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  • Open Access

Benchmarking quantum simulation of chemical Hamiltonians using the sorted-list encoding

Calvin Ku1,2, Yu-Cheng Chen1, Alice Hu2,3,*, and Min-Hsiu Hsieh1,†

  • *Contact author: alicehu@cityu.edu.hk
  • †Contact author: min-hsiu.hsieh@foxconn.com
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Phys. Rev. Research 8, 033091 – Published 22 July, 2026

DOI: https://doi.org/10.1103/6q7b-h9db

Abstract

Quantum phase estimation is a cornerstone algorithm for fault-tolerant quantum computation, especially for electronic structure calculations of chemical systems. Optimal simulation relies on a complex trade-offs across many parameters including Hamiltonian simulation techniques, basis sets, and the fermion-to-qubit encodings. Here, we characterize the trade-offs and quantify the quantum resource costs of the sorted-list encoding as a particle-conserving, low-qubit alternative to the Jordan-Wigner encoding. We identify specific regimes, across different simulation techniques and basis sets, where the sorted-list encoding would be favorable compared to existing methods. Our findings are further supported through numerical benchmarks of real-world chemical systems. We found the sorted-list encoding to be a viable alternative to the Jordan-Wigner encoding for the compact molecular orbital basis when the electron-filling ratio is low, which typically occurs when high-precision results are required. In the plane-wave basis, we found similar asymptotic gate and qubit scaling between the sorted-list and the first-quantized encoding, although the first-quantized encoding still retains lower constant factors.

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Phys. Rev. Research 8, 033091– Published 22 July, 2026
  • Received 9 December 2025
  • Accepted 22 June 2026
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