Tensor Network Simulation of the Heisenberg Model on Heavy-Hex Lattices

Abstract

We extend CppSim, a high-performance C++/HIP tensor network simulator, to the heavy-hex lattice geometry used in superconducting quantum processors. The heavy-hex graph -- a bipartite graph of degree-2 and degree-3 sites with a natural 3-color gate schedule -- is implemented as a drop-in grid class with no changes to the gate application or belief propagation (BP) kernels. We simulate the isotropic Heisenberg model on the heavy hex 3x3 graph (68 sites, 76 bonds) in the Heisenberg picture using Pauli transfer matrices (PTMs), and study the autocorrelation C(t) = <Zc (t)Zc (0)> and operator lightcone. We incorporate a fully parametric hardware noise model: per-bond, per-color-class 16 x 16 PTMs are loaded from device characterization data and interleaved with unitary gates, with noise scaling factor gamma in {1.0, 2.0, 3.0} for multi-product formula (MPF) extrapolation to zero noise. Chi convergence is demonstrated at chi = 200 (|error| < 10^-4, reference chi = 430) on a 32 GB GPU, with a ~10x wall-clock speedup over a Julia/AMDGPU.jl reference implementation at saturated bond dimension.