arXiv subjects

Carleton Coffrin

Publications and source records attributed to Carleton Coffrin.

At least 19 recordsLinked to original sources

arXiv2026

Conditions for Quantum Advantage in AC Power Flow

This paper aims to contextualize the requirements for Quantum Computing (QC) algorithms to achieve a quantum advantage in solving the alternating current power flow (ACPF) problem, with a focus on runtime complexity. First, we establish a benchmark for a QC iterative solver to demonstrate an advantage over the classical Newton-Raphson Load Flow (NRLF) algorithm. Next, we derive a baseline expression for the end-to-end runtime complexity of any Gate-based QC algorithm as $\Omega(N \kappa/\varepsilon),$ reflecting dependence on system size $N$, condition number $\kappa$, and error tolerance $\varepsilon$. Finally, we highlight key areas where QC algorithms may offer potential benefits over NRLF in addressing the standard ACPF problem.

quant-ph↗

arXiv2025

Classical Criticality via Quantum Annealing

Quantum annealing provides a powerful platform for simulating magnetic materials and realizing statistical physics models, presenting a compelling alternative to classical Monte Carlo methods. We demonstrate that quantum annealers can accurately reproduce phase diagrams and simulate critical phenomena without suffering from the critical slowing down that often affects classical algorithms. To illustrate this, we study the piled-up dominoes model, which interpolates between the ferromagnetic 2D Ising model and Villain's fully frustrated ``odd model''. We map out its phase diagram and for the first time, employ finite-size scaling and Binder cumulants on a quantum annealer to study critical exponents for thermal phase transitions. Our method achieves systematic temperature control by tuning the energy scale of the Hamiltonian, eliminating the need to adjust the physical temperature of the quantum hardware. This work demonstrates how, through fine-tuning and calibration, a quantum annealer can be employed to apply sophisticated finite-size scaling techniques from statistical mechanics. Our results establish quantum annealers as robust statistical physics simulators, offering a novel pathway for studying phase transitions and critical behavior.

cond-mat.stat-mech↗

arXiv2025

Autoregressive pairwise Graphical Models efficiently find ground state representations of stoquastic Hamiltonians

We introduce Autoregressive Graphical Models (AGMs) as an Ansatz for modeling the ground states of stoquastic Hamiltonians. Exact learning of these models for smaller systems show the dominance of the pairwise terms in the autoregressive decomposition, which informs our modeling choices when the Ansatz is used to find representations for ground states of larger systems. We find that simple AGMs with pairwise energy functions trained using first-order stochastic gradient methods often outperform more complex non-linear models trained using the more expensive stochastic reconfiguration method. We also test our models on Hamiltonians with frustration and observe that the simpler linear model used here shows faster convergence to the variational minimum in a resource-limited setting.

quant-ph↗

arXiv2025

Leveraging Quantum Computing for Accelerated Classical Algorithms in Power Systems Optimization

The recent advent of commercially available quantum annealing hardware (QAH) has expanded opportunities for research into quantum annealing-based algorithms. In the domain of power systems, this advancement has driven increased interest in applying such algorithms to mixed-integer problems (MIP) like Unit Commitment (UC). UC focuses on minimizing power generator operating costs while adhering to physical system constraints. Grid operators solve UC instances daily to meet power demand and ensure safe grid operations. This work presents a novel hybrid algorithm that leverages quantum and classical computing to solve UC more efficiently. We introduce a novel Benders-cut generation technique for UC, thereby enhancing cut quality, reducing expensive quantum-classical hardware interactions, and lowering qubit requirements. Additionally, we incorporate a $k$-local neighborhood search technique as a recovery step to ensure a higher quality solution than current QAH alone can achieve. The proposed algorithm, QC4UC, is evaluated on a modified instance of the IEEE RTS-96 test system. Results from both a simulated annealer and real QAH are compared, demonstrating the effectiveness of this algorithm in reducing qubit requirements and producing near-optimal solutions on noisy QAH.

math.OC↗

arXiv2025

Learning response functions of analog quantum computers: analysis of neutral-atom and superconducting platforms

Analog quantum computation is an attractive paradigm for the simulation of time-dependent quantum systems. Programmable analog quantum computers have been realized in hardware using a variety of physical principles, including neutral-atom and superconducting technologies. The input parameters of the physical Hamiltonians that are used to program the quantum simulator generally differ from the parameters that characterize the output distribution of data produced under a specified quantum dynamics. The relationship between the input and output parameters is known as the response function of the analog device. Here, we introduce a streaming algorithm for learning the response function of analog quantum computers from arbitrary user inputs, thus not requiring special calibration runs. We use the method to learn and compare the response functions of several generations of analog quantum simulators based on superconducting and neutral-atom programmable arrays.

quant-ph↗

arXiv2024

Potential Applications of Quantum Computing at Los Alamos National Laboratory

The emergence of quantum computing technology over the last decade indicates the potential for a transformational impact in the study of quantum mechanical systems. It is natural to presume that such computing technologies would be valuable to large scientific institutions, such as United States national laboratories. However, detailed descriptions of what these institutions would like to use these computers for are limited. To help provide some initial insights into this topic, this report develops detailed use cases of how quantum computing technology could be utilized to enhance a variety of quantum physics research activities at Los Alamos National Laboratory, including quantum magnetic materials, high-temperature superconductivity and nuclear astrophysics simulations. The report discusses how current high-performance computers are used for scientific discovery today and develops detailed descriptions of the types of quantum physics simulations that Los Alamos National Laboratory scientists would like to conduct, if a sufficient computing technology became available. While the report strives to highlight the breadth of potential application areas for quantum computation, this investigation has also indicated that many more use cases exist at Los Alamos National Laboratory, which could be documented in similar detail with sufficient time and effort.

quant-ph↗

arXiv2024

Applications of Lifted Nonlinear Cuts to Convex Relaxations of the AC Power Flow Equations

We demonstrate that valid inequalities, or lifted nonlinear cuts (LNC), can be projected to tighten the Second Order Cone (SOC), Convex DistFlow (CDF), and Network Flow (NF) relaxations of the AC Optimal Power Flow (AC-OPF) problem. We conduct experiments on 36 cases from the PGLib-OPF library for two objective functions, (1) power generation maximization and (2) generation cost minimization. Significant optimality gap improvements are shown for the maximization problem, where the LNC strengthen the SOC and CDF relaxations in 100% of the test cases, with average and maximum differences in the optimality gaps of 23.1% and 93.5% respectively. The NF relaxation is strengthened in 79.2% of test cases, with average and maximum differences in the optimality gaps of 3.45% and 21.2% respectively. We also study the trade-off between relaxation quality and solve time, demonstrating that the strengthened CDF relaxation outperforms the strengthened SOC formulation in terms of runtime and number of iterations needed, while the strengthened NF formulation is the most scalable with the lowest relaxation quality provided by these LNC.

math.OC↗

arXiv2024

QuantumAnnealing: A Julia Package for Simulating Dynamics of Transverse Field Ising Models

Analog Quantum Computers are promising tools for improving performance on applications such as modeling behavior of quantum materials, providing fast heuristic solutions to optimization problems, and simulating quantum systems. Due to the challenges of simulating dynamic quantum systems, there are relatively few classical tools for modeling the behavior of these devices and verifying their performance. QuantumAnnealing.jl provides a toolkit for performing simulations of Analog Quantum Computers on classical hardware. This package includes functionality for simulation of the time evolution of the Transverse Field Ising Model, replicating annealing schedules used by real world annealing hardware, implementing custom annealing schedules, and more. This allows for rapid prototyping of models expected to display interesting behavior, verification of the performance of quantum devices, and easy comparison against the expected behavior of quantum devices against classical approaches for small systems. The software is provided as open-source and is available through Julia's package registry system.

quant-ph↗

arXiv2024

Managing power balance and reserve feasibility in the AC unit commitment problem

Incorporating the AC power flow equations into unit commitment models has the potential to avoid costly corrective actions required by less accurate power flow approximations. However, research on unit commitment with AC power flow constraints has been limited to a few relatively small test networks. This work investigates large-scale AC unit commitment problems for the day-ahead market and develops decomposition algorithms capable of obtaining high-quality solutions at industry-relevant scales. The results illustrate that a simple algorithm that only seeks to satisfy unit commitment, reserve, and AC power balance constraints can obtain surprisingly high-quality solutions to this AC unit commitment problem. However, a naive strategy that prioritizes reserve feasibility leads to AC infeasibility, motivating the need to design heuristics that can effectively balance reserve and AC feasibility. Finally, this work explores a parallel decomposition strategy that allows the proposed algorithm to obtain feasible solutions on large cases within the two hour time limit required by typical day-ahead market operations.

eess.SY↗

arXiv2024

Cost of Emulating a Small Quantum Annealing Problem in the Circuit-Model

Demonstrations of quantum advantage for certain sampling problems have generated considerable excitement for quantum computing and have further spurred the development of circuit-model quantum computers, which represent quantum programs as a sequence of quantum gates acting on a finite number of qubits. Amongst this excitement, analog quantum computation has become less prominent, with the expectation that circuit-model quantum computers will eventually be sufficient for emulating analog quantum computation and thus rendering analog quantum computation obsolete. In this work we explore the basic requirements for emulating a specific analog quantum computation in the circuit model: the preparation of a biased superposition of degenerate ground states of an Ising Hamiltonian using an adiabatic evolution. We show that the overhead of emulation is substantial even for this simple problem. This supports using analog quantum computation for solving time-dependent Hamiltonian dynamics in the short term and midterm, assuming analog errors can be made low enough and coherence times long enough to solve problems of practical interest.

quant-ph↗

arXiv2024

Limitations of Fault-Tolerant Quantum Linear System Solvers for Quantum Power Flow

Quantum computers hold promise for solving problems intractable for classical computers, especially those with high time or space complexity. Practical quantum advantage can be said to exist for such problems when the end-to-end time for solving such a problem using a classical algorithm exceeds that required by a quantum algorithm. Reducing the power flow (PF) problem into a linear system of equations allows for the formulation of quantum PF (QPF) algorithms, which are based on solving methods for quantum linear systems such as the Harrow-Hassidim-Lloyd (HHL) algorithm. Speedup from using QPF algorithms is often claimed to be exponential when compared to classical PF solved by state-of-the-art algorithms. We investigate the potential for practical quantum advantage in solving QPF compared to classical methods on gate-based quantum computers. Notably, this paper does not present a new QPF solving algorithm but scrutinizes the end-to-end complexity of the QPF approach, providing a nuanced evaluation of the purported quantum speedup in this problem. Our analysis establishes a best-case bound for the HHL-based quantum power flow complexity, conclusively demonstrating that the HHL-based method has higher runtime complexity compared to the classical algorithm for solving the direct current power flow (DCPF) and fast decoupled load flow (FDLF) problem. Notably, our analysis and conclusions can be extended to any quantum linear system solver with rigorous performance guarantees, based on the known complexity lower bounds for this problem. Additionally, we establish that for potential practical quantum advantage (PQA) to exist it is necessary to consider DCPF-type problems with a very narrow range of condition number values and readout requirements.

quant-ph↗

arXiv2023

Challenges and Opportunities in Quantum Optimization

Recent advances in quantum computers are demonstrating the ability to solve problems at a scale beyond brute force classical simulation. As such, a widespread interest in quantum algorithms has developed in many areas, with optimization being one of the most pronounced domains. Across computer science and physics, there are a number of different approaches for major classes of optimization problems, such as combinatorial optimization, convex optimization, non-convex optimization, and stochastic extensions. This work draws on multiple approaches to study quantum optimization. Provably exact versus heuristic settings are first explained using computational complexity theory - highlighting where quantum advantage is possible in each context. Then, the core building blocks for quantum optimization algorithms are outlined to subsequently define prominent problem classes and identify key open questions that, if answered, will advance the field. The effects of scaling relevant problems on noisy quantum devices are also outlined in detail, alongside meaningful benchmarking problems. We underscore the importance of benchmarking by proposing clear metrics to conduct appropriate comparisons with classical optimization techniques. Lastly, we highlight two domains - finance and sustainability - as rich sources of optimization problems that could be used to benchmark, and eventually validate, the potential real-world impact of quantum optimization.

quant-ph↗

arXiv2023

Exploring Non-Linear Programming Formulations in QuantumCircuitOpt for Optimal Circuit Design

Given the limitations of current hardware, the theoretical gains promised by quantum computing remain unrealized across practical applications. But the gap between theory and hardware is closing, assisted by developments in quantum algorithmic modeling. One such recent development is QuantumCircuitOpt (QCOpt), an open-source software framework that leverages state-of-the-art optimization-based solvers to find provably optimal compact circuit decompositions, which are exact up to global phase and machine precision. The quantum circuit design problem can be modeled using non-linear, non-convex constraints. However, QCOpt reformulates these non-linear constraints using well-known linearization techniques such that the resulting design problem is solved as a Mixed-Integer Linear Programming (MILP) model. In this work, we instead explore whether the QCOpt could also be effective with a continuous Non-Linear Programming (NLP) model obtained via relaxation of the integer variables in the non-linear constraints. We are able to present not only multiple significant enhancements to QCOpt, with up to 11.3x speed-up in run times on average, but also opportunities for more generally exploring the behavior of gradient-based NLP solvers.

quant-ph↗

arXiv2023

Universal framework for simultaneous tomography of quantum states and SPAM noise

We present a general denoising algorithm for performing simultaneous tomography of quantum states and measurement noise. This algorithm allows us to fully characterize state preparation and measurement (SPAM) errors present in any quantum system. Our method is based on the analysis of the properties of the linear operator space induced by unitary operations. Given any quantum system with a noisy measurement apparatus, our method can output the quantum state and the noise matrix of the detector up to a single gauge degree of freedom. We show that this gauge freedom is unavoidable in the general case, but this degeneracy can be generally broken using prior knowledge on the state or noise properties, thus fixing the gauge for several types of state-noise combinations with no assumptions about noise strength. Such combinations include pure quantum states with arbitrarily correlated errors, and arbitrary states with block independent errors. This framework can further use available prior information about the setting to systematically reduce the number of observations and measurements required for state and noise detection. Our method effectively generalizes existing approaches to the problem, and includes as special cases common settings considered in the literature requiring an uncorrelated or invertible noise matrix, or specific probe states.

quant-ph↗

arXiv2023

Security Constrained Optimal Power Shutoff

Electric grid faults are increasingly the source of ignition for major wildfires. To reduce the likelihood of such ignitions in high risk situations, utilities use pre-emptive deenergization of power lines, commonly referred to as Public Safety Power Shut-offs (PSPS). Besides raising challenging trade-offs between power outages and wildfire safety, PSPS removes redundancy from the network just at a time when component faults are likely to happen. This may leave the network particularly vulnerable to unexpected line faults that may occur while the PSPS is in place. Previous works have not explicitly considered the impacts of such outages. To address this gap, we propose the Security-Constrained Optimal Power Shutoff (SC-OPS) problem which uses post-contingency security constraints to model the impact of unexpected line faults when planning a PSPS. This SC-OPS model enables, for the first time, the exploration of a wide range of trade-offs between both wildfire risk and pre- and post-contingency load shedding while designing PSPS plans, providing useful insights for utilities and policy makers considering different approaches to PSPS.We demonstrate the efficacy of our model using the EPRI 39-bus test system as a case study. The results highlight the potential risks of not considering security constraints when planning PSPS and show that incorporating security constraints into the PSPS design process improves the resilience of current PSPS plans.

eess.SY↗

arXiv2023

PowerModelsADA: A Framework for Solving Optimal Power Flow using Distributed Algorithms

This paper presents PowerModelsADA, an open-source framework for solving Optimal Power Flow (OPF) problems using Alternating Distributed Algorithms (ADA). PowerModelsADA provides a framework to test, verify, and benchmark both existing and new ADAs. This paper demonstrates use cases for PowerModelsADA and validates its implementation with multiple OPF formulations.

eess.SY↗

arXiv2023

Optimization Applications as Quantum Performance Benchmarks

Combinatorial optimization is anticipated to be one of the primary use cases for quantum computation in the coming years. The Quantum Approximate Optimization Algorithm (QAOA) and Quantum Annealing (QA) can potentially demonstrate significant run-time performance benefits over current state-of-the-art solutions. Inspired by existing methods to characterize classical optimization algorithms, we analyze the solution quality obtained by solving Max-Cut problems using gate-model quantum devices and a quantum annealing device. This is used to guide the development of an advanced benchmarking framework for quantum computers designed to evaluate the trade-off between run-time execution performance and the solution quality for iterative hybrid quantum-classical applications. The framework generates performance profiles through compelling visualizations that show performance progression as a function of time for various problem sizes and illustrates algorithm limitations uncovered by the benchmarking approach. As an illustration, we explore the factors that influence quantum computing system throughput, using results obtained through execution on various quantum simulators and quantum hardware systems.

quant-ph↗

arXiv2022

On the Emerging Potential of Quantum Annealing Hardware for Combinatorial Optimization

Over the past decade, the usefulness of quantum annealing hardware for combinatorial optimization has been the subject of much debate. Thus far, experimental benchmarking studies have indicated that quantum annealing hardware does not provide an irrefutable performance gain over state-of-the-art optimization methods. However, as this hardware continues to evolve, each new iteration brings improved performance and warrants further benchmarking. To that end, this work conducts an optimization performance assessment of D-Wave Systems' most recent Advantage Performance Update computer, which can natively solve sparse unconstrained quadratic optimization problems with over 5,000 binary decision variables and 40,000 quadratic terms. We demonstrate that classes of contrived problems exist where this quantum annealer can provide run time benefits over a collection of established classical solution methods that represent the current state-of-the-art for benchmarking quantum annealing hardware. Although this work does not present strong evidence of an irrefutable performance benefit for this emerging optimization technology, it does exhibit encouraging progress, signaling the potential impacts on practical optimization tasks in the future.

math.OC↗