Neural Network Assisted Fermionic Compression Encoding: A Lossy-QSCI Framework for Scalable Quantum Chemistry Simulations

Quantum-chemistry calculations on noisy hardware are bottlenecked by qubit count and measurement overhead. We introduce Lossy-QSCI -a compact form of Quantum Selected CI that (i) uses a chemistry-aware lossy Random Linear Encoder (Chemical-RLE) to compress an M-orbital, N-electron Hamiltonian to O(NlogM) qubits, and (ii) restores observables via a lightweight neural-network Fermionic Expectation Decoder (NN-FED). Applied to C2 and LiH, Lossy-QSCI attains chemical accuracy with roughly half the qubits and determinants required by standard QSCI, pointing to a practical route for accurate quantum-chemistry on NISQ and early fault-tolerant devices.