Universality of Quantum Gates in Particle and Symmetry Constrained Subspaces
Abstract
Simulating physical systems on near-term quantum computers often requires preparing states within constrained subspaces, like those with fixed particle number or spin. We use Lie algebraic techniques to prove that hardware-efficient gates are universal for state preparation in these subspaces. The key mechanism is Pauli Z dressing: commutators of overlapping gates produce Pauli Z operators on shared qubits, acting as spectator projectors that decompose multi-plane rotations into single-plane generators spanning the full so(w) algebra, where w is the dimension of the constrained subspace, thereby guaranteeing universality for real state preparation. Adding independent complex phases extends this to su(w), enabling arbitrary complex state preparation. We provide a computationally efficient Jacobian criterion for verifying that a circuit can explore any direction on the target manifold from almost any parameter configuration. Our findings are applicable to many problem areas, including Fermi-Hubbard models, Bose-Hubbard models, and molecular electronic structure. We apply our framework to two physical settings: we prove the completeness of the binary encoded multi-level particles ansatz on the conserved-particle-number subspace, and we construct symmetry-preserving circuits for the fuzzy sphere regularisation of the 3D Ising conformal field theory (CFT). For the latter, we variationally prepare the ground and excited states and extract some CFT data.
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BibTeX
@misc{stergiou2026universality,
title = {{Universality of Quantum Gates in Particle and Symmetry Constrained Subspaces}},
author = {Andreas Stergiou and Nicolas PD Sawaya},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.00979},
eprint = {2605.00979},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.00979},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Universality of Quantum Gates in Particle and Symmetry Constrained Subspaces
AU - Andreas Stergiou
AU - Nicolas PD Sawaya
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2605.00979
UR - https://arxiv.org/abs/2605.00979
AB - Simulating physical systems on near-term quantum computers often requires preparing states within constrained subspaces, like those with fixed particle number or spin. We use Lie algebraic techniques to prove that hardware-efficient gates are universal for state preparation in these subspaces. The key mechanism is Pauli Z dressing: commutators of overlapping gates produce Pauli Z operators on shared qubits, acting as spectator projectors that decompose multi-plane rotations into single-plane generators spanning the full so(w) algebra, where w is the dimension of the constrained subspace, thereby guaranteeing universality for real state preparation. Adding independent complex phases extends this to su(w), enabling arbitrary complex state preparation. We provide a computationally efficient Jacobian criterion for verifying that a circuit can explore any direction on the target manifold from almost any parameter configuration. Our findings are applicable to many problem areas, including Fermi-Hubbard models, Bose-Hubbard models, and molecular electronic structure. We apply our framework to two physical settings: we prove the completeness of the binary encoded multi-level particles ansatz on the conserved-particle-number subspace, and we construct symmetry-preserving circuits for the fuzzy sphere regularisation of the 3D Ising conformal field theory (CFT). For the latter, we variationally prepare the ground and excited states and extract some CFT data.
ER -