arXiv subjects

Thinh Viet Le

Publications and source records attributed to Thinh Viet Le.

3 recordsLinked to original sources

arXiv2026

Solving Conic Programs over Sparse Graphs using a Variational Quantum Approach: The Case of the AC Optimal Power Flow

Conic programs arising in physics, quantum information, machine learning, and engineering are often defined over sparse graphs. Although such problems can be solved in polynomial time using classical interior-point solvers, the computational complexity scales unfavorably with graph size. We propose a variational quantum paradigm for solving conic programs, including quadratically constrained quadratic programs and semidefinite programs. We encode primal variables via the state of a parameterized quantum circuit (PQC) and dual variables via the probability mass function associated with a second PQC. The Lagrangian function can thus be expressed as scaled expectations of quantum observables. We pursue approximately stationary points of the Lagrangian by minimizing/maximizing the Lagrangian over the parameters of the first/second PQC. This is accomplished in a hybrid fashion: gradients are estimated using the two PQCs, while their parameters are updated classically using a primal-dual method. We propose permuting primal variables so that related observables have a banded form, enabling efficient measurement. We provide a complexity analysis that is useful to determine which problem types may enjoy quantum advantage. The framework is applied to the AC OPF problem, a large-scale optimization problem central to electric power system operation. Numerical tests on the IEEE 57-node system using PennyLane's simulator show that the proposed doubly variational quantum framework can find high-quality OPF solutions. While this demonstration does not yield a quantum speedup, the results serve as a proof-of-concept and highlight challenges toward practical quantum advantage. Although showcased for OPF, the framework has broader scope, including conic programs with many variables and constraints, problems defined over sparse graphs, and training quantum machine learning models to satisfy constraints.

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arXiv2025

Learning AC Power Flow Solutions using a Data-Dependent Variational Quantum Circuit

Interconnection studies require solving numerous instances of the AC load or power flow (AC PF) problem to simulate diverse scenarios as power systems navigate the ongoing energy transition. To expedite such studies, this work leverages recent advances in quantum computing to find or predict AC PF solutions using a variational quantum circuit (VQC). VQCs are trainable models that run on modern-day noisy intermediate-scale quantum (NISQ) hardware to accomplish elaborate optimization and machine learning (ML) tasks. Our first contribution is to pose a single instance of the AC PF as a nonlinear least-squares fit over the VQC trainable parameters (weights) and solve it using a hybrid classical/quantum computing approach. The second contribution is to feed PF specifications as features into a data-embedded VQC and train the resultant quantum ML (QML) model to predict general PF solutions. The third contribution is to develop a novel protocol to efficiently measure AC-PF quantum observables by exploiting the graph structure of a power network. Preliminary numerical tests indicate that the proposed VQC models attain enhanced prediction performance over a deep neural network despite using much fewer weights. The proposed quantum AC-PF framework sets the foundations for addressing more elaborate grid tasks via quantum computing.

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arXiv2024

Variational Quantum Eigensolver with Constraints (VQEC): Solving Constrained Optimization Problems via VQE

Variational quantum approaches have shown great promise in finding near-optimal solutions to computationally challenging tasks. Nonetheless, enforcing constraints in a disciplined fashion has been largely unexplored. To address this gap, this work proposes a hybrid quantum-classical algorithmic paradigm termed VQEC that extends the celebrated VQE to handle optimization with constraints. As with the standard VQE, the vector of optimization variables is captured by the state of a variational quantum circuit (VQC). To deal with constraints, VQEC optimizes a Lagrangian function classically over both the VQC parameters as well as the dual variables associated with constraints. To comply with the quantum setup, variables are updated via a perturbed primal-dual method leveraging the parameter shift rule. Among a wide gamut of potential applications, we showcase how VQEC can approximately solve quadratically-constrained binary optimization (QCBO) problems, find stochastic binary policies satisfying quadratic constraints on the average and in probability, and solve large-scale linear programs (LP) over the probability simplex. Under an assumption on the error for the VQC to approximate an arbitrary probability mass function (PMF), we provide bounds on the optimality gap attained by a VQC. Numerical tests on a quantum simulator investigate the effect of various parameters and corroborate that VQEC can generate high-quality solutions.

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