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Jeffrey Larson

Publications and source records attributed to Jeffrey Larson.

At least 19 recordsLinked to original sources
arXiv2026

Branch-Extended Automatic Differentiation

We present branch-extended automatic differentiation (BEAD), a software package that provides information about inactive branches of piecewise-differentiable functions, intended for use in nonsmooth optimization algorithms. BEAD is implemented in Python, building on the popular JAX framework. For supported nonsmooth operations such as abs and max, BEAD identifies alternative branches within tolerance from the given input, and computes gradients of the resulting branches extended to the given input. Such information has been previously used for robust optimization methods, but has required error-prone and tedious manual differentiation, unlike BEAD, which is fully automated for functions written in NumPy-like JAX code. Our experiments show that our approach is as accurate as manually written derivative code, and offers more flexibility in modifying the function and choosing between branch-discovery rules. While we were originally motivated by the manifold sampling algorithm for nonsmooth composite objectives, we also integrate BEAD branch-extension gradients into a nonsmooth BFGS-SQP solver. On two small nonsmooth test problems, the resulting path-aware search resolves failures or substantially reduces the number of evaluations required by the BFGS-SQP solver.

math.OC↗
arXiv2026

A Feasible Direction Method with Active-Set Identification for Derivative-Free Optimization

We propose a model-based trust region method for derivative-free optimization with simulation-based inequality constraints. We are motivated by settings of simulation optimization in which both function evaluations at infeasible points may be unreliable and constraint evaluations are expensive. Our method maintains feasible incumbents and computes steps from a subproblem suitable for a feasible-direction method in order to encourage generation of feasible trial points. To reduce the computational cost of modeling the constraints, we describe an active-set estimation scheme that permits modeling with only a subset of constraints in each subproblem, as opposed to maintaining models of all constraints. We show that every limit point of the incumbents generated by our method is a Fritz-John point, and is additionally a KKT point under the Mangasarian-Fromovitz constraint qualification. Under standard nondegeneracy conditions, the active-set estimate identifies, within finite time, all constraints active at the limit point of the incumbents. Experiments on CUTEst problems show that our method generates feasible trial points more often than a comparable SQP-based approach and is competitive with an appropriate comparator in budgeted settings.

math.OC↗
arXiv2026

Birkhoff interpolation models for optimization with some available derivatives

We consider interpolation-based derivative-free optimization in settings where only some derivatives are available. Such situations arise in scientific computing applications involving simulations, adjoint-enabled components, legacy software, or partially differentiable models. We introduce a Birkhoff interpolation framework that permits arbitrary patterns of derivative availability and enables the construction of local polynomial models using mixtures of function values and partial derivative information. In contrast to Hermite interpolation approaches, the proposed framework does not require all available derivatives to be queried at every interpolation point. We develop conditions under which the resulting interpolation systems are poised and establish corresponding model-accuracy bounds for fully quadratic interpolation models. We develop a trust-region framework that maintains poised interpolation sets while selectively incorporating derivative information. The method generalizes an established class of interpolation-based derivative-free optimization algorithms and naturally bridges derivative-free and derivative-based settings. We evaluate our approach on a collection of CUTEst test problems with synthetically generated derivative-availability patterns, as well as a stellarator design problem in which only some derivatives are available.

math.OC↗
arXiv2026

Variational quantum state preparation within an entangle-rotate circuit framework for quantum-enhanced metrology in noisy systems

We investigate the generation of quantum states for precision metrology in noisy two-level systems. These states are obtained by optimizing a variational quantum circuit to maximize the quantum Fisher information (QFI) of the output state for a given decoherence rate and interaction Hamiltonian. The circuit architecture, inspired by twist-and-turn schemes, features a sequence of $n$ entangling layers, each consisting of entangling gates followed by a global rotation. We observe notable improvements in the QFI as the circuit layer depth increases, even for appreciable noise rates, demonstrating that our entangle-rotate architecture expands the accessible state space under realistic noise conditions. Our approach thus provides a general and efficient framework for generating quantum-enhanced sensing states. Our analysis extends to systems of power-law interactions spanning from all-to-all to nearest-neighbor interactions. We also analyze the capabilities of our circuit to prepare states for system sizes greater than $8$ qubits.

quant-ph↗
arXiv2026

AI-Accelerated Gyrokinetic Predictions of Turbulent Transport for Stellarator Design Optimization and Experimental Planning

Previous work built AI-based surrogates for a nonlinear gyrokinetic simulation code with the goal of using them for fast, direct calculations of turbulent ion heat flux in stellarator design optimizations and scenario planning for experiments. These AI surrogates were trained on data from >200k nonlinear, adiabatic electron gyrokinetic simulations with the gyrokinetic flux-tube code GX, using a wide range of stellarator magnetic configurations ($\sim$23k), positions in the plasma, and gradient scale lengths. In this paper, we demonstrate the use of the AI-based turbulence surrogate in the optimization of stellarator magnetic equilibrium and to speed up stellarator transport solvers. Due to its speed ($\sim$ms), the AI-based surrogate enables previously unattainable optimization objectives, such as full radial profiles of ion turbulent heat flux, or directly optimizing to maximize the turbulent critical gradient at multiple locations across the plasma. These direct calculations provide a potentially more accurate optimization target and reduce reliance on ad-hoc heuristics that may not accurately capture the variation of turbulent transport with magnetic configuration. By including the AI-based surrogate for turbulent heat flux in a transport solver, we can quickly postprocess and confirm the improved ion temperature resulting from the optimized equilibrium. Finally, we demonstrate the use of AI agents with strong reasoning AI models to automate the outer loop, exploring many objective and hyperparameter configurations with this AI-based turbulence surrogate to discover improved turbulence optimized magnetic equilibria.

physics.plasm-ph↗
arXiv2026

Adaptive Replication Strategies in Trust-Region-Based Bayesian Optimization of Stochastic Functions

We develop and analyze a method for stochastic simulation optimization based on Gaussian process models within a trust-region framework. We focus on settings where the variance of the objective function is large, making accurate estimation challenging and often requiring many evaluations. To address this regime, we combine local modeling with adaptive replication, allowing the method to allocate repeated evaluations where they are most beneficial. We introduce several mechanisms to promote and adapt replication, including modifications to the acquisition function and cost-aware evaluation strategies. These components enable our approach to scale effectively when high levels of sampling are required to reduce noise. We refer to the resulting method as OGPIT, for Optimization by Gaussian Processes In Trust regions. Numerical experiments show that adaptive replication can substantially improve computational efficiency while preserving solution accuracy compared to baseline methods, in particular when evaluation costs are taken into account.

math.OC↗
arXiv2026

Materials Behavior as Mechanism Ensembles: A Probabilistic Framework for Emergent Behaviors

Materials behavior is often treated as a deterministic mapping from structure to properties, yet many important phenomena emerge from the conditional activation of multiple mechanisms across scales. This is especially evident in fatigue of metals, where crack growth is typically modeled as monotonic and irreversible process, despite evidence that local microstructure, loading history, and competing unit processes can shift the balance among propagation, arrest, and self-healing. Here we present a probabilistic framework that describes materials behavior as an ensemble of constituent mechanisms whose activation, interaction, and evolution determine emergent outcomes. The framework connects mechanism activation, state evolution, and macroscopic observables in a probabilistic way. In the case of fatigue crack propagation, it reframes damage tolerance as an inference problem over mechanism competition and provides a basis for integrating multiscale simulation, multimodal characterization, and machine learning. The same logic extends to other physical and chemical systems suggesting a portable framework for any system in which emergent behavior reflects mechanism competition under changing conditions. The broader ambition of this perspective review is a shift from correlating structure and performance after the fact to identifying, in advance, the conditions that make desired emergent behavior probable.

cond-mat.mtrl-sci↗
arXiv2026

An Interacting System and Environment with Prior Correlations Plus Local Operations Can Mimic Uncorrelated Evolution

Initial system-environment correlations can induce reduced dynamics that depart from the standard completely positive (CP) description. We study when such dynamics can be reproduced by the same global unitary acting on an initial system-environment product state. We show that local preprocessing on the system, applied prior to the joint evolution, can lead to dynamics which are completely positive. We focus on two-qubit system-environment states, with a three-qubit extension when a single ancilla is used to implement Kraus channel preprocessing. We analyze three classes of local operations$-$measurements, unitaries, and Kraus channels$-$and characterize their ability to satisfy dynamics matching while minimally perturbing the initial system state. Local measurements can always enforce dynamics matching but necessarily reduce state fidelity. We numerically investigated local unitary preprocessing. Local unitaries enforce dynamics matching in all tested instances and typically preserve the system state: in 402 numerical cases the average fidelity is 99.8%, more than 92% of cases exceed 99% fidelity, and the minimum fidelity is 94.2%. We show that a two-term Kraus channel, realizable with a single ancillary qubit coupled to the system, achieves dynamics matching with unit fidelity in all tested cases. As a second contribution, we demonstrate that local preprocessing can prevent the emergence of non--completely positive (NCP) reduced dynamics in a time-dependent setting. For a correlated two-qubit experiment with a time-dependent global unitary U(t), the induced compatibility domain is fixed by the initial correlations. For every t in a nontrivial continuous interval, the reduced dynamics are NCP when defined over this domain. We then show that a single, time-independent local unitary applied prior to the joint evolution renders the reduced dynamics CP over the entire interval.

quant-ph↗
arXiv2026

Spin-Boson Mapping of the Quantum Approximate Optimization Algorithm

The Quantum Approximate Optimization Algorithm (QAOA) achieves monotonically improving performance with circuit depth $p$, yet the study of the high-depth regime has been obstructed by the exponential in $p$ cost of existing exact evaluation techniques. In this Letter, we prove that, in the infinite-size limit, the depth-$p$ QAOA state for the Sherrington-Kirkpatrick (SK) model converges to the state of a spin coupled to $p$ bosonic modes. We simulate the spin-boson system using matrix product states and provide numerical evidence that QAOA obtains a $(1-ε)$ approximation to the optimal energy of the SK model with circuit depth $O(n/ε^{1.13})$ in the average case. The modest computational cost of our approach allows us to optimize QAOA parameters and observe that QAOA achieves $\varepsilon\lesssim 2.2\%$ at $p=160$ in the infinite-size limit, extending far beyond $p\leq 20$ accessible to prior exact methods. Our mapping provides a many-body route to study and optimize high-depth QAOA in regimes previously inaccessible to exact evaluation.

quant-ph↗
arXiv2026

Routing Entanglement in Complex Quantum Networks Using GHZ States

Distributing entanglement to distant parties in a network is a central task in quantum information processing and quantum networking. The sensitivity of entangled states to loss necessitates the use of entanglement routing strategies. Recently, a routing strategy using Greenberger-Horne-Zeilinger (GHZ) measurements instead of Bell state measurements (BSM) has been proposed. We further this direction of research by explicitly considering the varying measurement success probabilities of GHZ measurements. Moreover, we extend the analysis beyond square grid networks to complex network models such as Waxman networks and scale-free networks, as well as SURFnet, a real-world network topology in the Netherlands. Taking into account the varying success probabilities, naive application of GHZ routing achieves rates much lower than the conventional BSM routing. Instead, we propose a hybrid GHZ-BSM routing strategy. The hybrid GHZ-BSM routing strategy outperforms BSM routing in square grid networks. In other networks, however, more sophisticated adaptations using global information are required.

quant-ph↗
arXiv2026

InterQnet: A Heterogeneous Full-Stack Approach to Co-designing Scalable Quantum Networks

Quantum communications have progressed significantly, moving from a theoretical concept to small-scale experiments to recent metropolitan-scale demonstrations. As the technology matures, it is expected to revolutionize quantum computing in much the same way that classical networks revolutionized classical computing. Quantum communications will also enable breakthroughs in quantum sensing, metrology, and other areas. However, scalability has emerged as a major challenge, particularly in terms of the number and heterogeneity of nodes, the distances between nodes, the diversity of applications, and the scale of user demand. This paper describes InterQnet, a multidisciplinary project that advances scalable quantum communications through a comprehensive approach that improves devices, error handling, and network architecture. InterQnet has a two-pronged strategy to address scalability challenges: InterQnet-Achieve focuses on practical realizations of heterogeneous quantum networks by building and then integrating first-generation quantum repeaters with error mitigation schemes and centralized automated network control systems. The resulting system will enable quantum communications between two heterogeneous quantum platforms through a third type of platform operating as a repeater node. InterQnet-Scale focuses on a systems study of architectural choices for scalable quantum networks by developing forward-looking models of quantum network devices, advanced error correction schemes, and entanglement protocols. Here we report our current progress toward achieving our scalability goals.

quant-ph↗
arXiv2026

Extreme-Scale EV Charging Infrastructure Planning for Last-Mile Delivery Using High-Performance Parallel Computing

This paper addresses stochastic charger location and allocation problems under queue congestion for last-mile delivery using electric vehicles (EVs). The objective is to decide where to open charging stations and how many chargers of each type to install, subject to budgetary and waiting-time constraints. We formulate the problem as a mixed-integer non-linear program, where each station-charger pair is modeled as a multiserver queue with stochastic arrivals and service times to capture the notion of waiting in fleet operations. The model is extremely large, with billions of variables and constraints for a typical metropolitan area; even loading the model in solver memory is difficult, let alone solving it. To address this challenge, we develop a Lagrangian-based dual decomposition framework that decomposes the problem by station and leverages parallelization on high-performance computing systems, where the subproblems are solved by using a cutting plane method and their solutions are collected at the master level. We also develop a three-step rounding heuristic to transform the fractional subproblem solutions into feasible integral solutions. Computational experiments on data from the Chicago metropolitan area with hundreds of thousands of households and thousands of candidate stations show that our approach produces high-quality solutions in cases where existing exact methods cannot even load the model in memory. We also analyze various policy scenarios, demonstrating that combining existing depots with newly built stations under multiagency collaboration substantially reduces costs and congestion. These findings offer a scalable and efficient framework for developing sustainable large-scale EV charging networks.

math.OC↗
arXiv2025

Roadblocks and Opportunities in Quantum Algorithms -- Insights from the National Quantum Initiative Joint Algorithms Workshop, May 20--22, 2024

The National Quantum Initiative Joint Algorithms Workshop brought together researchers across academia, national laboratories, and industry to assess the current landscape of quantum algorithms and discuss roadblocks to progress. The workshop featured discussions on emerging algorithmic techniques, resource constraints in near-term hardware, and opportunities for co-design across software and systems. Presented here are seven topics from the workshop, each highlighting a critical challenge or promising opportunity discussed during the event. Together, they offer a snapshot of the field's evolving priorities and a shared vision for what is needed to advance quantum computational capabilities.

quant-ph↗
arXiv2025

End-to-End Protocol for High-Quality QAOA Parameters with Few Shots

The quantum approximate optimization algorithm (QAOA) is a quantum heuristic for combinatorial optimization that has been demonstrated to scale better than state-of-the-art classical solvers for some problems. For a given problem instance, QAOA performance depends crucially on the choice of the parameters. While average-case optimal parameters are available in many cases, meaningful performance gains can be obtained by fine-tuning these parameters for a given instance. This task is especially challenging, however, when the number of circuit executions (shots) is limited. In this work, we develop an end-to-end protocol that combines multiple parameter settings and fine-tuning techniques. We use large-scale numerical experiments to optimize the protocol for the shot-limited setting and observe that optimizers with the simplest internal model (linear) perform best. We implement the optimized pipeline on a trapped-ion processor using up to 32 qubits and 5 QAOA layers, and we demonstrate that the pipeline is robust to small amounts of hardware noise. To the best of our knowledge, these are the largest demonstrations of QAOA parameter fine-tuning on a trapped-ion processor in terms of 2-qubit gate count.

quant-ph↗
arXiv2025

Exploring Non-Multiplicativity in the Geometric Measure of Entanglement

The geometric measure of entanglement (GME) quantifies how close a multi-partite quantum state is to the set of separable states under the Hilbert-Schmidt inner product. The GME can be non-multiplicative, meaning that the closest product state to two states is entangled across subsystems. In this work, we explore the GME in two families of states: those that are invariant under bilateral orthogonal $(O \otimes O)$ transformations, and mixtures of singlet states. In both cases, a region of GME non-multiplicativity is identified around the anti-symmetric projector state. We employ state-of-the-art numerical optimization methods and models to quantitatively analyze non-multiplicativity in these states for d = 3. We also investigate a constrained form of GME that measures closeness to the set of real product states and show that this measure can be non-multiplicative even for real separable states.

quant-ph↗
arXiv2025

Certified randomness using a trapped-ion quantum processor

While quantum computers have the potential to perform a wide range of practically important tasks beyond the capabilities of classical computers, realizing this potential remains a challenge. One such task is to use an untrusted remote device to generate random bits that can be certified to contain a certain amount of entropy. Certified randomness has many applications but is fundamentally impossible to achieve solely by classical computation. In this work, we demonstrate the generation of certifiably random bits using the 56-qubit Quantinuum H2-1 trapped-ion quantum computer accessed over the internet. Our protocol leverages the classical hardness of recent random circuit sampling demonstrations: a client generates quantum "challenge" circuits using a small randomness seed, sends them to an untrusted quantum server to execute, and verifies the server's results. We analyze the security of our protocol against a restricted class of realistic near-term adversaries. Using classical verification with measured combined sustained performance of $1.1\times10^{18}$ floating-point operations per second across multiple supercomputers, we certify $71,313$ bits of entropy under this restricted adversary and additional assumptions. Our results demonstrate a step towards the practical applicability of today's quantum computers.

quant-ph↗
arXiv2024

Classical Pre-optimization Approach for ADAPT-VQE: Maximizing the Potential of High-Performance Computing Resources to Improve Quantum Simulation of Chemical Applications

The ADAPT-VQE algorithm is a promising method for generating a compact ansatz based on derivatives of the underlying cost function, and it yields accurate predictions of electronic energies for molecules. In this work we report the implementation and performance of ADAPT-VQE with our recently developed sparse wavefunction circuit solver (SWCS) in terms of accuracy and efficiency for molecular systems with up to 52 spin-orbitals. The SWCS can be tuned to balance computational cost and accuracy, which extends the application of ADAPT-VQE for molecular electronic structure calculations to larger basis sets and larger number of qubits. Using this tunable feature of the SWCS, we propose an alternative optimization procedure for ADAPT-VQE to reduce the computational cost of the optimization. By pre-optimizing a quantum simulation with a parameterized ansatz generated with ADAPT-VQE/SWCS, we aim to utilize the power of classical high-performance computing in order to minimize the work required on noisy intermediate-scale quantum hardware, which offers a promising path toward demonstrating quantum advantage for chemical applications.

quant-ph↗
arXiv2024

An Empirical Quantile Estimation Approach to Nonlinear Optimization Problems with Chance Constraints

We investigate an empirical quantile estimation approach to solve chance-constrained nonlinear optimization problems. Our approach is based on the reformulation of the chance constraint as an equivalent quantile constraint to provide stronger signals on the gradient. In this approach, the value of the quantile function is estimated empirically from samples drawn from the random parameters, and the gradient of the quantile function is estimated via a finite-difference approximation on top of the quantile-function-value estimation. We establish a convergence theory of this approach within the framework of an augmented Lagrangian method for solving general nonlinear constrained optimization problems. The foundation of the convergence analysis is a concentration property of the empirical quantile process, and the analysis is divided based on whether or not the quantile function is differentiable. In contrast to the sampling-and-smoothing approach used in the literature, the method developed in this paper does not involve any smoothing function and hence the quantile-function gradient approximation is easier to implement and there are less accuracy-control parameters to tune. We demonstrate the effectiveness of this approach and compare it with a smoothing method for the quantile-gradient estimation. Numerical investigation shows that the two approaches are competitive for certain problem instances.

math.OC↗