2025/10/08 by Ivana Miháliková, J. Carlson, Miháliková, Ivana +5 · 1 citation
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum many-body systems
paper · pdf · doi:10.48550/arxiv.2510.06702
openalex publication_date 2025/10/08 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28
We demonstrate the importance of symmetries in Variational Quantum Eigensolver (VQE) algorithms to prepare the ground or specific low-lying states of quantum Hamiltonians. We examine two spin problems, one with random all-to-all couplings inspired by neutrino flavor evolution in supernovae, and the standard Heisenberg spin Hamiltonian on a 4 × 3 lattice. The neutrino Hamiltonian has the total spin J and third component J_\rmz as its only symmetries. The Heisenberg model has these symmetries plus translational invariance and reflection symmetry. We demonstrate that the convergence of variational methods is dramatically improved by keeping all symmetries. In both cases a nearly exact solution can be obtained in cases where standard unconstrained variational algorithms fail. Since variational algorithms can use standard Trotter steps as part of the optimization, allowing additional correlations that obey all the symmetries of the Hamiltonian will speed convergence of variational algorithms. This will lead to faster convergence than standard projection algorithms.