arXiv subjects

Carleton Coffrin

Publications and source records attributed to Carleton Coffrin.

At least 37 records · Page 2Linked to original sources

arXiv2022

Signatures of Open and Noisy Quantum Systems in Single-Qubit Quantum Annealing

We propose a quantum annealing protocol that more effectively probes the dynamics of a single qubit on D-Wave's quantum annealing hardware. This protocol uses D-Wave's h-gain schedule functionality, which allows the rapid quenching of the longitudinal magnetic field at arbitrary points during the anneal. This features enables us to distinguish between open and closed system dynamics as well as the presence or absence of longitudinal magnetic field noise. We show that both thermal and magnetic field fluctuations are key sources of noise that need to be included in an open quantum system model to reproduce the output statistics of the hardware.

quant-ph↗

arXiv2022

Polyhedral Relaxations for Optimal Pump Scheduling of Potable Water Distribution Networks

The classic pump scheduling or Optimal Water Flow (OWF) problem for water distribution networks (WDNs) minimizes the cost of power consumption for a given WDN over a fixed time horizon. In its exact form, the OWF is a computationally challenging mixed-integer nonlinear program (MINLP). It is complicated by nonlinear equality constraints that model network physics, discrete variables that model operational controls, and intertemporal constraints that model changes to storage devices. To address the computational challenges of the OWF, this paper develops tight polyhedral relaxations of the original MINLP, derives novel valid inequalities (or cuts) using duality theory, and implements novel optimization-based bound tightening and cut generation procedures. The efficacy of each new method is rigorously evaluated by measuring empirical improvements in OWF primal and dual bounds over forty-five literature instances. The evaluation suggests that our relaxation improvements, model strengthening techniques, and a thoughtfully selected polyhedral relaxation partitioning scheme can substantially improve OWF primal and dual bounds, especially when compared with similar relaxation-based techniques that do not leverage these new methods.

math.OC↗

arXiv2022

Quantum Algorithm Implementations for Beginners

As quantum computers become available to the general public, the need has arisen to train a cohort of quantum programmers, many of whom have been developing classical computer programs for most of their careers. While currently available quantum computers have less than 100 qubits, quantum computing hardware is widely expected to grow in terms of qubit count, quality, and connectivity. This review aims to explain the principles of quantum programming, which are quite different from classical programming, with straightforward algebra that makes understanding of the underlying fascinating quantum mechanical principles optional. We give an introduction to quantum computing algorithms and their implementation on real quantum hardware. We survey 20 different quantum algorithms, attempting to describe each in a succinct and self-contained fashion. We show how these algorithms can be implemented on IBM's quantum computer, and in each case, we discuss the results of the implementation with respect to differences between the simulator and the actual hardware runs. This article introduces computer scientists, physicists, and engineers to quantum algorithms and provides a blueprint for their implementations.

cs.ET↗

arXiv2022

Vector Field Visualization of Single-Qubit State Tomography

As the variety of commercially available quantum computers continues to increase so does the need for tools that can characterize, verify and validate these computers. This work explores using quantum state tomography for characterizing the performance of individual qubits and develops a vector field visualization for presentation of the results. The proposed protocol is demonstrated in simulation and on quantum computing hardware developed by IBM. The results identify qubit performance features that are not reflected in the standard models of this hardware, indicating opportunities to improve the accuracy of these models. The proposed qubit evaluation protocol is provided as free open-source software to streamline the task of replicating the process on other quantum computing devices.

quant-ph↗

arXiv2022

Recursive Restoration Refinement: A Fast Heuristic for Near-Optimal Restoration Prioritization in Power Systems

The prioritization of restoration actions after large power system outages plays a key role in how quickly power can be restored. It has been shown that fast and intuitive heuristics for restoration prioritization most often result in low-quality restoration plans. Meanwhile, mathematical optimization tools that find high-quality restoration plans are too slow to be applied to restoration planning problems of practical interest. This work makes a significant step in closing this quality vs compute time gap by proposing the Recursive Restoration Refinement heuristic for power system restoration. This heuristic is shown to produce near-optimal restoration plans up to 1,000 times faster than other state-of-the-art solution methods on a range of test cases with up to 500 buses and 700 damaged components. The potential impact of this new heuristic is demonstrated by a preliminary analysis of the key features of high-quality restoration plans. The recursive restoration refinement algorithm and other methods explored in this work have been made available as part of the open-source software package, PowerModelsRestoration, to support ongoing research in power restoration algorithms.

eess.SY↗

arXiv2022

High-quality Thermal Gibbs Sampling with Quantum Annealing Hardware

Quantum Annealing (QA) was originally intended for accelerating the solution of combinatorial optimization tasks that have natural encodings as Ising models. However, recent experiments on QA hardware platforms have demonstrated that, in the operating regime corresponding to weak interactions, the QA hardware behaves like a noisy Gibbs sampler at a hardware-specific effective temperature. This work builds on those insights and identifies a class of small hardware-native Ising models that are robust to noise effects and proposes a procedure for executing these models on QA hardware to maximize Gibbs sampling performance. Experimental results indicate that the proposed protocol results in high-quality Gibbs samples from a hardware-specific effective temperature. Furthermore, we show that this effective temperature can be adjusted by modulating the annealing time and energy scale. The procedure proposed in this work provides an approach to using QA hardware for Ising model sampling presenting potential new opportunities for applications in machine learning and physics simulation.

quant-ph↗

arXiv2021

QuantumCircuitOpt: An Open-source Framework for Provably Optimal Quantum Circuit Design

In recent years, the quantum computing community has seen an explosion of novel methods to implement non-trivial quantum computations on near-term hardware. An important direction of research has been to decompose an arbitrary entangled state, represented as a unitary, into a quantum circuit, that is, a sequence of gates supported by a quantum processor. It has been well known that circuits with longer decompositions and more entangling multi-qubit gates are error-prone for the current noisy, intermediate-scale quantum devices. To this end, there has been a significant interest to develop heuristic-based methods to discover compact circuits. We contribute to this effort by proposing QuantumCircuitOpt (QCOpt), a novel open-source framework which implements mathematical optimization formulations and algorithms for decomposing arbitrary unitary gates into a sequence of hardware-native gates. A core innovation of QCOpt is that it provides optimality guarantees on the quantum circuits that it produces. In particular, we show that QCOpt can find up to 57% reduction in the number of necessary gates on circuits with up to four qubits, and in run times less than a few minutes on commodity computing hardware. We also validate the efficacy of QCOpt as a tool for quantum circuit design in comparison with a naive brute-force enumeration algorithm. We also show how the QCOpt package can be adapted to various built-in types of native gate sets, based on different hardware platforms like those produced by IBM, Rigetti and Google. We hope this package will facilitate further algorithmic exploration for quantum processor designers, as well as quantum physicists.

quant-ph↗

arXiv2021

Convex Relaxations of Maximal Load Delivery for Multi-contingency Analysis of Joint Electric Power and Natural Gas Transmission Networks

Recent increases in gas-fired power generation have engendered increased interdependencies between natural gas and power transmission systems. These interdependencies have amplified existing vulnerabilities to gas and power grids, where disruptions can require the curtailment of load in one or both systems. Although typically operated independently, coordination of these systems during severe disruptions can allow for targeted delivery to lifeline services, including gas delivery for residential heating and power delivery for critical facilities. To address the challenge of estimating maximum joint network capacities under such disruptions, we consider the task of determining feasible steady-state operating points for severely damaged systems while ensuring the maximal delivery of gas and power loads simultaneously, represented mathematically as the nonconvex joint Maximal Load Delivery (MLD) problem. To increase its tractability, we present a mixed-integer convex relaxation of the MLD problem. Then, to demonstrate the relaxation's effectiveness in determining bounds on network capacities, exact and relaxed MLD formulations are compared across various multi-contingency scenarios on nine joint networks ranging in size from 25 to 1,191 nodes. The relaxation-based methodology is observed to accurately and efficiently estimate the impacts of severe joint network disruptions, often converging to the relaxed MLD problem's globally optimal solution within ten seconds.

math.OC↗

arXiv2021

Single-Qubit Cross Platform Comparison of Quantum Computing Hardware

As a variety of quantum computing models and platforms become available, methods for assessing and comparing the performance of these devices are of increasing interest and importance. Despite being built of the same fundamental computational unit, radically different approaches have emerged for characterizing the performance of qubits in gate-based and quantum annealing computers, limiting and complicating consistent cross-platform comparisons. To fill this gap, this work proposes a single-qubit protocol (Q-RBPN) for measuring some basic performance characteristics of individual qubits in both models of quantum computation. The proposed protocol scales to large quantum computers with thousands of qubits and provides insights into the distribution of qubit properties within a particular hardware device and across families of devices. The efficacy of the Q-RBPN protocol is demonstrated through the analysis of more than 300 gate-based qubits spanning eighteen machines and 2000 annealing-based qubits from one machine, revealing some unexpected differences in qubit performance. Overall, the proposed Q-RBPN protocol provides a new platform-agnostic tool for assessing the performance of a wide range of emerging quantum computing devices.

quant-ph↗

arXiv2021

Single-Qubit Fidelity Assessment of Quantum Annealing Hardware

As a wide variety of quantum computing platforms become available, methods for assessing and comparing the performance of these devices are of increasing interest and importance. Inspired by the success of single-qubit error rate computations for tracking the progress of gate-based quantum computers, this work proposes a Quantum Annealing Single-qubit Assessment (QASA) protocol for quantifying the performance of individual qubits in quantum annealing computers. The proposed protocol scales to large quantum annealers with thousands of qubits and provides unique insights into the distribution of qubit properties within a particular hardware device. The efficacy of the QASA protocol is demonstrated by analyzing the properties of a D-Wave 2000Q system, revealing unanticipated correlations in the qubit performance of that device. A study repeating the QASA protocol at different annealing times highlights how the method can be utilized to understand the impact of annealing parameters on qubit performance. Overall, the proposed QASA protocol provides a useful tool for assessing the performance of current and emerging quantum annealing devices.

quant-ph↗

arXiv2021

Graph-Based Modeling and Decomposition of Energy Infrastructures

Nonlinear optimization problems are found at the heart of real-time operations of critical infrastructures. These problems are computationally challenging because they embed complex physical models that exhibit space-time dynamics. We propose modeling these problems as graph-structured optimization problems, and illustrate how their structure can be exploited at the modeling level (for parallelizing function/derivative computations) and at the solver level (for parallelizing linear algebra operations). Specifically, we present a restricted additive Schwarz scheme that enables flexible decomposition of complex graph structures within an interior-point algorithm. The proposed approach is implemented as a general-purpose nonlinear programming solver that we call MadNLP.jl; this Julia-based solver is interfaced to the graph-based modeling package Plasmo.jl. The efficiency of this framework is demonstrated via problems arising in transient gas network optimization and multi-period AC optimal power flow. We show that our framework accelerates the solution (compared to off-the-shelf tools) by over 300%; specifically, solution times are reduced from 72.36 sec to 23.84 sec for the gas problem and from 515.81 sec to 149.45 sec for the power flow problem.

math.OC↗

arXiv2021

The Power Grid Library for Benchmarking AC Optimal Power Flow Algorithms

In recent years, the power systems research community has seen an explosion of novel methods for formulating the AC power flow equations. Consequently, benchmarking studies using the seminal AC Optimal Power Flow (AC-OPF) problem have emerged as the primary method for evaluating these emerging methods. However, it is often difficult to directly compare these studies due to subtle differences in the AC-OPF problem formulation as well as the network, generation, and loading data that are used for evaluation. To help address these challenges, this IEEE PES Task Force report proposes a standardized AC-OPF mathematical formulation and the PGLib-OPF networks for benchmarking AC-OPF algorithms. A motivating study demonstrates some limitations of the established network datasets in the context of benchmarking AC-OPF algorithms and a validation study demonstrates the efficacy of using the PGLib-OPF networks for this purpose. In the interest of scientific discourse and future additions, the PGLib-OPF benchmark library is open-access and all the of network data is provided under a creative commons license.

math.OC↗

arXiv2020

Programmable Quantum Annealers as Noisy Gibbs Samplers

Drawing independent samples from high-dimensional probability distributions represents the major computational bottleneck for modern algorithms, including powerful machine learning frameworks such as deep learning. The quest for discovering larger families of distributions for which sampling can be efficiently realized has inspired an exploration beyond established computing methods and turning to novel physical devices that leverage the principles of quantum computation. Quantum annealing embodies a promising computational paradigm that is intimately related to the complexity of energy landscapes in Gibbs distributions, which relate the probabilities of system states to the energies of these states. Here, we study the sampling properties of physical realizations of quantum annealers which are implemented through programmable lattices of superconducting flux qubits. Comprehensive statistical analysis of the data produced by these quantum machines shows that quantum annealers behave as samplers that generate independent configurations from low-temperature noisy Gibbs distributions. We show that the structure of the output distribution probes the intrinsic physical properties of the quantum device such as effective temperature of individual qubits and magnitude of local qubit noise, which result in a non-linear response function and spurious interactions that are absent in the hardware implementation. We anticipate that our methodology will find widespread use in characterization of future generations of quantum annealers and other emerging analog computing devices.

quant-ph↗

arXiv2020

The Potential of Quantum Annealing for Rapid Solution Structure Identification

The recent emergence of novel computational devices, such as quantum computers, coherent Ising machines, and digital annealers presents new opportunities for hardware-accelerated hybrid optimization algorithms. Unfortunately, demonstrations of unquestionable performance gains leveraging novel hardware platforms have faced significant obstacles. One key challenge is understanding the algorithmic properties that distinguish such devices from established optimization approaches. Through the careful design of contrived optimization tasks, this work provides new insights into the computation properties of quantum annealing and suggests that this model has the potential to quickly identify the structure of high-quality solutions. A meticulous comparison to a variety of algorithms spanning both complete and local search suggests that quantum annealing's performance on the proposed optimization tasks is distinct. This result provides new insights into the time scales and types of optimization problems where quantum annealing has the potential to provide notable performance gains over established optimization algorithms and suggests the development of hybrid algorithms that combine the best features of quantum annealing and state-of-the-art classical approaches.

math.OC↗

arXiv2020

Natural Gas Maximal Load Delivery for Multi-contingency Analysis

As the use of renewable generation has increased, electric power systems have become increasingly reliant on natural gas-fired power plants as fast ramping sources for meeting fluctuating bulk power demands. This dependence has introduced new vulnerabilities to the power grid, including disruptions to gas transmission networks from natural and man-made disasters. To address the operational challenges arising from these disruptions, we consider the task of determining a feasible steady-state operating point for a damaged gas pipeline network while ensuring the maximal delivery of load. We formulate the mixed-integer nonconvex maximal load delivery (MLD) problem, which proves difficult to solve on large-scale networks. To address this challenge, we present a mixed-integer convex relaxation of the MLD problem and use it to determine bounds on the transport capacity of a gas pipeline system. To demonstrate the effectiveness of the relaxation, the exact and relaxed formulations are compared across a large number of randomized damage scenarios on nine natural gas pipeline network models ranging in size from 11 to 4197 junctions. A proof of concept application, which assumes network damage from a set of synthetically generated earthquakes, is also presented to demonstrate the utility of the proposed optimization-based capacity evaluation in the context of risk assessment for natural disasters. For all but the largest network, the relaxation-based method is found to be suitable for use in evaluating the impacts of multi-contingency network disruptions, often converging to the optimal solution of the relaxed formulation in less than ten seconds.

math.OC↗

arXiv2020

Fully analog memristive circuits for optimization tasks: a comparison

We introduce a Lyapunov function for the dynamics of memristive circuits, and compare the effectiveness of memristors in minimizing the function to widely used optimization software. We study in particular three classes of problems which can be directly embedded in a circuit topology, and show that memristors effectively attempt at (quickly) extremizing these functionals.

nlin.AO↗

arXiv2020

The Impacts of Convex Piecewise Linear Cost Formulations on AC Optimal Power Flow

Despite strong connections through shared application areas, research efforts on power market optimization (e.g., unit commitment) and power network optimization (e.g., optimal power flow) remain largely independent. A notable illustration of this is the treatment of power generation cost functions, where nonlinear network optimization has largely used polynomial representations and market optimization has adopted piecewise linear encodings. This work combines state-of-the-art results from both lines of research to understand the best mathematical formulations of the nonlinear AC optimal power flow problem with piecewise linear generation cost functions. An extensive numerical analysis of non-convex models, linear approximations, and convex relaxations across fifty-four realistic test cases illustrates that nonlinear optimization methods are surprisingly sensitive to the mathematical formulation of piecewise linear functions. The results indicate that a poor formulation choice can slow down algorithm performance by a factor of ten, increasing the runtime from seconds to minutes. These results provide valuable insights into the best formulations of nonlinear optimal power flow problems with piecewise linear cost functions, a important step towards building a new generation of energy markets that incorporate the nonlinear AC power flow model.

math.OC↗

arXiv2020

A Flexible Storage Model for Power Network Optimization

This paper proposes a simple and flexible storage model for use in a variety of multi-period optimal power flow problems. The proposed model is designed for research use in a broad assortment of contexts enabled by the following key features: (i) the model can represent the dynamics of an energy buffer at a wide range of scales, from residential battery storage to grid-scale pumped hydro; (ii) it is compatible with both balanced and unbalanced formulations of the power flow equations; (iii) convex relaxations and linear approximations to allow seamless integration of the proposed model into applications where convexity or linearity is required are developed; (iv) a minimalist and standardized data model is presented, to facilitate easy of use by the research community. The proposed model is validated using a proof-of-concept twenty-four hour storage scheduling task that demonstrates the value of the model's key features. An open-source implementation of the model is provided as part of the PowerModels and PowerModelsDistribution optimization toolboxes.

eess.SY↗