Efficient Quantum Circuits for Electronic Hamiltonian Simulation without Pauli Expansion
Abstract
Electronic Hamiltonian simulation is commonly formulated by mapping fermionic operators to qubit operators and subsequently expanding the resulting ladder-operator products into Pauli strings. While general, this procedure obscures the higher-level fermionic structure and can hide opportunities for circuit optimization. Building on ladder-string-pair (Lasp) diagonalization originally developed for Hamiltonian simulation of partial differential equations, we construct time-evolution circuits for the second-quantized electronic Hamiltonian without performing a Pauli expansion. For the most general case of complex-valued coefficients, we present a time-evolution circuit for a two-body fermionic Lasp operator that corresponds to 16 Pauli strings in the Pauli-expansion approach but does not suffer from Trotter error at this stage. Expanding the optimization scope from a single operator to a triad of three fermionic Lasp operators sharing the same four spin-orbital indices enables systematic cancellation of CX gates, reducing the CX-gate count from 36 to 12 in the example considered, still without introducing Trotter error at this stage. For n spin orbitals, further expanding the optimization scope to a sequence of O(n) suitably ordered triads enables a cascade of CX-gate reductions across triad boundaries, reducing the CX-gate count from O(n2) to O(n). The Lasp-based approach also naturally accommodates controlled time evolution and yields further optimizations for real-valued Hamiltonians. These results demonstrate that the Lasp-based approach enables more efficient time-evolution circuits by preserving high-level circuit structures and thereby expanding the scope of optimization, providing a systematic route toward more efficient electronic Hamiltonian simulation.
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BibTeX
@misc{onodera2026efficient,
title = {{Efficient Quantum Circuits for Electronic Hamiltonian Simulation without Pauli Expansion}},
author = {Tamiya Onodera and Takeshi Sato},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06285},
eprint = {2609.06285},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06285},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Efficient Quantum Circuits for Electronic Hamiltonian Simulation without Pauli Expansion
AU - Tamiya Onodera
AU - Takeshi Sato
PY - 2026
DA - 2026/09/05
PB - arXiv
DO - 10.48550/arxiv.2609.06285
UR - https://arxiv.org/abs/2609.06285
AB - Electronic Hamiltonian simulation is commonly formulated by mapping fermionic operators to qubit operators and subsequently expanding the resulting ladder-operator products into Pauli strings. While general, this procedure obscures the higher-level fermionic structure and can hide opportunities for circuit optimization. Building on ladder-string-pair (Lasp) diagonalization originally developed for Hamiltonian simulation of partial differential equations, we construct time-evolution circuits for the second-quantized electronic Hamiltonian without performing a Pauli expansion. For the most general case of complex-valued coefficients, we present a time-evolution circuit for a two-body fermionic Lasp operator that corresponds to 16 Pauli strings in the Pauli-expansion approach but does not suffer from Trotter error at this stage. Expanding the optimization scope from a single operator to a triad of three fermionic Lasp operators sharing the same four spin-orbital indices enables systematic cancellation of CX gates, reducing the CX-gate count from 36 to 12 in the example considered, still without introducing Trotter error at this stage. For n spin orbitals, further expanding the optimization scope to a sequence of O(n) suitably ordered triads enables a cascade of CX-gate reductions across triad boundaries, reducing the CX-gate count from O(n^2) to O(n). The Lasp-based approach also naturally accommodates controlled time evolution and yields further optimizations for real-valued Hamiltonians. These results demonstrate that the Lasp-based approach enables more efficient time-evolution circuits by preserving high-level circuit structures and thereby expanding the scope of optimization, providing a systematic route toward more efficient electronic Hamiltonian simulation.
ER -