analiza aiqbench
This research introduces symmetry-guided algorithms that utilize Hilbert-Schmidt asymmetry to optimize variational quantum eigensolvers, effectively keeping simulations within the correct physical sector without modifying the preparation circuit. By targeting singlet ground states in systems ranging from five to twelve particles, the method significantly improves energy accuracy and ground-state fidelity compared to standard direct minimization approaches. The technique offers a robust pathway for enhancing the reliability of quantum optimization in larger spin models where generic ansatzes often fail to preserve necessary symmetries.
Symmetry-guided algorithms for variational quantum optimization
arXiv:2611.05865v1 Announce Type: new Abstract: Quantum numbers associated with symmetries classify quantum states and identify the sectors relevant to a given simulation. Generic hardware-efficient ansatzes do not necessarily preserve the quantum numbers and may therefore explore states outside the target sector. We develop symmetry-guided algorithms based on the quantum-accessible Hilbert--Schmidt asymmetry (\(\AHS\)), which quantifies the deviation of a quantum state from invariance under a specified symmetry group. This quantity guides the optimization toward a highly reduced symmetry-based target sector, without enforcing the symmetry on the preparation circuit. We demonstrate the approach as a proof of principle in variational quantum eigensolver calculations targeting singlet ground states with collective SU(2) symmetry. The applications include a five-qubit \(S\)-wave \(p+{}^3\mathrm{He}\) two-cluster Hamiltonian, deduced from \textit{ab initio} many-body calculations, and collective spin models with up to 12 particles, which provide a many-particle benchmark of asymmetry-guided optimization. Across these applications, \(\AHS\)-based guidance increases the singlet probability. Overall, the proposed algorithms improve energy accuracy during optimization and ground-state fidelity compared with direct energy minimization, with substantial fidelity improvements in the larger spin systems. These results demonstrate the utility of an asymmetry objective determined by the group action, independently of the Hamiltonian energy, for improving the reliability of variational quantum optimization.
Abstract:Quantum numbers associated with symmetries classify quantum states and identify the sectors relevant to a given simulation. Generic hardware-efficient ansatzes do not necessarily preserve the quantum numbers and may therefore explore states outside the target sector. We develop symmetry-guided algorithms based on the quantum-accessible Hilbert--Schmidt asymmetry (\(\AHS\)), which quantifies the deviation of a quantum state from invariance under a specified symmetry group. This quantity guides the optimization toward a highly reduced symmetry-based target sector, without enforcing the symmetry on the preparation circuit. We demonstrate the approach as a proof of principle in variational quantum eigensolver calculations targeting singlet ground states with collective SU(2) symmetry. The applications include a five-qubit \(S\)-wave \(p+{}^3\mathrm{He}\) two-cluster Hamiltonian, deduced from \textit{ab initio} many-body calculations, and collective spin models with up to 12 particles, which provide a many-particle benchmark of asymmetry-guided optimization. Across these applications, \(\AHS\)-based guidance increases the singlet probability. Overall, the proposed algorithms improve energy accuracy during optimization and ground-state fidelity compared with direct energy minimization, with substantial fidelity improvements in the larger spin systems. These results demonstrate the utility of an asymmetry objective determined by the group action, independently of the Hamiltonian energy, for improving the reliability of variational quantum optimization.
arXiv:2611.05865 [quant-ph]
(or arXiv:2611.05865v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2611.05865 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Text integral sub licența deschisă a publicației · 289 cuvinte