Shot and Architecture Adaptive Subspace Variational Quantum Eigensolver for Microwave Simulation

TL;DR

The paper tackles efficient computation of electromagnetic waveguide eigenmodes on NISQ hardware by marrying Subspace Variational Eigensolvers with reinforcement-learning-based circuit design and adaptive shot allocation. The proposed framework decomposes the waveguide Hamiltonian into Pauli terms, automates circuit construction with a DDQN-driven RL agent, and dynamically allocates measurement shots to reduce quantum-resource overhead. Across 3- and 5-qubit rectangular waveguides, the approach achieves substantial gate-count reductions, up to 20× faster convergence, and energy accuracies comparable to classical solutions under ideal conditions, while showing improved resilience to noise. This work advances practical quantum electromagnetic simulations and points toward scalable designs for complex microwave components as quantum hardware matures.

Abstract

Quantum computing offers a promising paradigm for electromagnetic eigenmode analysis, enabling compact representations of complex field interactions and potential exponential speedup over classical numerical solvers. Recent efforts have applied variational quantum eigensolver (VQE) based methods to compute waveguide modes, demonstrating the feasibility of simulating TE and TM field distributions on noisy intermediate-scale quantum (NISQ) hardware. However, these studies typically employ manually designed, fixed-depth parameterized quantum circuits and uniform measurement-shot strategies, resulting in excessive quantum resource consumption, limited circuit expressivity, and reduced robustness under realistic noise conditions. To address these limitations, we propose an architecture and shot adaptive subspace variational quantum eigensolver for efficient microwave waveguide eigenmode simulation on NISQ devices. The proposed framework integrates a reinforcement learning (RL) based circuit design strategy and an adaptive shot allocation mechanism to jointly reduce quantum resource overhead. Specifically, the RL agent autonomously explores the quantum circuit space to generate hardware-efficient parameterized quantum circuits, while the adaptive measurement scheme allocates sampling resources according to Hamiltonian term weights. Numerical experiments on three- and five-qubit systems demonstrate that the proposed framework achieves accurate estimation of TE and TM mode eigenvalues, with a minimum absolute error down to $10^{-8}$ and reconstructed field distributions under noiseless conditions in excellent agreement with classical electromagnetic solutions.

Figures (11)

• Figure 1: Workflow of the proposed SSVQE-based framework for estimating eigenmodes in rectangular waveguides.
• Figure 2: Weighted SSVQE optimization workflow.
• Figure 3: DDQN-based RL framework for automated circuit design.
• Figure 4: One-hot encoding of the actions and sequential action selection of quantum gates at each time step
• Figure 5: Reconstructed field distributions for three-qubit waveguide modes from the obtained eigenstates.