Periodic Symmetry-Adapted Encoding: Qubit Reduction in Crystalline Electronic Structure

arXiv:2606.05777v1 Announce Type: new Abstract: We extend the symmetry-adapted encoding (SAE) framework to periodic electronic structure, enabling qubit-efficient quantum simulation of crystalline materials. By constructing a $\Gamma$-point supercell Hamiltonian from a folded $k$-point calculation and systematically identifying all applicable space-group symmetry generators -- including spin-parity, point-group, and crystal translation symmetries -- we obtain qubit Hamiltonians with fewer qubits than the Jordan--Wigner starting point. We benchmark diamond, silicon, 3C-SiC, MgO, NaCl, CsCl, h-BN, wurtzite AlN, $\alpha$-quartz SiO$_2$, and MgF$_2$ using active spaces chosen to preserve complete near-degenerate frontier manifolds across cubic, hexagonal, trigonal, and tetragonal space groups. Across the suite the periodic SAE removes 4--8 qubits. The B2 CsCl benchmark realises eight independent Boolean generators, i.e. a symmetry group isomorphic to $\mathbb{Z}_2^8$, reducing CAS(6,7) from 14 to 6 qubits. This exceeds the $\mathbb{Z}_2^5$ maximum of molecular SAE, where only two spin parities and at most three independent Boolean point-group generators are available, because the folded crystal supplies three additional half-translation symmetries. Noiseless UCCSD-VQE benchmarks against exact diagonalisation in the active-space sector show that the reduced encodings preserve the target energies to well below chemical accuracy while reducing variational parameter counts by $3$--$8\times$ and CNOT counts by up to $309\times$. The largest circuit savings occur when translation and point-group generators act independently in the active space, demonstrating that periodic symmetry can be converted directly into both qubit and ansatz compression. The method is implemented in the open-source QuantumSymmetry package and requires no manual specification of symmetry generators.

Abstract:We extend the symmetry-adapted encoding (SAE) framework to periodic electronic structure, enabling qubit-efficient quantum simulation of crystalline materials. By constructing a $\Gamma$-point supercell Hamiltonian from a folded $k$-point calculation and systematically identifying all applicable space-group symmetry generators -- including spin-parity, point-group, and crystal translation symmetries -- we obtain qubit Hamiltonians with fewer qubits than the Jordan--Wigner starting point. We benchmark diamond, silicon, 3C-SiC, MgO, NaCl, CsCl, h-BN, wurtzite AlN, $\alpha$-quartz SiO$_2$, and MgF$_2$ using active spaces chosen to preserve complete near-degenerate frontier manifolds across cubic, hexagonal, trigonal, and tetragonal space groups. Across the suite the periodic SAE removes 4--8 qubits. The B2 CsCl benchmark realises eight independent Boolean generators, i.e. a symmetry group isomorphic to $\mathbb{Z}_2^8$, reducing CAS(6,7) from 14 to 6 qubits. This exceeds the $\mathbb{Z}_2^5$ maximum of molecular SAE, where only two spin parities and at most three independent Boolean point-group generators are available, because the folded crystal supplies three additional half-translation symmetries. Noiseless UCCSD-VQE benchmarks against exact diagonalisation in the active-space sector show that the reduced encodings preserve the target energies to well below chemical accuracy while reducing variational parameter counts by $3$--$8\times$ and CNOT counts by up to $309\times$. The largest circuit savings occur when translation and point-group generators act independently in the active space, demonstrating that periodic symmetry can be converted directly into both qubit and ansatz compression. The method is implemented in the open-source QuantumSymmetry package and requires no manual specification of symmetry generators.

arXiv:2606.05777 [quant-ph]

(or arXiv:2606.05777v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2606.05777 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Periodic Symmetry-Adapted Encoding: Qubit Reduction in Crystalline Electronic Structure

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