Optimal number-conserved linear encoding for practical fermionic simulation - Cheng,MH; Chen,Y-C; Wang,Q; Bartsch,V; Medina,AC; Kim,MS; Hu,A; Hsieh,M-H (Physical Review Research, 2025)
Number-conserved subspace encoding reduces resources needed for quantum simulations, but scalable com plexity trade-off bounds for M modes and N particles with O(N log M) qubits have remained unknown. We studyqubit-gate-measurement trade-offs through the lens of classical/quantum error correction complexity and developa framework of fermionic gate and measurement complexity based on classical encoder/decoder appearing inthe error correction framework. We demonstrate optimal encoding with random classical parity check code andpropose the Fermionic Expectation Decoder for scalable probability decoding in O(M4 ) bases. The protocol istested with variational quantum eigensolver on LiH in the STO-3G and 6-31G bases, and H2 potential energycurve in the 6-311G basis.