Quantum Complexity and Stabilizer-State Expansions: From Pairing to Deformation in Fermionic Systems
Abstract
Understanding how collective phenomena such as pairing and deformation emerge in interacting fermionic systems, and how the correlations underlying them shape the resources required for their simulation, is a central challenge in many-body physics. We investigate various aspects of quantum complexity in a fermionic system exhibiting two main forms of collectivity, specifically deformation and pairing, through entanglement, non-stabilizerness, and fermionic non-Gaussianity. In the deformed phase, high entanglement coexists with low non-stabilizerness, while the superfluid pairing phase, by contrast, exhibits substantial multipartite entanglement and non-stabilizerness, together with maximal fermionic anti-flatness. In a second step we examine how to describe the phase diagram of the system in a classically scalable and symmetry-preserving way, by combining stabilizer-state expansion and variational basis optimization. A physics-guided decomposition of the Hamiltonian identifies the relevant stabilizer states, which can be constructed from graph states. A single stabilizer state captures the deformed phase to a large extent, and, although the number of stabilizer states required to describe the pairing phase grows exponentially with system size, a symmetry-preserving basis rotation yields a high-fidelity approximation using far fewer states. This rotated state can then serve as a practical starting point for quantum refinement.
Related
- Majorana-Pauli stabilizer codes and duality webs of fermionic topological phases
- Impact of deformation parameters on the greybody factor and Joule-Thomson expansions of Schwarzschild-AdS black hole
- Complexity and Applications of Nearest Stabilizer Product State Problems
- Kerr/CFT Traversable Wormhole with Fermionic Double-Trace Deformation
- Practical fermionic shadows enabled by improved sample-complexity bounds
BibTeX
@misc{hengstenberg2026quantum,
title = {{Quantum Complexity and Stabilizer-State Expansions: From Pairing to Deformation in Fermionic Systems}},
author = {S. Momme Hengstenberg and Caroline E. P. Robin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31792},
eprint = {2610.31792},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31792},
}
RIS
TY - UNPB
TI - Quantum Complexity and Stabilizer-State Expansions: From Pairing to Deformation in Fermionic Systems
AU - S. Momme Hengstenberg
AU - Caroline E. P. Robin
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31792
UR - https://arxiv.org/abs/2610.31792
AB - Understanding how collective phenomena such as pairing and deformation emerge in interacting fermionic systems, and how the correlations underlying them shape the resources required for their simulation, is a central challenge in many-body physics. We investigate various aspects of quantum complexity in a fermionic system exhibiting two main forms of collectivity, specifically deformation and pairing, through entanglement, non-stabilizerness, and fermionic non-Gaussianity. In the deformed phase, high entanglement coexists with low non-stabilizerness, while the superfluid pairing phase, by contrast, exhibits substantial multipartite entanglement and non-stabilizerness, together with maximal fermionic anti-flatness. In a second step we examine how to describe the phase diagram of the system in a classically scalable and symmetry-preserving way, by combining stabilizer-state expansion and variational basis optimization. A physics-guided decomposition of the Hamiltonian identifies the relevant stabilizer states, which can be constructed from graph states. A single stabilizer state captures the deformed phase to a large extent, and, although the number of stabilizer states required to describe the pairing phase grows exponentially with system size, a symmetry-preserving basis rotation yields a high-fidelity approximation using far fewer states. This rotated state can then serve as a practical starting point for quantum refinement.
ER -