Stochastic Quantum Power Flow for Risk Assessment in Power Systems

TL;DR

This work presents the first framework for Stochastic Quantum Power Flow (SQPF) that integrates classical probability distributions of uncertain injections into quantum states and uses Quantum Monte Carlo via Quantum Amplitude Estimation to assess line-overloading risk. The method relies on a linear DC power-flow formulation with a PTDF-based mapping, utilizing a unitaryized matrix decomposition (M_sc) to encode the line-flow distribution within a quantum circuit, and extracts metrics such as mean loading and overload probability through amplitude-based measurements. Key contributions include the encoding of multi-bus distributions, a SVD-based unitary realization of the linear mapping, and a quantifiable sample-complexity advantage (IQAE achieving ~12–16% of classical MC samples) demonstrated on 3-bus and 5-bus test systems. The results, obtained from simulated and limited real hardware, indicate potential speedups in SPF risk assessment with near-term quantum devices, while highlighting substantial challenges in circuit depth and noise, and pointing to future extensions toward AC power flow and larger systems.

Abstract

This paper introduces the first quantum computing framework for Stochastic Quantum Power Flow (SQPF) analysis in power systems. The proposed method leverages quantum states to encode power flow distributions, enabling the use of Quantum Monte Carlo (QMC) sampling to efficiently assess the probability of line overloads. Our approach significantly reduces the required sample size compared to traditional Monte Carlo methods, making it particularly suited for risk assessments in scenarios involving high uncertainty, such as renewable energy integration. We validate the method on two test systems, demonstrating the computational advantage of quantum algorithms in reducing sample complexity while maintaining accuracy. This work represents a foundational step toward scalable quantum power flow analysis, with potential applications in future power system operations and planning. The results show promising computational speedups, underscoring the potential of quantum computing in addressing the increasing uncertainty in modern power grids.

Figures (6)

• Figure 1: Proposed framework for estimating the risk of line overload using the Stochastic Quantum Power Flow method
• Figure 2: Test systems used for SQPF
• Figure 3: Power distribution of the generator at bus $B_1$ and the quantum circuit used for creating it
• Figure 4: Quantum circuit encoding $M_{sc}=UV^H$
• Figure 5: Quantum circuit for computing an estimated value of a line flow distribution in the three bus system