arXiv subjects

Jeffrey Larson

Publications and source records attributed to Jeffrey Larson.

At least 37 records · Page 2Linked to original sources

arXiv2024

Portable, heterogeneous ensemble workflows at scale using libEnsemble

libEnsemble is a Python-based toolkit for running dynamic ensembles, developed as part of the DOE Exascale Computing Project. The toolkit utilizes a unique generator--simulator--allocator paradigm, where generators produce input for simulators, simulators evaluate those inputs, and allocators decide whether and when a simulator or generator should be called. The generator steers the ensemble based on simulation results. Generators may, for example, apply methods for numerical optimization, machine learning, or statistical calibration. libEnsemble communicates between a manager and workers. We overview the unique characteristics of libEnsemble as well as current and potential interoperability with other packages in the workflow ecosystem. We highlight libEnsemble's dynamic resource features: libEnsemble can detect system resources, such as available nodes, cores, and GPUs, and assign these in a portable way. These features allow users to specify the number of processors and GPUs required for each simulation; and resources will be automatically assigned on a wide range of systems, including Frontier, Aurora, and Perlmutter. Such ensembles can include multiple simulation types, some using GPUs and others using only CPUs, sharing nodes for maximum efficiency. We also describe the benefits of libEnsemble's generator--simulator coupling, which easily exposes to the user the ability to cancel, and portably kill, running simulations based on models that are updated with intermediate simulation output. We demonstrate libEnsemble's capabilities, scalability, and scientific impact via a Gaussian process surrogate training problem for the longitudinal density profile at the exit of a plasma accelerator stage. The study uses gpCAM for the surrogate model and employs either Wake-T or WarpX simulations, highlighting efficient use of resources that can easily extend to exascale.

cs.DC↗

arXiv2024

Challenges with Differentiable Quantum Dynamics

Differentiable quantum dynamics require automatic differentiation of a complex-valued initial value problem, which numerically integrates a system of ordinary differential equations from a specified initial condition, as well as the eigendecomposition of a matrix. We explored several automatic differentiation frameworks for these tasks, finding that no framework natively supports our application requirements. We therefore demonstrate a need for broader support of complex-valued, differentiable numerical integration in scientific computing libraries.

quant-ph↗

arXiv2024

A Novel Noise-Aware Classical Optimizer for Variational Quantum Algorithms

A key component of variational quantum algorithms (VQAs) is the choice of classical optimizer employed to update the parameterization of an ansatz. It is well recognized that quantum algorithms will, for the foreseeable future, necessarily be run on noisy devices with limited fidelities. Thus, the evaluation of an objective function (e.g., the guiding function in the quantum approximate optimization algorithm (QAOA) or the expectation of the electronic Hamiltonian in variational quantum eigensolver (VQE)) required by a classical optimizer is subject not only to stochastic error from estimating an expected value but also to error resulting from intermittent hardware noise. Model-based derivative-free optimization methods have emerged as popular choices of a classical optimizer in the noisy VQA setting, based on empirical studies. However, these optimization methods were not explicitly designed with the consideration of noise. In this work we adapt recent developments from the ``noise-aware numerical optimization'' literature to these commonly used derivative-free model-based methods. We introduce the key defining characteristics of these novel noise-aware derivative-free model-based methods that separate them from standard model-based methods. We study an implementation of such noise-aware derivative-free model-based methods and compare its performance on demonstrative VQA simulations to classical solvers packaged in \texttt{scikit-quant}.

quant-ph↗

arXiv2024

Evidence of Scaling Advantage for the Quantum Approximate Optimization Algorithm on a Classically Intractable Problem

The quantum approximate optimization algorithm (QAOA) is a leading candidate algorithm for solving optimization problems on quantum computers. However, the potential of QAOA to tackle classically intractable problems remains unclear. Here, we perform an extensive numerical investigation of QAOA on the low autocorrelation binary sequences (LABS) problem, which is classically intractable even for moderately sized instances. We perform noiseless simulations with up to 40 qubits and observe that the runtime of QAOA with fixed parameters scales better than branch-and-bound solvers, which are the state-of-the-art exact solvers for LABS. The combination of QAOA with quantum minimum finding gives the best empirical scaling of any algorithm for the LABS problem. We demonstrate experimental progress in executing QAOA for the LABS problem using an algorithm-specific error detection scheme on Quantinuum trapped-ion processors. Our results provide evidence for the utility of QAOA as an algorithmic component that enables quantum speedups.

quant-ph↗

arXiv2024

Electric Vehicle Supply Equipment Location and Capacity Allocation for Fixed-Route Networks

Electric vehicle (EV) supply equipment location and allocation (EVSELCA) problems for freight vehicles are becoming more important because of the trending electrification shift. Some previous works address EV charger location and vehicle routing problems simultaneously by generating vehicle routes from scratch. Although such routes can be efficient, introducing new routes may violate practical constraints, such as drive schedules, and satisfying electrification requirements can require dramatically altering existing routes. To address the challenges in the prevailing adoption scheme, we approach the problem from a fixed-route perspective. We develop a mixed-integer linear program, a clustering approach, and a metaheuristic solution method using a genetic algorithm (GA) to solve the EVSELCA problem. The clustering approach simplifies the problem by grouping customers into clusters, while the GA generates solutions that are shown to be nearly optimal for small problem cases. A case study examines how charger costs, energy costs, the value of time (VOT), and battery capacity impact the cost of the EVSELCA. Charger equipment costs were found to be the most significant component in the objective function, leading to a substantial reduction in cost when decreased. VOT costs exhibited a significant decrease with rising energy costs. An increase in VOT resulted in a notable rise in the number of fast chargers. Longer EV ranges decrease total costs up to a certain point, beyond which the decrease in total costs is negligible.

math.OC↗

arXiv2024

Binary Quantum Control Optimization with Uncertain Hamiltonians

Optimizing the controls of quantum systems plays a crucial role in advancing quantum technologies. The time-varying noises in quantum systems and the widespread use of inhomogeneous quantum ensembles raise the need for high-quality quantum controls under uncertainties. In this paper, we consider a stochastic discrete optimization formulation of a binary optimal quantum control problem involving Hamiltonians with predictable uncertainties. We propose a sample-based reformulation that optimizes both risk-neutral and risk-averse measurements of control policies, and solve these with two gradient-based algorithms using sum-up-rounding approaches. Furthermore, we discuss the differentiability of the objective function and prove upper bounds of the gaps between the optimal solutions to binary control problems and their continuous relaxations. We conduct numerical studies on various sized problem instances based of two applications of quantum pulse optimization; we evaluate different strategies to mitigate the impact of uncertainties in quantum systems. We demonstrate that the controls of our stochastic optimization model achieve significantly higher quality and robustness compared to the controls of a deterministic model.

quant-ph↗

arXiv2023

Large-Scale Dynamic Ridesharing with Iterative Assignment

Transportation network companies (TNCs) have become a highly utilized transportation mode over the past years. At their emergence, TNCs were serving ride requests one by one. However, the economic and environmental benefits of ridesharing encourages them to dynamically pool multiple ride requests to enable people to share vehicles. In a dynamic ridesharing (DRS) system, a fleet operator seeks to minimize the overall travel cost while a rider desires to experience a faster (and cheaper) service. While the DRS may provide relatively cheaper trips by pooling requests, the service speed is contingent on the objective of the vehicle-to-rider assignments. Moreover, the operator must quickly assign a vehicle to requests to prevent customer loss. In this study we develop an iterative assignment (IA) algorithm with a balanced objective to conduct assignments quickly. A greedy algorithm from the literature is also tailored to further reduce the computational time. The IA was used to measure the impact on service quality of fleet size; assignment frequency; the weight control parameter of the two objectives on vehicle occupancy -- rider wait time and vehicle hours traveled. A case study in Austin, TX, reveals that the key performance metrics are the most sensitive to the weight parameter in the objective function.

math.OC↗

arXiv2023

Switching Time Optimization for Binary Quantum Optimal Control

Quantum optimal control is a technique for controlling the evolution of a quantum system and has been applied to a wide range of problems in quantum physics. We study a binary quantum control optimization problem, where control decisions are binary-valued and the problem is solved in diverse quantum algorithms. In this paper, we utilize classical optimization and computing techniques to develop an algorithmic framework that sequentially optimizes the number of control switches and the duration of each control interval on a continuous time horizon. Specifically, we first solve the continuous relaxation of the binary control problem based on time discretization and then use a heuristic to obtain a controller sequence with a penalty on the number of switches. Then, we formulate a switching time optimization model and apply sequential least-squares programming with accelerated time-evolution simulation to solve the model. We demonstrate that our computational framework can obtain binary controls with high-quality performance and also reduce computational time via solving a family of quantum control instances in various quantum physics applications.

quant-ph↗

arXiv2023

Hardware-Conscious Optimization of the Quantum Toffoli Gate

While quantum computing holds great potential in combinatorial optimization, electronic structure calculation, and number theory, the current era of quantum computing is limited by noisy hardware. Many quantum compilation approaches can mitigate the effects of imperfect hardware by optimizing quantum circuits for objectives such as critical path length. Few approaches consider quantum circuits in terms of the set of vendor-calibrated operations (i.e., native gates) available on target hardware. This manuscript expands the analytical and numerical approaches for optimizing quantum circuits at this abstraction level. We present a procedure for combining the strengths of analytical native gate-level optimization with numerical optimization. Although we focus on optimizing Toffoli gates on the IBMQ native gate set, the methods presented are generalizable to any gate and superconducting qubit architecture. Our optimized Toffoli gate implementation demonstrates an $18\%$ reduction in infidelity compared with the canonical implementation as benchmarked on IBM Jakarta with quantum process tomography. Assuming the inclusion of multi-qubit cross-resonance (MCR) gates in the IBMQ native gate set, we produce Toffoli implementations with only six multi-qubit gates, a $25\%$ reduction from the canonical eight multi-qubit implementations for linearly connected qubits.

quant-ph↗

arXiv2023

Multi-Angle QAOA Does Not Always Need All Its Angles

Introducing additional tunable parameters to quantum circuits is a powerful way of improving performance without increasing hardware requirements. A recently introduced multiangle extension of the quantum approximate optimization algorithm (ma-QAOA) significantly improves the solution quality compared with QAOA by allowing the parameters for each term in the Hamiltonian to vary independently. Prior results suggest, however, considerable redundancy in parameters, the removal of which would reduce the cost of parameter optimization. In this work we show numerically the connection between the problem symmetries and the parameter redundancy by demonstrating that symmetries can be used to reduce the number of parameters used by ma-QAOA without decreasing the solution quality. We study Max-Cut on all 7,565 connected, non-isomorphic 8-node graphs with a nontrivial symmetry group and show numerically that in 67.4% of these graphs, symmetry can be used to reduce the number of parameters with no decrease in the objective, with the average ratio of parameters reduced by 28.1%. Moreover, we show that in 35.9% of the graphs this reduction can be achieved by simply using the largest symmetry. For the graphs where reducing the number of parameters leads to a decrease in the objective, the largest symmetry can be used to reduce the parameter count by 37.1% at the cost of only a 6.1% decrease in the objective. We demonstrate the central role of symmetries by showing that a random parameter reduction strategy leads to much worse performance.

quant-ph↗

arXiv2023

Structure-Aware Methods for Expensive Derivative-Free Nonsmooth Composite Optimization

We present new methods for solving a broad class of bound-constrained nonsmooth composite minimization problems. These methods are specially designed for objectives that are some known mapping of outputs from a computationally expensive function. We provide accompanying implementations of these methods: in particular, a novel manifold sampling algorithm (\mspshortref) with subproblems that are in a sense primal versions of the dual problems solved by previous manifold sampling methods and a method (\goombahref) that employs more difficult optimization subproblems. For these two methods, we provide rigorous convergence analysis and guarantees. We demonstrate extensive testing of these methods. Open-source implementations of the methods developed in this manuscript can be found at \url{github.com/POptUS/IBCDFO/}.

math.OC↗

arXiv2023

Parameter Transfer for Quantum Approximate Optimization of Weighted MaxCut

Finding high-quality parameters is a central obstacle to using the quantum approximate optimization algorithm (QAOA). Previous work partially addresses this issue for QAOA on unweighted MaxCut problems by leveraging similarities in the objective landscape among different problem instances. However, we show that the more general weighted MaxCut problem has significantly modified objective landscapes, with a proliferation of poor local optima. Our main contribution is a simple rescaling scheme that overcomes these deleterious effects of weights. We show that for a given QAOA depth, a single "typical" vector of QAOA parameters can be successfully transferred to weighted MaxCut instances. This transfer leads to a median decrease in the approximation ratio of only 2.0 percentage points relative to a considerably more expensive direct optimization on a dataset of 34,701 instances with up to 20 nodes and multiple weight distributions. This decrease can be reduced to 1.2 percentage points at the cost of only 10 additional QAOA circuit evaluations with parameters sampled from a pretrained metadistribution, or the transferred parameters can be used as a starting point for a single local optimization run to obtain approximation ratios equivalent to those achieved by exhaustive optimization in $96.35\%$ of our cases.

quant-ph↗

arXiv2023

QContext: Context-Aware Decomposition for Quantum Gates

In this paper we propose QContext, a new compiler structure that incorporates context-aware and topology-aware decompositions. Because of circuit equivalence rules and resynthesis, variants of a gate-decomposition template may exist. QContext exploits the circuit information and the hardware topology to select the gate variant that increases circuit optimization opportunities. We study the basis-gate-level context-aware decomposition for Toffoli gates and the native-gate-level context-aware decomposition for CNOT gates. Our experiments show that QContext reduces the number of gates as compared with the state-of-the-art approach, Orchestrated Trios.

quant-ph↗

arXiv2022

Binary Control Pulse Optimization for Quantum Systems

Quantum control aims to manipulate quantum systems toward specific quantum states or desired operations. Designing highly accurate and effective control steps is vitally important to various quantum applications, including energy minimization and circuit compilation. In this paper we focus on discrete binary quantum control problems and apply different optimization algorithms and techniques to improve computational efficiency and solution quality. Specifically, we develop a generic model and extend it in several ways. We introduce a squared $L_2$-penalty function to handle additional side constraints, to model requirements such as allowing at most one control to be active. We introduce a total variation (TV) regularizer to reduce the number of switches in the control. We modify the popular gradient ascent pulse engineering (GRAPE) algorithm, develop a new alternating direction method of multipliers (ADMM) algorithm to solve the continuous relaxation of the penalized model, and then apply rounding techniques to obtain binary control solutions. We propose a modified trust-region method to further improve the solutions. Our algorithms can obtain high-quality control results, as demonstrated by numerical studies on diverse quantum control examples.

quant-ph↗

arXiv2022

Exploiting In-Constraint Energy in Constrained Variational Quantum Optimization

A central challenge of applying near-term quantum optimization algorithms to industrially relevant problems is the need to incorporate complex constraints. In general, such constraints cannot be easily encoded in the circuit, and the quantum circuit measurement outcomes are not guaranteed to respect the constraints. Therefore, the optimization must trade off the in-constraint probability and the quality of the in-constraint solution by adding a penalty for constraint violation into the objective. We propose a new approach for solving constrained optimization problems with unconstrained, easy-to-implement quantum ansatze. Our method leverages the in-constraint energy as the objective and adds a lower-bound constraint on the in-constraint probability to the optimizer. We demonstrate significant gains in solution quality over directly optimizing the penalized energy. We implement our method in QVoice, a Python package that interfaces with Qiskit for quick prototyping in simulators and on quantum hardware.

quant-ph↗

arXiv2022

Modeling Approaches for Addressing Simple Unrelaxable Constraints with Unconstrained Optimization Methods

We explore novel approaches for solving nonlinear optimization problems with unrelaxable bound constraints, which must be satisfied before the objective function can be evaluated. Our method reformulates the unrelaxable bound-constrained problem as an unconstrained optimization problem that is amenable to existing unconstrained optimization methods. The reformulation relies on a domain warping to form a merit function; the choice of the warping determines the level of exactness with which the unconstrained problem can be used to find solutions to the bound-constrained problem, as well as key properties of the unconstrained formulation such as smoothness. We develop theory when the domain warping is a multioutput sigmoidal warping, and we explore the practical elements of applying unconstrained optimization methods to the formulation. We develop an algorithm that exploits the structure of the sigmoidal warping to guarantee that unconstrained optimization algorithms applied to the merit function will find a stationary point to the desired tolerance.

math.OC↗

arXiv2022

Comparison of Multiobjective Optimization Methods for the LCLS-II Photoinjector

Particle accelerators are among some of the largest science experiments in the world and can consist of thousands of components with a wide variety of input ranges. These systems can easily become unwieldy optimization problems during design and operations studies. Starting in the early 2000s, searching for better beam dynamics configurations became synonymous with heuristic optimization methods in the accelerator physics community. Genetic algorithms and particle swarm optimization are currently the most widely used. These algorithms can take thousands of simulation evaluations to find optimal solutions for one machine prototype. For large facilities such as the Linac Coherent Light Source (LCLS) and others, this equates to a limited exploration of many possible design configurations. In this paper, the LCLS-II photoinjector is optimized with three optimization algorithms. All optimizations were started from both a uniform random and Latin hypercube sample. In all cases, the optimizations started from Latin hypercube samples outperformed optimizations started from uniform samples. All three algorithms were able to optimize the photoinjector, with the model-based methods approximating the Pareto front in fewer simulation evaluations. This work, in combination with previous optimization observations, indicates objective penalties have a strong impact on the efficiency of such methods. In general, we recommend heuristic methods for initial optimizations and model-based methods when information about the objective space is available.

physics.acc-ph↗

arXiv2022

A Time-Constrained Capacitated Vehicle Routing Problem in Urban E-Commerce Delivery

Electric vehicle routing problems can be particularly complex when recharging must be performed mid-route. In some applications such as the e-commerce parcel delivery truck routing, however, mid-route recharging may not be necessary because of constraints on vehicle capacities and maximum allowed time for delivery. In this study, we develop a mixed-integer optimization model that exactly solves such a time-constrained capacitated vehicle routing problem, especially of interest to e-commerce parcel delivery vehicles. We compare our solution method with an existing metaheuristic and carry out exhaustive case studies considering four U.S. cities -- Austin, TX; Bloomington, IL; Chicago, IL; and Detroit, MI -- and two vehicle types: conventional vehicles and battery electric vehicles (BEVs). In these studies we examine the impact of vehicle capacity, maximum allowed travel time, service time (dwelling time to physically deliver the parcel), and BEV range on system-level performance metrics including vehicle miles traveled (VMT). We find that the service time followed by the vehicle capacity plays a key role in the performance of our approach. We assume an 80-mile BEV range as a baseline without mid-route recharging. Our results show that BEV range has a minimal impact on performance metrics because the VMT per vehicle averages around 72 miles. In a case study for shared-economy parcel deliveries, we observe that VMT could be reduced by 38.8\% in Austin if service providers were to operate their distribution centers jointly.

math.OC↗