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We present a comprehensive theory for a novel method to discretize the spectral density of a bosonic heat bath, as introduced in [H. Takahashi and R. Borrelli, J. Chem. Phys. \textbf{161}, 151101 (2024)]. The approach leverages a low-rank decomposition of the Fourier-transform relation connecting the bath correlation function to its spectral density. By capturing the time, frequency, and temperature dependencies encoded in the spectral density-autocorrelation function relation, our method significantly reduces the degrees of freedom required for simulating open quantum system dynamics. We benchmark our approach against existing methods and demonstrate its efficacy through applications to both simple models and a realistic electron transfer process in biological systems. Additionally, we show that this new approach can be effectively combined with the tensor-train formalism to investigate the quantum dynamics of systems interacting with complex non-Markovian environments. Finally, we provide a perspective on the selection and application of various spectral density discretization techniques.

In this perspective article, we revisit and critically evaluate prevailing viewpoints on the capabilities and limitations of near-term quantum computing and its potential transition toward fully fault-tolerant quantum computing. We examine theoretical no-go results and their implications, addressing misconceptions about the practicality of quantum error mitigation techniques and variational quantum algorithms. By emphasizing the nuances of error scaling, circuit depth, and algorithmic feasibility, we highlight viable near-term applications and synergies between error mitigation and early fault-tolerant architectures. Our discussion explores strategies for addressing current challenges, such as barren plateaus in variational circuits and the integration of quantum error mitigation and quantum error correction techniques. We aim to underscore the importance of continued innovation in hardware and algorithmic design to bridge the gap between theoretical potential and practical utility, paving the way for meaningful quantum advantage in the era of late noisy intermediate scale and early fault-tolerant quantum devices., Comment: Comments welcome

Graphene is a monolayer graphitic film where electrons behave like two-dimensional Dirac fermions without mass. Its study has attracted a wide interest in the domain of condensed matter physics. In particular, it represents an ideal system to test the comprehension of 2D massless relativistic particles in a laboratory, the Fermi velocity being $300$ times smaller than the speed of light. In this work, we present a global well-posedness result for graphene in the Hartree-Fock approximation. The model allows to describe the time evolution of graphene in the presence of external electric fields, such as those induced by local defects in the monolayer of carbon atoms. Our approach is based on a well established non-perturbative framework originating from the study of three-dimensional quantum electrodynamics., Comment: 19 pages

We introduce an Implicit Game-Theoretic MPC (IGT-MPC), a decentralized algorithm for two-agent motion planning that uses a learned value function that predicts the game-theoretic interaction outcomes as the terminal cost-to-go function in a model predictive control (MPC) framework, guiding agents to implicitly account for interactions with other agents and maximize their reward. This approach applies to competitive and cooperative multi-agent motion planning problems which we formulate as constrained dynamic games. Given a constrained dynamic game, we randomly sample initial conditions and solve for the generalized Nash equilibrium (GNE) to generate a dataset of GNE solutions, computing the reward outcome of each game-theoretic interaction from the GNE. The data is used to train a simple neural network to predict the reward outcome, which we use as the terminal cost-to-go function in an MPC scheme. We showcase emerging competitive and coordinated behaviors using IGT-MPC in scenarios such as two-vehicle head-to-head racing and un-signalized intersection navigation. IGT-MPC offers a novel method integrating machine learning and game-theoretic reasoning into model-based decentralized multi-agent motion planning., Comment: Submitted to 2025 Learning for Dynamics and Control Conference (L4DC)

We propose a novel Stochastic Model Predictive Control (MPC) for uncertain linear systems subject to probabilistic constraints. The proposed approach leverages offline learning to extract key features of affine disturbance feedback policies, significantly reducing the computational burden of online optimization. Specifically, we employ offline data-driven sampling to learn feature components of feedback gains and approximate the chance-constrained feasible set with a specified confidence level. By utilizing this learned information, the online MPC problem is simplified to optimization over nominal inputs and a reduced set of learned feedback gains, ensuring computational efficiency. In a numerical example, the proposed MPC approach achieves comparable control performance in terms of Region of Attraction (ROA) and average closed-loop costs to classical MPC optimizing over disturbance feedback policies, while delivering a 10-fold improvement in computational speed., Comment: Submitted to L4DC 2025

Nonadiabatic coupling between electrons and molecular motion at metal surfaces leads to energy dissipation and dynamical steering effects during chemical surface dynamics. We present a theoretical approach to the scattering of molecules from metal surfaces that incorporates all nonadiabatic and quantum nuclear effects due to the coupling of the molecular degrees of freedom to the electrons in the metal. This is achieved with the hierarchical equations of motion (HEOM) approach combined with a matrix product state representation in twin space. The method is applied to the scattering of nitric oxide from Au(111), for which strongly nonadiabatic energy loss during scattering has been experimentally observed, thus presenting a significant theoretical challenge. Since the HEOM approach treats the molecule-surface coupling exactly, it captures the interplay between nonadiabatic and quantum nuclear effects. Finally, the data obtained by the HEOM approach is used as a rigorous benchmark to assess various mixed quantum-classical methods, from which we derive insights into the mechanisms of energy dissipation and the suitable working regimes of each method.

This Letter introduces a generalization of known duplication-divergence models for growing random graphs. This general duplication-divergence model includes a new coupled divergence asymmetry rate, which allows to obtain the structure of random growing networks by duplication-divergence in a continuous range of configurations between two known limit cases (i) complete asymmetric divergence, i.e., divergence rates affect only edges of either the original or the copy vertex, and (ii) symmetric divergence, i.e., divergence rates affect equiprobably both the original and the copy vertex. Multiple connected sub-graphs (of order greater than one) (of order greater than one) emerge as the divergence asymmetry rate slightly moves from the complete asymmetric divergence case. Mean-field results of priorly published models are nicely reproduced by this generalization. In special cases, the connected components size distribution $C_s$ suggests a power-law scaling of the form $C_s \sim s^{-\lambda}$ for $s>1$, e.g., with $\lambda \approx 5/3$ for divergence rate $\delta \approx 0.7$., Comment: 7 pages, 9 figures, minor edits, some typos correction and rephrasing

Achieving high-precision measurements on near-term quantum devices is critical for advancing quantum computing applications. In this paper, we explore several practical techniques to enhance measurement accuracy using randomized measurements, focusing on minimizing shot overhead, circuit overhead, measurement noise, and time-dependent measurement noise. Our approach leverages locally biased random measurements to reduce shot overhead, in addition to repeated settings and parallel quantum detector tomography to reduce circuit overhead and mitigate measurement noise. Additionally, we employ a blended scheduling technique to mitigate time-dependent measurement noise. We demonstrate the effectiveness of these techniques through a case study on the molecular energy estimation of the BODIPY molecule using the Hartree-Fock state on an IBM Eagle r3 computer, showcasing significant improvements in measurement precision. These strategies pave the way for more reliable and accurate quantum computations, particularly in applications requiring precise molecular energy calculations., Comment: 15 pages, 8 figures

The accurate description of the interaction of a quantum system with a its environment is a challenging problem ubiquitous across all areas of physics, and lies at the foundation of quantum mechanics theory. Here we pioneer a new strategy to create discrete low-rank models of the system-environment interaction, by exploiting the frequency and time domain information encoded in the fluctuation-dissipation relation connecting the system-bath correlation function and the spectral density. We demonstrate the effectiveness of our methodology by combining it with tensor-network methodologies and simulating the quantum dynamics of a complex excitonic systems in a highly structured bosonic environment. The new modeling framework sets the basis for a leap in the analysis of open quantum systems providing controlled accuracy at significantly reduced computational costs, with benefits in all connected research areas.

We present a Learning Model Predictive Controller (LMPC) for multi-modal systems performing iterative control tasks. Assuming availability of historical data, our goal is to design a data-driven control policy for the multi-modal system where the current mode is unknown. First, we propose a novel method to select local data for constructing affine time-varying (ATV) models of a multi-modal system in the context of LMPC. Then we present how to build a sampled safe set from multi-modal historical data. We demonstrate the effectiveness of our method through simulation results of automated driving on a friction-varying track., Comment: Submitted to 2024 IEEE Conference on Decision and Control

We present a novel control-oriented motorcycle model and use it for computing racing lines on a nonplanar racetrack. The proposed model combines recent advances in nonplanar road models with the dynamics of motorcycles. Our approach considers the additional camber degree of freedom of the motorcycle body with a simplified model of the rider and front steering fork bodies. We demonstrate the effectiveness of our model by computing minimum-time racing trajectories on a nonplanar racetrack.

We present an approach for predictive braking of a four-wheeled vehicle on a nonplanar road. Our main contribution is a methodology to consider friction and road contact safety on general smooth road geometry. We use this to develop an active safety system to preemptively reduce vehicle speed for upcoming road geometry, such as off-camber turns. Our system may be used for human-driven or autonomous vehicles and we demonstrate it with a simulated ADAS scenario. We show that loss of control due to driver error on nonplanar roads can be mitigated by our approach.

This paper presents a data-driven Model Predictive Control (MPC) for energy-efficient urban road driving for connected, automated vehicles. The proposed MPC aims to minimize total energy consumption by controlling the vehicle's longitudinal motion on roads with traffic lights and front vehicles. Its terminal cost function and terminal constraints are learned from data, which consists of the closed-loop state and input trajectories. The terminal cost function represents the remaining energy-to-spend starting from a given terminal state. The terminal constraints are designed to ensure that the controlled vehicle timely crosses the upcoming traffic light, adheres to traffic laws, and accounts for the front vehicles. We validate the effectiveness of our method through both simulations and vehicle-in-the-loop experiments, demonstrating 19% improvement in average energy efficiency compared to conventional approaches that involve solving a long-horizon optimal control problem for speed planning and employing a separate controller for speed tracking., Comment: Accepted for IEEE Transactions of Intelligent Vehicles. arXiv admin note: text overlap with arXiv:2402.01059

Multi-Objective Learning Model Predictive Control is a novel data-driven control scheme which improves a linear system's closed-loop performance with respect to several convex control objectives over iterations of a repeated task. At each task iteration, collected system data is used to construct terminal components of a Model Predictive Controller. The formulation presented in this paper ensures that closed-loop control performance improves between successive iterations with respect to each objective. We provide proofs of recursive feasibility and performance improvement, and show that the converged policy is Pareto optimal. Simulation results demonstrate the applicability of the proposed approach.

We report a comparative study on microwave control lines for a transmon qubit using: (i) flexible stripline transmission lines, and (ii) semi-rigid coaxial cables. During each experiment we performed repeated measurements of the energy relaxation and coherence times of a transmon qubit using one of the wiring configurations. Each measurement run spanned 70 h to 250 h of measurement time, and four separate cooldowns were performed so that each configuration could be tested twice. From these datasets we observe that changing the microwave control lines from coaxial cables to flexible stripline transmission lines does not have a measurable effect on coherence compared to thermal cycling the system, or random coherence fluctuations. Our results open up the possibility of large scale integration of qubit control lines with integrated component with planar layouts on flexible substrate., Comment: 6 pages, 2 figures

Quantum chemistry simulations offer a cost-effective way for computational design of BODIPY photosensitizers with potential use in photodynamic therapy (PDT). However, accurate predictions of photophysical properties, such as excitation energies, pose a challenge for the popular time-dependent density functional theory (TDDFT) and equation-of-motion coupled cluster with singles and doubles (EOM-CCSD) methods. By contrast, reliable descriptions can be achieved by multi-reference quantum chemistry methods, though unfortunately, their computational cost grows exponentially with the number of correlated electrons. Alternatively, quantum computing holds a great potential for exact simulation of photophysical properties in a computationally more efficient way. To this end, we introduce the state-specific $\Delta$UCCSD-VQE (unitary coupled cluster with singles and doubles variational quantum eigensolver) and $\Delta$ADAPT-VQE methods in which the electronically excited state is calculated via a non-Aufbau electronic configuration. The accuracy and capability of the developed methods are assessed against experimentally determined excitation energies for six BODIPY-derivatives. We show that the proposed methods predict accurate vertical excitation energies that are not only in good agreement with experimental reference data but also outperform popular quantum chemistry methods, such as TDDFT and EOM-CCSD. Spurred by its impressive performance and simplicity, we are confident that $\Delta$ADAPT will emerge as the method of choice for guiding the rational design of photosensitizers for PDT and photocatalysis in the era of near-term quantum computing.

Dynamic games can be an effective approach for modeling interactive behavior between multiple competitive agents in autonomous racing and they provide a theoretical framework for simultaneous prediction and control in such scenarios. In this work, we propose DG-SQP, a numerical method for the solution of local generalized Nash equilibria (GNE) for open-loop general-sum dynamic games for agents with nonlinear dynamics and constraints. In particular, we formulate a sequential quadratic programming (SQP) approach which requires only the solution of a single convex quadratic program at each iteration. The three key elements of the method are a non-monotonic line search for solving the associated KKT equations, a merit function to handle zero sum costs, and a decaying regularization scheme for SQP step selection. We show that our method achieves linear convergence in the neighborhood of local GNE and demonstrate the effectiveness of the approach in the context of head-to-head car racing, where we show significant improvement in solver success rate when comparing against the state-of-the-art PATH solver for dynamic games. An implementation of our solver can be found at https://github.com/zhu-edward/DGSQP., Comment: arXiv admin note: text overlap with arXiv:2203.16478

This paper introduces a novel data-driven hierarchical control scheme for managing a fleet of nonlinear, capacity-constrained autonomous agents in an iterative environment. We propose a control framework consisting of a high-level dynamic task assignment and routing layer and low-level motion planning and tracking layer. Each layer of the control hierarchy uses a data-driven Model Predictive Control (MPC) policy, maintaining bounded computational complexity at each calculation of a new task assignment or actuation input. We utilize collected data to iteratively refine estimates of agent capacity usage, and update MPC policy parameters accordingly. Our approach leverages tools from iterative learning control to integrate learning at both levels of the hierarchy, and coordinates learning between levels in order to maintain closed-loop feasibility and performance improvement of the connected architecture., Comment: 16 pages, 4 figures

This paper focuses on the design of hierarchical control architectures for autonomous systems with energy constraints. We focus on systems where energy storage limitations and slow recharge rates drastically affect the way the autonomous systems are operated. Using examples from space robotics and public transportation, we motivate the need for formally designed learning hierarchical control systems. We propose a learning control architecture which incorporates learning mechanisms at various levels of the control hierarchy to improve performance and resource utilization. The proposed hierarchical control scheme relies on high-level energy-aware task planning and assignment, complemented by a low-level predictive control mechanism responsible for the autonomous execution of tasks, including motion control and energy management. Simulation examples show the benefits and the limitations of the proposed architecture when learning is used to obtain a more energy-efficient task allocation.

The paper presents an approach to solving the Robust Energy Capacitated Vehicle Routing Problem (RECVRP), focusing on electric vehicles and their limited battery capacity. A finite number of customers, each with their own demand, have to be serviced by an electric vehicle fleet while ensuring that none of the vehicles run out of energy. The time and energy it takes to travel between any two points is modeled as a random variable with known distribution. We propose a Mixed Integer Program (MIP) for computing an exact solution and introduce clustering heuristics to enhance the solution speed. This enables efficient re-planning of routes in dynamic scenarios. The methodology transforms the RECVRP into smaller problems, yielding good quality solutions quickly compared to existing methods. We demonstrate the effectiveness of this approach using a well-known benchmark problem set as well as a set of randomly generated problems.

This paper introduces a novel approach to optimize the parking efficiency for fleets of Connected and Automated Vehicles (CAVs). We present a novel multi-vehicle parking simulator, equipped with hierarchical path planning and collision avoidance capabilities for individual CAVs. The simulator is designed to capture the key decision-making processes in parking, from low-level vehicle control to high-level parking assignment, and it enables the effective assessment of parking strategies for large fleets of ground vehicles. We formulate and compare different strategic parking spot assignments to minimize a collective cost. While the proposed framework is designed to optimize various objective functions, we choose the total parking time for the experiment, as it is closely related to the reduction of vehicles' energy consumption and greenhouse gas emissions. We validate the effectiveness of the proposed strategies through empirical evaluation against a dataset of real-world parking lot dynamics, realizing a substantial reduction in parking time by up to 43.8%. This improvement is attributed to the synergistic benefits of driving automation, the utilization of shared infrastructure state data, the exclusion of pedestrian traffic, and the real-time computation of optimal parking spot allocation.

Dynamics of the sub-Ohmic spin-boson model under polarized initial conditions at finite temperature is investigated by employing both analytical tools and the numerically accurate hierarchical equations of motion-tensor train method. By analyzing the features of nonequilibrium dynamics, we discovered a bifurcation phenomenon which separates two regimes of the dynamics. It is found that before the bifurcation time, increasing temperature slows down the population dynamics, while the opposite effect occurs after the bifurcation time. The dynamics is highly sensitive to both initial preparation of the bath and thermal effects.

We propose a hierarchical architecture designed for scalable real-time Model Predictive Control (MPC) in complex, multi-modal traffic scenarios. This architecture comprises two key components: 1) RAID-Net, a novel attention-based Recurrent Neural Network that predicts relevant interactions along the MPC prediction horizon between the autonomous vehicle and the surrounding vehicles using Lagrangian duality, and 2) a reduced Stochastic MPC problem that eliminates irrelevant collision avoidance constraints, enhancing computational efficiency. Our approach is demonstrated in a simulated traffic intersection with interactive surrounding vehicles, showcasing a 12x speed-up in solving the motion planning problem. A video demonstrating the proposed architecture in multiple complex traffic scenarios can be found here: https://youtu.be/-pRiOnPb9_c. GitHub: https://github.com/MPC-Berkeley/hmpc_raidnet, Comment: Accepted at IEEE Intelligent Vehicles Symposium 2024

This paper addresses the eco-driving problem for connected vehicles on urban roads, considering localization uncertainty. Eco-driving is defined as longitudinal speed planning and control on roads with the presence of a sequence of traffic lights. We solve the problem by using a data-driven model predictive control (MPC) strategy. This approach involves learning a cost-to-go function and constraints from state-input data. The cost-to-go function represents the remaining energy-to-spend from the given state, and the constraints ensure that the controlled vehicle passes the upcoming traffic light timely while obeying traffic laws. The resulting convex optimization problem has a short horizon and is amenable for real-time implementations. We demonstrate the effectiveness of our approach through real-world vehicle experiments. Our method demonstrates $12\%$ improvement in energy efficiency compared to the traditional approaches, which plan longitudinal speed by solving a long-horizon optimal control problem and track the planned speed using another controller, as evidenced by vehicle experiments., Comment: Accepted for IEEE IV 2024

We propose a Model Predictive Control (MPC) with a single-step prediction horizon to solve infinite horizon optimal control problems with the expected sum of convex stage costs for constrained linear uncertain systems. The proposed method relies on two techniques. First, we estimate the expected values of the convex costs using a computationally tractable approximation, achieved by sampling across the space of disturbances. Second, we implement a data-driven approach to approximate the optimal value function and its corresponding domain, through systematic exploration of the system's state space. These estimates are subsequently used as the terminal cost and terminal set within the proposed MPC. We prove recursive feasibility, robust constraint satisfaction, and convergence in probability to the target set. Furthermore, we prove that the estimated value function converges to the optimal value function in a local region. The effectiveness of the proposed MPC is illustrated with detailed numerical simulations and comparisons with a value iteration method and a Learning MPC that minimizes a certainty equivalent cost., Comment: Submitted to the IEEE Transactions on Automatic Control

We study the problem of stereo singing voice cancellation, a subtask of music source separation, whose goal is to estimate an instrumental background from a stereo mix. We explore how to achieve performance similar to large state-of-the-art source separation networks starting from a small, efficient model for real-time speech separation. Such a model is useful when memory and compute are limited and singing voice processing has to run with limited look-ahead. In practice, this is realised by adapting an existing mono model to handle stereo input. Improvements in quality are obtained by tuning model parameters and expanding the training set. Moreover, we highlight the benefits a stereo model brings by introducing a new metric which detects attenuation inconsistencies between channels. Our approach is evaluated using objective offline metrics and a large-scale MUSHRA trial, confirming the effectiveness of our techniques in stringent listening tests.

We study a two-dimensional Pauli operator describing a charged quantum particle with spin $1/2$ moving on a plane in presence of an orthogonal Aharonov-Bohm magnetic flux. We classify all the admissible self-adjont realizations and give a complete picture of their spectral and scattering properties. Symmetries of the resulting Hamiltonians are also discussed, as well as their connection with the Dirac operator perturbed by an Aharonov-Bohm singularity., Comment: 33 pages, pdfLaTeX, slightly enlarged and updated with respect to the previous version, to appear in J. Spectr. Theory. Prop. 2.26 corrected and Remark 2.27 added. Additional minor modifications

Motivated by various geometric problems, we study the nodal set of solutions to Dirac equations on manifolds, of general form. We prove that such set has Hausdorff dimension less than or equal to $n-2$, $n$ being the ambient dimension. We extend this result, previously known only in the smooth case or in specific cases, working with locally Lipschitz coefficients. Under some additional, but still quite general, structural assumptions we provide a stratification result for the nodal set, which appears to be new already in the smooth case. This is achieved by exploiting the properties of a suitable Almgren-type frequency function, which is of independent interest., Comment: 34 pages