Billion-Scale Quantum Darwinism: Matrix-Free von Neumann Entropy Estimation via FP8 Ozaki Scheme on NVIDIA Blackwell

Abstract

We present the first integration of the Ozaki error-free transformation with FP8 Tensor Core acceleration for matrix-free von Neumann entropy estimation in a quantum many-body simulation. Our application is Quantum Darwinism on a scrambled Spin-Star model: a one-qubit system entangled with 32 environment qubits whose S_32 permutation symmetry is deliberately destroyed by heterogeneous disorder coupling and a three-layer 1D brick-wall scrambling circuit. This construction forces the simulation into the full 2^33 = 8.59 × 10^9-dimensional Hilbert space, precluding both the Dicke-subspace shortcut and tensor-network compression. Entropy is estimated via Stochastic Lanczos Quadrature (SLQ) with N_v = 100 Hutchinson probe vectors and m = 40 Lanczos steps, never materializing the 2^32 × 2^32 reduced density matrix. The dominant partial-trace matrix-vector kernel is accelerated with torch._scaled_mm, targeting native FP8 E4M3 Tensor Cores of a single NVIDIA B300 SXM6 AC GPU (288 GB HBM3e). The FP8 Ozaki 2-slice configuration achieves an 8.17× steady-state speedup over an FP32 baseline while incurring only 1.30% pure quantization error (± 0.17% across T=5 trials)—isolated from statistical variance by a shared Hutchinson seed—outperforming naive FP8 (13.95×, 3.47%) on accuracy and the 3-slice variant (5.76×, same ≈ 1.3% error but slower) on speed. Physical correctness is validated to 0.007% relative error by exact recovery of the Quantum Darwinism saturation identity I(S:F)|_f=1 = 2H(S). Contrary to the plateau expected of the idealized permutation-symmetric Spin-Star model, the mutual information curve of this disordered, scrambled construction rises smoothly across the full range of environment fraction f with no flat redundancy plateau—a finding we confirm is not a numerical artifact via independent exact-diagonalization and cross-precision checks at smaller and larger scales. To the best of our knowledge, this is the first work at the intersection of FP8 Ozaki emulation, matrix-free SLQ, and quantum entropy estimation at billion-dimensional scale.