Symmetry conservation with Trotterization and Quantum Phase Estimation

Quantum Physics arXiv:2607.01560 (quant-ph) [Submitted on 2 Jul 2026] Title:Symmetry conservation with Trotterization and Quantum Phase Estimation Authors:Edith Leal-Sánchez, Fanny Vain, Jong-Kwon Ha, Ryan J. MacDonell View a PDF of the paper titled Symmetry conservation with Trotterization and Quantum Phase Estimation, by Edith Leal-S\'anchez and 3 other authors View PDF HTML (experimental) Abstract:Quantum algorithms for quantum chemistry and other many-body fermionic systems work by expressing the Hamiltonian in a basis of qubits and fragmenting the Hamiltonian into a sum of products of Pauli operators whose exponentials are easily encoded on a quantum device. Applying the product of exponentials, known as Trotterization, leads to an error associated with the non-commutativity of operators. This error can lead to breaking the symmetries of the Hamiltonian because the fragments are not symmetry conserving in general. Nonetheless, many algorithms for time evolution rely on Trotterization, including time evolution and quantum phase estimation. We show that we can express the Hamiltonian in terms of Hermitian excitation operators which map to sums of commuting Pauli strings for any encoding and conserve symmetries corresponding to Abelian groups of symmetry operators. Symmetries corresponding to non-Abelian groups, on the other hand, are not fully conserved by Trotterized Hermitian excitation operators, so we developed ``operator kirigami'' to cut the sum of non-commuting operators by orthogonal projection and to fold terms together using unitary rotations. We tested pools of operators for small molecules and basis sets, and found that electron number and spin symmetry conserving pools led to greater errors that decreased for larger molecules and were negated with second-order Trotterization. Our work shows the potential for testing quantum computing algorithms on classical computers by adapting tools used in electronic structure theory with conserved symmetries. Comments: Subjects: Quantum Physics (quant-ph); Chemical Physics (physics.chem-ph) Cite as: arXiv:2607.01560 [quant-ph] (or arXiv:2607.01560v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2607.01560 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Ryan MacDonell [view email] [v1] Thu, 2 Jul 2026 00:35:53 UTC (4,323 KB) Full-text links: Access Paper: View a PDF of the paper titled Symmetry conservation with Trotterization and Quantum Phase Estimation, by Edith Leal-S\'anchez and 3 other authorsView PDFHTML (experimental)TeX Source view license Ancillary-file links: Ancillary files (details): README dynamics/H2O_sto3g/h2o_csf_order.txt dynamics/H2O_sto3g/h2o_qubit_order.txt dynamics/H2O_sto3g/h2o_slater_order.txt dynamics/H2_631g/h2_631_csf_order.txt dynamics/H2_631g/h2_631_qubit_order.txt dynamics/H2_631g/h2_631_slater_order.txt dynamics/H2_ccpvdz/h2_cc_csf_order.txt dynamics/H2_ccpvdz/h2_cc_qubit_order.txt dynamics/H2_ccpvdz/h2_cc_slater_order.txt dynamics/H2_sto3g/h2_sto_csf_order.txt dynamics/H2_sto3g/h2_sto_qubit_order.txt dynamics/H2_sto3g/h2_sto_slater_order.txt dynamics/LiH_631g/lih_631_csf_order.txt dynamics/LiH_631g/lih_631_qubit_order.txt dynamics/LiH_631g/lih_631_slater_order.txt dynamics/LiH_sto3g/lih_sto3g_qubit_order.txt dynamics/LiH_sto3g/lih_sto_csf_order.txt dynamics/LiH_sto3g/lih_sto_slater_order.txt h2_631_csf.dat h2_631_qubit.dat h2_631_slater.dat h2_cc_csf.dat h2_cc_qubit.dat h2_cc_slater.dat h2_sto_csf.dat h2_sto_qubit.dat h2_sto_slater.dat h2o_csf.dat h2o_qubit.dat h2o_slater.dat lih_631_csf.dat lih_631_qubit.dat lih_631_slater.dat lih_sto_csf.dat lih_sto_qubit.dat lih_sto_slater.dat logarithm/H2O_sto3g/h2o_sto_csf_fot.txt logarithm/H2O_sto3g/h2o_sto_csf_sot.txt logarithm/H2O_sto3g/h2o_sto_qubit_fot.txt logarithm/H2O_sto3g/h2o_sto_qubit_sot.txt logarithm/H2O_sto3g/h2o_sto_slater_fot.txt logarithm/H2O_sto3g/h2o_sto_slater_sot.txt logarithm/H2_631g/h2_631_csf_fot.txt logarithm/H2_631g/h2_631_csf_sot.txt logarithm/H2_631g/h2_631_qubit_fot.txt logarithm/H2_631g/h2_631_qubit_sot.txt logarithm/H2_631g/h2_631_slater_fot.txt logarithm/H2_631g/h2_631_slater_sot.txt logarithm/H2_ccpvdz/h2_cc_csf_fot.txt logarithm/H2_ccpvdz/h2_cc_csf_sot.txt logarithm/H2_ccpvdz/h2_cc_qubit_fot.txt logarithm/H2_ccpvdz/h2_cc_qubit_sot.txt logarithm/H2_ccpvdz/h2_cc_slater_fot.txt logarithm/H2_ccpvdz/h2_cc_slater_sot.txt logarithm/H2_sto3g/h2_sto_csf_fot.txt logarithm/H2_sto3g/h2_sto_csf_sot.txt logarithm/H2_sto3g/h2_sto_qubit_fot.txt logarithm/H2_sto3g/h2_sto_qubit_sot.txt logarithm/H2_sto3g/h2_sto_slater_fot.txt logarithm/H2_sto3g/h2_sto_slater_sot.txt logarithm/LiH_631g/lih_631_csf_fot.txt logarithm/LiH_631g/lih_631_csf_sot.txt logarithm/LiH_631g/lih_631_qubit_fot.txt logarithm/LiH_631g/lih_631_qubit_sot.txt logarithm/LiH_631g/lih_631_slater_fot.txt logarithm/LiH_631g/lih_631_slater_sot.txt logarithm/LiH_sto3g/lih_631_csf_sot.txt logarithm/LiH_sto3g/lih_631_qubit_sot.txt logarithm/LiH_sto3g/lih_631_slater_sot.txt logarithm/LiH_sto3g/lih_sto_csf_fot.txt logarithm/LiH_sto3g/lih_sto_csf_sot.txt logarithm/LiH_sto3g/lih_sto_qubit_fot.txt logarithm/LiH_sto3g/lih_sto_qubit_sot.txt logarithm/LiH_sto3g/lih_sto_slater_fot.txt logarithm/LiH_sto3g/lih_sto_slater_sot.txt(71 additional files not shown) You must enabled JavaScript to view entire file list. 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