Quantum-Circuit Framework for Two-Stage Stochastic Programming via QAOA Integrated with a Quantum Generative Neural Network

TL;DR

This paper introduces qGAN-QAOA, a quantum-circuit approach combining a quantum generative neural network and QAOA to efficiently solve two-stage stochastic programming problems with many scenarios.

Contribution

It presents a novel quantum workflow that encodes scenario distributions and optimizes first-stage decisions, reducing complexity compared to traditional methods.

Findings

Demonstrates polynomial scaling of quantum circuits with scenario count.

Shows improved expected cost in stochastic unit commitment problems.

Validates the approach against classical baselines.

Abstract

Two-stage stochastic programming often discretizes uncertainty into scenarios, but scenario enumeration makes expected recourse evaluation scale at least linearly in the scenario count. We propose qGAN-QAOA, a unified quantum-circuit workflow in which a pre-trained quantum generative adversarial network encodes the scenario distribution and QAOA optimizes first-stage decisions by minimizing the full two-stage objective, including expected recourse cost. With the qGAN parameters fixed after training, we evaluate the objective as the expectation value of a problem Hamiltonian and optimize only the QAOA variational parameters. We interpret non-anticipativity as a condition on measurement outcome statistics and prove that the first-stage measurement marginal is independent of the scenario. For uniformly discretized uncertainty, the diagonal operator encoding the uncertainty admits a sparse Pauli-Z expansion via the Walsh--Hadamard transform, yielding polylogarithmic scaling of gate count and circuit depth with the number of scenarios. Numerical experiments on the stochastic unit commitment problem (UCP) with photovoltaic (PV) uncertainty compare the expected cost of the proposed method with classical expected-value and two-stage stochastic programming baselines, demonstrating the effectiveness of qGAN-QAOA as a two-stage decision model.