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Optimal number-conserved linear encoding for practical fermionic simulation

M. H. Cheng1,2,*, Yu-Cheng Chen3,4,*, Qian Wang3, V. Bartsch5, A. C. Medina2, M. S. Kim1,†, Alice Hu3,6,‡, and Min-Hsiu Hsieh4,§

  • *These authors contributed equally to this work.
  • †Contact author: m.kim@imperial.ac.uk
  • ‡Contact author: alicehu@cityu.edu.hk
  • §Contact author: min-hsiu.hsieh@foxconn.com
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Phys. Rev. Research 7, 033280 – Published 24 September, 2025

DOI: https://doi.org/10.1103/lzf5-x6hc

Abstract

Number-conserved subspace encoding reduces resources needed for quantum simulations, but scalable complexity trade-off bounds for M modes and N particles with O(NlogM) qubits have remained unknown. We study qubit-gate-measurement trade-offs through the lens of classical/quantum error correction complexity and develop a framework of fermionic gate and measurement complexity based on classical encoder/decoder appearing in the error correction framework. We demonstrate optimal encoding with random classical parity check code and propose the Fermionic Expectation Decoder for scalable probability decoding in O(M4) bases. The protocol is tested with variational quantum eigensolver on LiH in the STO-3G and 6-31G bases, and H2 potential energy curve in the 6-311G* basis.

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Phys. Rev. Research 7, 033280– Published 24 September, 2025
  • Received 14 October 2023
  • Revised 13 August 2024
  • Accepted 15 August 2025
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