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This research presents a significant advancement in quantum chemistry by deriving compact circuit implementations for symmetry-adapted fermionic unitaries using Lie algebra methods. The developed protocols reduce the quantum resources required for simulating molecular systems while maintaining exact conservation of symmetries, addressing a critical bottleneck beyond simple excitation classes. By optimizing parameter structures and extending formalisms to Krylov subspaces, this work directly enhances the efficiency and feasibility of near-term fault-tolerant quantum simulations in chemistry.
Spin-Adapted Fermionic Unitaries: From Lie Algebras to Compact Quantum Circuits
arXiv:2511.13485v2 Announce Type: replace Abstract: Conservation of symmetries is crucial for reliable quantum simulations of molecular systems, yet compact circuit implementations of fully symmetry-adapted fermionic unitaries have remained elusive beyond the simplest excitation classes. Here we address this issue for the set of singlet spin-adapted generalized singles and doubles operators (saGSD). Using the Wei--Norman approach, we derive exact product formulas that express spin-adapted fermionic unitaries as products of elementary spin-orbital unitaries. To obtain closed-form parameters in the more challenging 28- and 84-dimensional dynamical Lie algebras, we develop a computational discovery-and-verification protocol combining numerical optimization, parameter-structure identification, closed-form inference, and exact validation against reduced Wei--Norman equations. We also introduce an algorithm for constructing closed-form fermionic unitary transformations on Krylov subspaces and extend the fermionic-excitation-based circuit formalism to generators consisting of an anti-Hermitian fermionic string multiplied by arbitrary linear combinations of number-operator products. Together, these developments yield the most compact circuits to date for exact implementation of saGSD unitaries. Finally, for non fully spin-polarized systems, we identify a compact universal symmetry-adapted subset of saGSD that further reduces the quantum resources required for chemically relevant simulations.
Abstract:Conservation of symmetries is crucial for reliable quantum simulations of molecular systems, yet compact circuit implementations of fully symmetry-adapted fermionic unitaries have remained elusive beyond the simplest excitation classes. Here we address this issue for the set of singlet spin-adapted generalized singles and doubles operators (saGSD). Using the Wei--Norman approach, we derive exact product formulas that express spin-adapted fermionic unitaries as products of elementary spin-orbital unitaries. To obtain closed-form parameters in the more challenging 28- and 84-dimensional dynamical Lie algebras, we develop a computational discovery-and-verification protocol combining numerical optimization, parameter-structure identification, closed-form inference, and exact validation against reduced Wei--Norman equations. We also introduce an algorithm for constructing closed-form fermionic unitary transformations on Krylov subspaces and extend the fermionic-excitation-based circuit formalism to generators consisting of an anti-Hermitian fermionic string multiplied by arbitrary linear combinations of number-operator products. Together, these developments yield the most compact circuits to date for exact implementation of saGSD unitaries. Finally, for non fully spin-polarized systems, we identify a compact universal symmetry-adapted subset of saGSD that further reduces the quantum resources required for chemically relevant simulations.
Quantum Physics (quant-ph); Chemical Physics (physics.chem-ph)
arXiv:2511.13485 [quant-ph]
(or arXiv:2511.13485v2 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2511.13485 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 273 words
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