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iEnergy

World's first practical power flow algorithm operating on today's noisy quantum computers

Jinliang He

Published Mar 1, 2023• 1 citation
Publisher

Abstract

Power flow is an indispensable foundation for power system analytics. Under the deep penetration of renewables, modern power system analytics often becomes intractable because it needs to run an enormous amount of power flow analyses to quantify the impact of uncertainties. Unlike classical power flow methods that scale polynomially with the system size, quantum computing enables using logarithmically-scaled number of qubits to solve linear equations in power flow analysis. Thus, quantum power flow (QPF) provides a promising direction to make today's intractable power system analytics tractable. However, a major obstacle to the development of a practical quantum power flow algorithm lies in the fact that today's mainstream quantum computers are still noisy-intermediate-scale quantum (NISQ) devices whose capability is restricted by the limited number of qubits and considerable noises. To bridge this gap, Stony Brook University establishes a variational quantum power flow that allows for practical and noise-resilient power flow analysis on today's NISQ devices.

DOI
10.23919/ien.2023.0009

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Power flow is an indispensable foundation for power system analytics. Under the deep penetration of renewables, modern power system analytics often becomes intractable because it needs to run an enormous amount of power flow analyses to quantify the impact of uncertainties. Unlike classical power flow methods that scale polynomially with the system size, quantum computing enables using logarithmically-scaled number of qubits to solve linear equations in power flow analysis. Thus, quantum power flow (QPF) provides a promising direction to make today's intractable power system analytics tractable. However, a major obstacle to the development of a practical quantum power flow algorithm lies in the fact that today's mainstream quantum computers are still noisy-intermediate-scale quantum (NISQ) devices whose capability is restricted by the limited number of qubits and considerable noises. To bridge this gap, Stony Brook University establishes a variational quantum power flow that allows for practical and noise-resilient power flow analysis on today's NISQ devices.
Quantum power flow (QPF) offers an inspiring direction for overcoming the computation challenge of power flow through quantum computing. However, the practical implementation of existing QPF algorithms in today's noisy-intermediate-scale quantum (NISQ) era remains limited because of their sensitivity to noise. This paper establishes an NISQ-QPF algorithm that enables power flow computation on noisy quantum devices. The main contributions include: (1) a variational quantum circuit (VQC)-based alternating current (AC) power flow formulation, which enables QPF using short-depth quantum circuits; (2) NISQ-compatible QPF solvers based on the variational quantum linear solver (VQLS) and modified fast decoupled power flow; and (3) an error-resilient QPF scheme to relieve the QPF iteration deviations caused by noise; (3) a practical NISQ-QPF framework for implementable and reliable power flow analysis on noisy quantum machines. Extensive simulation tests validate the accuracy and generality of NISQ-QPF for solving practical power flow on IBM's real, noisy quantum computers.
Power flow (PF) analysis is a foundational computational method to study the flow of power in an electrical network. This analysis involves solving a set of non-linear and non-convex differential-algebraic equations. State-of-the-art solvers for PF analysis, therefore, face challenges with scalability and convergence, specifically for large-scale and/or ill-conditioned cases characterized by high penetration of renewable energy sources, among others. The adiabatic quantum computing paradigm has been proven to efficiently find solutions for combinatorial problems in the noisy intermediate-scale quantum (NISQ) era, and it can potentially address the limitations posed by state-of-the-art PF solvers. For the first time, we propose a novel adiabatic quantum computing approach for efficient PF analysis. Our key contributions are (i) a combinatorial PF algorithm and a modified version that aligns with the principles of PF analysis, termed the adiabatic quantum PF algorithm (AQPF), both of which use Quadratic Unconstrained Binary Optimization (QUBO) and Ising model formulations; (ii) a scalability study of the AQPF algorithm; and (iii) an extension of the AQPF algorithm to handle larger problem sizes using a partitioned approach. Numerical experiments are conducted using different test system sizes on D-Wave's Advantage™ quantum annealer, Fujitsu's digital annealer V3, D-Wave's quantum-classical hybrid annealer, and two simulated annealers running on classical computer hardware. The reported results demonstrate the effectiveness and high accuracy of the proposed AQPF algorithm and its potential to speed up the PF analysis process while handling ill-conditioned cases using quantum and quantum-inspired algorithms.
The integration of high-penetration renewable energy introduces significant stochasticity and non-convexity into power system dispatching, challenging the computational limits of classical optimization. While Variational Quantum Algorithms (VQAs) on Noisy Intermediate-Scale Quantum (NISQ) devices offer a promising path for combinatorial acceleration, existing approaches typically treat the power grid as a "black box", suffering from poor scalability (barren plateaus) and frequent violations of physical constraints. Bridging these gaps, this paper proposes a Physics-Informed Hybrid Quantum-Classical Dispatching (PI-HQCD) framework. We construct a topology-aware Hamiltonian that explicitly embeds linearized power flow equations, storage dynamics, and multi-timescale coupling directly into the quantum substrate, significantly reducing the search space dimensionality. We further derive a noise-adaptive regularization mechanism that theoretically bounds the effective Lipschitz constant of the objective function, guaranteeing convergence stability under realistic quantum measurement noise. Numerical experiments on the IEEE 39-bus benchmark and a 118-bus regional grid demonstrate that PI-HQCD achieves superior economic efficiency and higher renewable utilization compared to stochastic dual dynamic programming (SDDP). Theoretical analysis confirms that this topology-aware design leads to an O(1/N) gradient variance scaling, effectively mitigating barren plateaus and ensuring scalability for larger networks. This work establishes a rigorous paradigm for embedding engineering physics into quantum computing, paving the way for practical quantum advantage in next-generation grid operations.
Quantum power system state estimation (QPSSE) offers an inspiring direction for tackling the challenge of state estimation through quantum computing. Nevertheless, the current bottlenecks originate from the scarcity of practical and scalable QPSSE methodologies in the noisy intermediate-scale quantum (NISQ) era. This paper devises a NISQ-QPSSE algorithm that facilitates state estimation on real NISQ devices. Our new contributions include: (1) A variational quantum circuit (VQC)-based QPSSE formulation that empowers QPSSE analysis utilizing shallow-depth quantum circuits; (2) A variational quantum linear solver (VQLS)-based QPSSE solver integrating QPSSE iterations with VQC optimization; (3) An advanced NISQ-compatible QPSSE methodology for tackling the measurement and coefficient matrix issues on real quantum computers; (4) A noise-resilient method to alleviate the detrimental effects of noise disturbances. The encouraging test results on the simulator and real-scale systems affirm the precision, universality, and scalability of our QPSSE algorithm and demonstrate the vast potential of QPSSE in the thriving NISQ era.
The rapid development of quantum computing has provided a ground-breaking tool for solving problems that are insurmountable on classical computers. In the power system domain, quantum computing is still in the nascent stage, with limited but ongoing studies. The Quantum Approximation Optimization Algorithm (QAOA) has been applied in solving several NPhard problems and can be further studied to address challenging problems in power systems. Key applications include contingency analysis, optimal power flow, and unit commitment, among others. With the significant integration of renewable energy, the intermittent nature of renewable energy introduces substantial volatility to the system. An overhead contingency analysis is required to evaluate the possible system outage scenarios, which will identify critical contingencies to maintain system stability. However, the contingency analysis is a prototypical NP-Hard problem, requiring substantial classical computation resources. In this work, QAOA is developed for theN−kN-kN−kcontingency analysis on line contingency as well as the general contingency scenarios, with the aim of minimizing the shedding of the power load while ensuring the power flow constraints. A tailored objective function is developed to encode theN−kN-kN−kcontingency condition as well as the power flow loss constraints into a problem Hamiltonian for QAOA computation. The developed method is verified on IEEE 9- and 14-bus systems compared with classical methods as the baseline. In addition, a QAOA parameter study including the number of QAOA parameters, the number of repetitions of the quantum circuits execution, and the number of iteration steps of the classical optimization algorithm, is conducted to offer insights for the parameter tuning under different problem sizes. This work is anticipated to establish a quantum framework for solving critical and complex power system problems in the Noisy intermediate-scale quantum (NISQ) era.
Quantum computers hold promise for solving problems intractable for classical computers, especially those with high time or space complexity. Practicalquantum advantagecan 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.