Neural Network Assisted Fermionic Compression Encoding: A Lossy-QSCI Framework for Resource-Efficient Ground-State Simulations

Quantum computing promises to revolutionize many-body simulations for quantum chemistry, but its potential is constrained by limited qubits and noise in current devices. In this work, we introduce the Lossy Quantum Selected Configuration Interaction (Lossy-QSCI) framework, which combines a lossy subspace Hamiltonian preparation pipeline with a generic QSCI selection process. This framework integrates a chemistry-inspired lossy Random Linear Encoder (Chemical-RLE) with a neural network-assisted Fermionic Expectation Decoder (NN-FED). The RLE leverages fermionic number conservation to compress quantum states, reducing qubit requirements to O(N log M) for M spin orbitals and N electrons, while preserving crucial ground state information and enabling self-consistent configuration recovery. NN-FED, powered by a neural network trained with minimal data, efficiently decodes these compressed states, overcoming the measurement challenges common in the approaches of the traditional QSCI and its variants. Through iterative quantum sampling and classical post-processing, our hybrid method refines ground state estimates with high efficiency. This framework offers a resource-efficient pathway for ground-state simulations on near-term noisy hardware and could inspire resource-efficient extensions to future devices by minimizing qubit overhead.