A Batchwise Quantum Discrete Adiabatic Linear System Solver

Quantum discrete adiabatic linear‐system algorithms may require increasingly long coherent circuit sequences as the number of evolution steps grows. A batchwise quantum discrete adiabatic linear‐system solver is presented, in which the evolution is partitioned into sequentially dependent circuit batches. Each batch is followed by computational‐basis measurement, classical state reconstruction, and state re‐preparation for the next batch, thereby reducing the longest uninterrupted coherent circuit depth while preserving the intended discrete evolution structure. The reconstruction exploits the real–imaginary structure of the evolving state together with a sign‐prediction procedure. Selected DeepQuantum simulations evaluate the conditional solution fidelity under different evolution settings, sampling budgets, noise levels, sign‐prediction thresholds, condition numbers, and matrix dimensions. The results indicate that high conditional solution fidelity can be retained under suitable discretization and reconstruction settings and clarify the trade‐off among coherent depth, measurement overhead, and classical processing. The proposed framework provides a simulation‐based foundation and practical design guidance for future quantum‐hardware studies of adiabatic linear‐system solvers.