Sparse Quantum State Simulation at Unlimited Scale: Block-Sparse Representation for QEC Verification and Beyond

We introduce a deterministic, block-sparse simulation framework for quantum states with bounded amplitude support. For states with k non-zero amplitudes over n qubits, we achieve O(k) memory and O(nk) time complexity—independent of the exponential 2ⁿ Hilbert space dimension. Key results: 1M-qubit GHZ states (53s, 4 KB, 100% fidelity), 100K-qubit W-states, and polynomial-weight Dicke states. Provides 6,600× speedup over Qiskit at 25 qubits for sparse states. Applications include quantum error correction verification and quantum networking protocol simulation.