first numerical calculations of finite key rates for several different protocols, such as BB84, B92, and twin-field QKD. Our numerical approach democratizes the composable security proofs for QKD protocols where the derived keys can be used as an input to another cryptosystem.

Quantum key distribution (QKD) promises provably secure cryptography, even to attacks from an all-powerful adversary. However, with quantum computing development lagging behind QKD, the assumption that there exists an adversary equipped with a universal fault-tolerant quantum computer is unrealistic for at least the near future. Here, we explore the effect of restricting the eavesdropper's computational capabilities on the security of QKD, and find that improved secret key rates are possible. Specifically, we show that for a large class of discrete variable protocols higher key rates are possible if the eavesdropper is restricted to a unitary operation from the Clifford group. Further, we consider Clifford-random channels consisting of mixtures of Clifford gates. We numerically calculate a secret key rate lower bound for BB84 with this restriction, and show that in contrast to the case of a single restricted unitary attack, the mixture of Clifford based unitary attacks does not result in an improved key rate., Comment: 6 pages + 8 pages appendices, 2 figures

We introduce a light dark photon $A_\mu^\prime$ to the minimal Higgs portal model, by coupling the Higgs boson to "dark QED" containing fermionic dark matter, which gives rise to rich and interesting collider phenomenology. There are two prominent features in such a simple extension -- the Higgs boson could have decays into the long-lived dark photon through the "mono-$A^\prime$ channel," or into multiple collimated leptons via "darkonium," depending on the mixing parameter of the $A_\mu^\prime$ with the visible photon. We initiate a study on the possibility of probing the parameter space of the model in both the energy and the lifetime frontiers at the Large Hadron Collider., Comment: 12 pages, 10 figures, v2: some footnotes added

Operation in a real world traffic requires autonomous vehicles to be able to plan their motion in complex environments (multiple moving participants). Planning through such environment requires the right search space to be provided for the trajectory or maneuver planners so that the safest motion for the ego vehicle can be identified. Given the current states of the environment and its participants, analyzing the risks based on the predicted trajectories of all the traffic participants provides the necessary search space for the planning of motion. This paper provides a fresh taxonomy of safety / risks that an autonomous vehicle should be able to handle while navigating through traffic. It provides a reference system architecture that needs to be implemented as well as describes a novel way of identifying and predicting the behaviors of the traffic participants using classic Multi Model Adaptive Estimation (MMAE). Preliminary simulation results of the implemented model are included.