Hierarchical Discovery of Adiabatic Hamiltonian Paths and RL Schedules for Quantum Linear System Solvers

Wang chenglong

Additional Submission Instructions: For the camera-ready version, please include the author names and affiliations, funding disclosures, and acknowledgements.

Track: Track 1: Original Research/Position/Education/Attention Track

Keywords: quantum linear systems problem;Adiabatic quantum algorithms;RL

Abstract:

Quantum linear-system solvers can provide
asymptotic speedups under structured access as-
sumptions, but finite-size performance depends
strongly on the spectral encoding, Hamiltonian
path, traversal schedule, and implementation
model. We study a hierarchical framework for the
quantum linear systems problem (QLSP) that sep-
arates admissible Hamiltonian-path design from
adaptive traversal control. The outer loop searches
constrained deformations of analytically valid adi-
abatic backbones within implementable opera-
tor libraries, while the inner loop is restricted
to residual schedule control around a derivative-
aware local-adiabatic prior. This residual class
can be optimized by derivative-free search, dif-
ferentiable optimal control, or family-wise RL;
the present experiments instantiate derivative-
free residual search and frame RL as the nat-
ural amortized-control extension rather than as
unconstrained Hamiltonian invention. In this
sense, the framework acts as a two-stage auto-
matic algorithm-design pipeline: the outer layer
automatically adapts valid path families, while the
inner layer automatically refines residual traversal
schedules. We do not seek to improve worst-case
asymptotic query complexity beyond optimal-
scaling QLSP solvers; instead, the framework tar-
gets engineering-relevant finite-size fidelity–time
tradeoffs, family-dependent adaptation, and diag-
nostic transparency. Simulations show the clearest
gains on structured gap-amplified and precondi-
tioned families. Ancilla-assisted extensions can
improve gap structure, subspace anchoring, and
preconditioning, but do not evade known optimal-
scaling query-complexity limits.

Submission Number: 348