Quantum-Enabled Probabilistic Optimal Power Flow with Built-in Differential Privacy

TL;DR

This paper introduces a quantum computing framework for probabilistic optimal power flow that uses fewer qubits, leverages quantum noise for differential privacy, and demonstrates improved privacy and accuracy in power system optimization.

Contribution

A qubit-efficient quantum approach for probabilistic power flow that incorporates built-in differential privacy through quantum noise, reducing qubit requirements significantly.

Findings

Achieves 2.1× smaller privacy budgets than classical methods.

Maintains lower infeasibility and prediction error at similar privacy levels.

Requires only 5 qubits for a 69-bus system, compared to over 600 in traditional quantum methods.

Abstract

Quantum computing has been regarded as a promising approach to accelerate power system optimization. However, challenges such as limited qubits and inherent noise hinder their widespread adoption in power systems. In this paper, we propose a qubit-efficient framework for solving a crucial power system optimization problem, the probabilistic optimal power flow (POPF). We demonstrate that quantum noise, traditionally viewed as a drawback, can in fact be leveraged to provide a built-in differential privacy (DP) guarantee. Specifically, we first linearize POPF into a multi-parametric linear program (MP-LP) with renewable uncertainties being the parameters. This decomposes the parameter space into critical regions with precomputed solution maps. Second, a variational quantum circuit (VQC) classifies the critical region based on each uncertainty realization and then recovers the final solution. In this way, the required qubits scale with the uncertain parameters instead of the network size, with only 5 qubits versus 600+ for direct quantum OPF in a 69-bus system. Moreover, we prove the depolarizing noise of VQC provides DP guarantees and characterize the privacy-cost tradeoff. Case studies validate the proposed VQC achieves 2.1$\times$ smaller privacy budgets compared to its classical counterpart. At matched privacy levels, the VQC also maintains lower infeasibility and prediction error.