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 $Ω(N κ/\varepsilon),$ reflecting dependence on system size $N$, condition number $κ$, and error tolerance $\varepsilon$. Finally, we highlight key areas where QC algorithms may offer potential benefits over NRLF in addressing the standard ACPF problem.
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 Ω(Nκ/ε), reflecting dependence on system size N, condition number κ, and error tolerance ε. Finally, we highlight key areas where QC algorithms may offer potential benefits over NRLF in addressing the standard ACPF problem.
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.
We present the first direct comparison between gate-based quantum computing (GQC) and adiabatic quantum computing (AQC) paradigms for solving the AC power flow (PF) equations. The PF problem is reformulated as a combinatorial optimization problem. For the GQC approach, the Quantum Approximate Optimization Algorithm (QAOA) is employed, while for the AQC approach, the problem is formulated as an Ising model. Numerical experiments on a 4-bus test system evaluate solution accuracy and computational performance. Results obtained using QAOA are benchmarked against those produced by D-Wave's Advantage system and Fujitsu's latest-generation Digital Annealer, implemented through the Quantum-Inspired Integrated Optimization (QIIO) software. The findings provide quantitative insights into the performance trade-offs, scalability, and practical viability of GQC and AQC paradigms for PF analysis, highlighting the potential of quantum optimization algorithms to address the computational challenges associated with the operation of modern electricity grids in the fault-tolerant era.
Quantum computing provides alternative algorithmic approaches to solve computationally challenging problems and has shown potential advantages compared to classical methods for specific problem classes. This thesis explores variational quantum algorithms (VQAs) for solving the alternating current optimal power flow (AC OPF) problem and the AC power flow (PF) problem. Both tasks are fundamental to power system analysis, operation, and planning, but they become increasingly challenging as grid size and complexity grow. The first main contribution of the thesis introduces a variational quantum framework for solving the OPF problem, formulated as a nonconvex quadratically constrained quadratic program. The proposed method encodes primal and dual optimization variables using two parameterized quantum circuits (PQCs), allowing the OPF Lagrangian to be expressed as expectations over quantum observables. An OPF solution can be found by minimizing the Lagrangian over the parameters of the first PQC and maximizing it over the parameters of the second PQC. The proposed framework seeks saddle points of the Lagrangian in a hybrid fashion. The gradients of the Lagrangian are estimated using the two PQCs, and PQC parameters are updated classically using a primal-dual method. A key innovation is to permute the primal variables of the original problem, so the corresponding quantum observables adhere to a banded form that facilitates a novel qubit-efficient quantum measurement protocol. The second main contribution presents a quantum machine learning (QML) approach for learning AC PF solutions using a data-embedded PQC. The method first poses a single PF instance as a nonlinear least-squares problem over PQC parameters. Second, the PF specifications are embedded as features into another PQC, and the resultant QML model is trained to learn the PF mapping. Once presented with a new problem instance, the trained QML model can perform the prediction step efficiently in real-time operation. Third, a novel protocol is devised to efficiently measure PF observables by leveraging the graph structure of a power network. The proposed quantum AC PF/OPF framework sets the foundations for addressing more elaborate grid tasks via quantum computing. More broadly, the proposed quantum paradigms can be used to achieve safe QML as PQCs are trained to comply with data-dependent constraints.
The rise of quantum computing technology has brought new prospects and opportunities for optimal power flow calculation and optimal scheduling of power systems. In the face of complex network topology, variable load demand, and changing energy supply, traditional power systems often rely on algorithms based on classical computing for power flow calculation and optimal scheduling. However, as power systems continue to grow in size and complexity, traditional approaches have shown limitations in computing power when dealing with large-scale data and multi-constraint problems. Quantum computing, with its parallel computing power and the potential for efficient algorithms, offers new possibilities for solving these complex problems. The advantage of quantum computing is its ability to simultaneously handle multiple power flow paths and multivariate interactions, which make it a significant advantage in optimizing energy distribution, reducing energy consumption, and improving grid stability and responsiveness in power systems.
Quantum mechanics (QM) can be understood as a set of rules that forms the basis for developing all quantum theories. One of these theories is quantum computation (QC), i.e., computation based on QM logic. It is believed that QC provides paths to the problem solution that may not be possible for classical computers. Therefore, it has received attention to solve complex computational problems in different areas. Most of the research efforts, however, have concentrated on problems in theoretical physics and computer science, leaving little attention to solve practical problems in industrial applications. This is particularly true in power system applications where QC is mostly unknown. This paper mainly aims to attract the attention of power system researchers/engineers to QC as a potential solution to address emerging computational challenges of power systems. To this end, the historical development of QC and its fundamental concepts are first described. Then, recent contributions to solving computationally-demanding power system problems such as AC and DC power flow (PF), contingency analysis, state estimation, electromagnetic transients simulation (EMT), fault diagnosis, unit commitment (UC), and facility location–allocation (FLA) problems are discussed. Unfortunately, power system researchers have not yet been able to convincingly demonstrate a quantum advantage in solving large-scale power system problems mainly because we are in the noisy intermediate-scale quantum (NISQ) era, where quantum devices are noisy and have limited quantum resources. However, it may be demonstrated in the future with technological advances and increased research efforts in the area.
Alternating Current Optimal Power Flow Unit Commitment (AC-OPF-UC) is a difficult mixed-integer nonlinear optimization problem that combines binary generator commitment decisions with nonconvex continuous AC power-flow constraints. In this work, we investigate whether hybrid quantum-classical variational algorithms can improve the solution of single-period AC-OPF-UC relative to classical approaches. To the best of our knowledge, this is the first study to directly evaluate quantum or hybrid quantum-classical algorithms for the full AC-OPF-UC problem. We consider two candidate algorithms for improving AC-OPF-UC solution quality relative to purely classical methods on ideal quantum hardware. The first applies QAOA directly to a fully discretized formulation of the problem, with equality and inequality constraints incorporated through penalty terms and slack variables. Although conceptually straightforward, this approach requires a prohibitively large number of qubits even for small instances. The second, qubit-efficient approach encodes only the binary generator status variables on a quantum computer, while optimizing the continuous power-flow variables classically for each sampled bitstring. We benchmark this method on randomly generated AC-OPF-UC instances with 5 to 13 generators and compare it against SCIP, SMAC, and uniform random sampling. Our simulations show that the qubit-efficient hybrid method does not outperform uniform sampling. These results suggest that in order to establish potential advantage of the variational hybrid strategy considered here over the best classical algorithms, if any, much larger system sizes (25+ generators) need to be tested, which is beyond our computational capacity. Alternatively, different approaches, such as quantum versions of branch-and-bound methods, may be more promising.