Practical Scalability of Tensor Network Quantum Emulators for Molecular Hamiltonian Simulation
Quantum computing holds promise for computational chemistry, but near-term quantum hardware remains limited by noise and scale, motivating classical bridging technologies such as quantum emulators. We present an application-specific systems-level benchmark of matrix product state (MPS) tensor-network emulation for real-time Hamiltonian evolution of a density matrix embedding theory (DMET)-embedded sulfonyl-fluoride pharmaceutical fragment, using state-vector simulation as reference. We evaluate runtime, accuracy, resource requirements, and entanglement growth across active spaces from 4 to 24 qubits for a one-body temporal observable used as a quantum fingerprint for reactivity prediction. The results identify a practical boundary for this workflow. At fixed bond dimension, MPS emulation retains favorable scaling, but the bond dimension required to estimate the observable within a 1.6 mHa chemical-accuracy threshold grows rapidly with active-space size. At 20-24 qubits, it approaches the maximum available MPS representation, eliminating the runtime advantage over state-vector simulation. Entanglement entropy analysis shows that increasing bipartite entanglement in the time-evolved state drives this cost growth, consistent with a mismatch between a one-dimensional MPS ansatz and the non-local correlations generated by molecular electronic dynamics. We do not claim a universal crossover across molecules, observables, mappings, or tensor-network geometries. Rather, this study measures where MPS emulation ceases to be an efficient classical surrogate for this chemically motivated Hamiltonian-simulation workflow. The results motivate entanglement-aware algorithm design, orbital-ordering and mapping optimization, alternative tensor-network geometries, and ultimately fault-tolerant quantum hardware for regimes where accurate molecular dynamics generate non-compressible entanglement.