On the Computational Viability of Quantum Optimization for PMU Placement

Jones, Eric B.; Kapit, Eliot; Chang, Chin-Yao; Biagioni, David; Vaidhynathan, Deepthi; Gräf, Peter; Jones, Wesley B.

doi:10.1109/pesgm41954.2020.9281420

Cited by 7 publications

(6 citation statements)

References 15 publications

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“…As observed in previous work, |J | and |Q| track closely to one another over multiple orders of magnitude (Jones et al 2020). In addition, at γ = 0.6 and γ = 0.9 as shown, |Q| and |V | both increase by roughly two orders of magnitude between |S| = 4 and |S| = 8.…”

Section: Hardware Requirements For the K-spin Mdpsupporting

confidence: 86%

K-spin Hamiltonian for quantum-resolvable Markov decision processes

Jones

Gräf

Kapit

et al. 2020

Quantum Mach. Intell.

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The Markov decision process is the mathematical formalization underlying the modern field of reinforcement learning when transition and reward functions are unknown. We derive a pseudo-Boolean cost function that is equivalent to a K-spin Hamiltonian representation of the discrete, finite, discounted Markov decision process with infinite horizon. This K-spin Hamiltonian furnishes a starting point from which to solve for an optimal policy using heuristic quantum algorithms such as adiabatic quantum annealing and the quantum approximate optimization algorithm on near-term quantum hardware. In arguing that the variational minimization of our Hamiltonian is approximately equivalent to the Bellman optimality condition for a prevalent class of environments we establish an interesting analogy with classical field theory. Along with proof-ofconcept calculations to corroborate our formulation by simulated and quantum annealing against classical Q-Learning, we analyze the scaling of physical resources required to solve our Hamiltonian on quantum hardware. Keywords K-spin hamiltonian • Markov decision process • Quantum optimization • Quantum annealing • Simulated annealing • Quantum approximate optimization algorithm Electronic supplementary material The online version of this article (

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Section: Hardware Requirements For the K-spin Mdpsupporting

confidence: 86%

K-spin Hamiltonian for quantum-resolvable Markov decision processes

Jones

Gräf

Kapit

et al. 2020

Quantum Mach. Intell.

Self Cite

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“…The time for completing a quantum computation is given by T Q ≈ T P + ρ(T A + T R ), where T Q is the QPU access time, T P is the quantum programming time, ρ is the number of times an anneal-read cycle is repeated, T A is the annealing time and T R is the time required to read a measurement. It is conventional to report ρT A as an equivalent to the classical CPU time [27], however, T Q is reported in Tables III and IV for the cut selection component for the sake of completeness.…”

Section: Resultsmentioning

confidence: 99%

“…In [27] the solution of the phasor measurement unit (PMU) placement problem using the D-Wave Systems 2000Q QA was investigated. The PMU placement problem was formulated as the minimum dominating set problem.…”

Section: B Qc Applications In the Power And Energy Sectormentioning

confidence: 99%

“…It was found that for some instances the QA outperformed the classical solver CPLEX. The optimization model presented in [27] is easily converted into a QUBO, however, it does not capture the complexity of the actual problem. Similarly, in [28] fairness during the design of a heat grid was evaluated by solving a QUBO problem on a QA and the quality of the solutions was benchmarked against a graph partitioning solver without observing significant differences.…”

Section: B Qc Applications In the Power And Energy Sectormentioning

confidence: 99%

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Hybrid Quantum-Classical Multi-cut Benders Approach with a Power System Application

Paterakis¹

2021

Preprint

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Leveraging the current generation of quantum devices to solve optimization problems of practical interest necessitates the development of hybrid quantum-classical (HQC) solution approaches. In this paper, a multi-cut Benders decomposition (BD) approach that exploits multiple feasible solutions of the master problem (MP) to generate multiple valid cuts is adapted, so as to be used as an HQC solver for general mixed-integer linear programming (MILP) problems. The use of different cut selection criteria and strategies to manage the size of the MP by eliciting a subset of cuts to be added in each iteration of the BD scheme using quantum computing is discussed. The HQC optimization algorithm is applied to the Unit Commitment (UC) problem. UC is a prototypical use case of optimization applied to electrical power systems, a critical sector that may benefit from advances in quantum computing. The validity and computational viability of the proposed approach are demonstrated using the D-Wave Advantage 4.1 quantum annealer.

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“…The power system is identified as observable when the voltages of all buses in it are known. In [45], the feasibility of QC is studied in solving optimal PMU placement optimization problems. The computational capability of D‐Wave systems 2000Q annealer was compared with the industry‐standard CPLEX Optimizer.…”

Section: Smart Grid Applicationsmentioning

confidence: 99%

Quantum computing for smart grid applications

Ullah

Eskandarpour

Zheng

et al. 2022

IET Generation Trans & Dist

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Computational complexities in modern power systems are reportedly increasing daily, and it is anticipated that traditional computers might be inadequate to provide the computation prerequisite in future complex power grids. In that given context, quantum computing (QC) can be considered a next‐generation alternative solution to deal with upcoming computational challenges in smart grids. The QC is a relatively new yet promising technology that leverages the unique phenomena of quantum mechanics in processing information and computations. This emerging paradigm shows a significant potential to overcome the barrier of computational limitations with better and faster solutions in optimization, simulations, and machine learning problems. In recent years, substantial progress in developing advanced quantum hardware, software, and algorithms have made QC more feasible to apply in various research areas, including smart grids. It is evident that considerable research has already been carried out, and such efforts are remarkably continuing. As QC is a highly evolving field of study, a brief review of the existing literature will be vital to realize the state‐of‐art on QC for smart grid applications. Therefore, this article summarizes the research outcomes of the most recent papers, highlights their suggestions for utilizing QC techniques for various smart grid applications, and further identifies the potential smart grid applications. Several real‐world QC case studies in various research fields besides power and energy systems are demonstrated. Moreover, a brief overview of available quantum hardware specifications, software tools, and algorithms is described with a comparative analysis.

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On the Computational Viability of Quantum Optimization for PMU Placement

Cited by 7 publications

References 15 publications

K-spin Hamiltonian for quantum-resolvable Markov decision processes

K-spin Hamiltonian for quantum-resolvable Markov decision processes

Hybrid Quantum-Classical Multi-cut Benders Approach with a Power System Application

Quantum computing for smart grid applications

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