Abstract We consider randomized QMC methods for approximating the expected recourse in two-stage stochastic optimization problems containing mixed-integer decisions in the second stage. It is known that the second-stage optimal value function is piecewise linear-quadratic with possible kinks and discontinuities at the boundaries of certain convex polyhedral sets. This structure is exploited to provide conditions implying that first and higher order terms of the integrand’s ANOVA decomposition (Math. Comp. 79 (2010), 953–966) have mixed weak first order partial derivatives. This leads to a good smooth approximation of the integrand and, hence, to good convergence rates of randomized QMC methods if the effective (superposition) dimension is low.
Distribution network reconfiguration (DNR) is a combinatorial optimization problem that seeks a low-loss network topology subject to topological and electrical operating constraints. In this work, we propose a two-stage quantum-classical method for DNR. First, an iterative linear-ramp Quantum Alternating Operator Ansatz (LR-QAOA) searches topologically feasible subspaces constructed using a novel cycle-edge encoding. The encoding guarantees that every represented configuration is a spanning tree while allowing the size and coverage of each subspace to be adjusted to the available qubit budget. Second, the resulting sample distribution is used to guide a mixed-integer second-order-cone programming (MISOCP) solver. The method is evaluated on six distribution networks ranging from 33 to 417 buses through ideal simulation and execution on trapped-ion quantum hardware. For the 417-bus network, quantum hardware sampling identifies a configuration within approximately
1.4% of the literature reference loss. Across all six test systems, the MISOCP solver guided by hardware-derived distributions reaches an incumbent within
1% of the target with a lower median solver time than the corresponding unguided solver. These findings establish a concrete framework for applying current quantum hardware to DNR, with the potential to become increasingly competitive as hardware improves.
The growing integration of power grids with communication networks underscores the critical importance of cybersecurity. Quantum key distribution (QKD) offers a potent approach to secure power information based on physics laws. However, the challenge of limited quantum keys due to low key rates remains unresolved, necessitating the optimal planning of QKD networks. Therefore, this paper proposes a QKD network planning method to address uncertainties in power communication. First, the fiber QKD-based communication network is introduced. Then, the QKD network planning problem is formulated as a two-stage stochastic mixed-integer linear programming (MILP) model. The first stage models the quantum device deployment considering QKD processes and investment budgets. The second stage takes demand response as an example, considering scenario-dependent communication requests that fluctuate with the output of renewable energy resources. Finally, the proposed method is validated by a modified IEEE 30-bus system, with numerical results verifying its effectiveness in improving power cybersecurity.