aiqbench analysis
This research establishes the minimal set of operations required to construct universal quantum circuits for molecular electronic states while strictly preserving spin symmetry and particle number. By identifying specific generators that eliminate energy-error plateaus at maximal-spin boundaries, the study provides a concrete pathway to reduce CNOT gate counts in practical quantum chemistry simulations.
Minimal building blocks for molecular quantum circuits with exact spin symmetry
arXiv:2609.37101v1 Announce Type: new Abstract: Preserving particle number and spin helps quantum circuits target molecular electronic states, but does not guarantee access to every state with the required quantum numbers. We determine which additional operations, combined with spin-independent orbital rotations connecting all spatial orbitals, generate every real state-space rotation within each complete subspace of fixed particle number $N$, total spin $S$, and spin projection $M_S$. We consider spin-free molecular calculations in real orbitals, without an additional spatial-symmetry restriction, and continuously tunable operations that preserve particle number, full spin symmetry, and real amplitudes. Below the maximal-spin limits set by the electron and hole numbers, repeated singlet-pair transfer between any two fixed spatial orbitals is sufficient. On nontrivial maximal-spin boundaries, pair transfer vanishes, and an additional generator built from one- and two-electron terms is sufficient exactly when its action in the target subspace is not a linear combination of orbital-rotation generators. The minimum number of spatial orbitals needed by one additional generator is two in the interior and three on nontrivial boundaries, even when terms involving more than two electrons are allowed. Both minima are attained using only one- and two-electron terms. The three-orbital optimum rotates two orbitals according to the occupation of a third, and its unitary factors exactly into eight commuting Pauli rotations. Molecular benchmarks show that this operation removes the observed boundary energy-error plateaus, while sparse interior constructions attain the prescribed energy accuracy with fewer compiled CNOT gates in selected fixed-orbital comparisons.
Abstract:Preserving particle number and spin helps quantum circuits target molecular electronic states, but does not guarantee access to every state with the required quantum numbers. We determine which additional operations, combined with spin-independent orbital rotations connecting all spatial orbitals, generate every real state-space rotation within each complete subspace of fixed particle number $N$, total spin $S$, and spin projection $M_S$. We consider spin-free molecular calculations in real orbitals, without an additional spatial-symmetry restriction, and continuously tunable operations that preserve particle number, full spin symmetry, and real amplitudes. Below the maximal-spin limits set by the electron and hole numbers, repeated singlet-pair transfer between any two fixed spatial orbitals is sufficient. On nontrivial maximal-spin boundaries, pair transfer vanishes, and an additional generator built from one- and two-electron terms is sufficient exactly when its action in the target subspace is not a linear combination of orbital-rotation generators. The minimum number of spatial orbitals needed by one additional generator is two in the interior and three on nontrivial boundaries, even when terms involving more than two electrons are allowed. Both minima are attained using only one- and two-electron terms. The three-orbital optimum rotates two orbitals according to the occupation of a third, and its unitary factors exactly into eight commuting Pauli rotations. Molecular benchmarks show that this operation removes the observed boundary energy-error plateaus, while sparse interior constructions attain the prescribed energy accuracy with fewer compiled CNOT gates in selected fixed-orbital comparisons.
72 pages, 7 figures; includes 25 pages of Supplementary Information. Data and code: this https URL
Quantum Physics (quant-ph); Chemical Physics (physics.chem-ph)
arXiv:2609.37101 [quant-ph]
(or arXiv:2609.37101v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2609.37101 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 351 words
