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Stabilizer-accelerated quantum many-body ground-state estimation

Caroline E. P. Robin*

  • *Contact author: crobin@physik.uni-bielefeld.de
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Phys. Rev. A 112, 052408 – Published 3 November, 2025

DOI: https://doi.org/10.1103/5qr5-7jkz

Abstract

We investigate how the stabilizer formalism, in particular highly entangled stabilizer states, can be used to describe the emergence of many-body shape collectivity from individual constituents in a symmetry-preserving and classically efficient way. The method that we adopt is based on determining an optimal separation of the Hamiltonian into a stabilizer component and a residual part inducing nonstabilizerness. The corresponding stabilizer ground state is efficiently prepared using techniques of graph states and stabilizer tableaux. We demonstrate this technique in context of the Lipkin-Meshkov-Glick model, a fully connected spin system presenting a second-order phase transition from spherical to deformed state. The resulting stabilizer ground state is found to capture to a large extent both bipartite and collective multipartite entanglement features of the exact solution in the region of large deformation. We also explore several methods for injecting nonstabilizerness into the system, including adaptive derivative-assembled pseudo-Trotter variational quantum eigensolver and imaginary-time evolution (ITE) techniques. Stabilizer ground states are found to accelerate ITE convergence due to a larger overlap with the exact ground state. While further investigations are required, the present work suggests that collective features may be associated with high but simple large-scale entanglement which can be captured by stabilizer states, while the interplay with single-particle motion may be responsible for inducing nonstabilizerness. This study motivates applications of the proposed approach to more realistic quantum many-body systems, whose stabilizer ground states can be used in combinations with powerful classical many-body techniques and/or quantum methods.

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Phys. Rev. A 112, 052408– Published 3 November, 2025
  • Received 30 May 2025
  • Accepted 10 October 2025
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