Quantum

Quantum Complexity and Stabilizer-State Expansions: From Pairing to Deformation in Fermionic Systems

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Briefings

A new study analyzes quantum complexity in fermionic systems with two collective phenomena: deformation and pairing. It finds that the deformed phase has high entanglement but low non-stabilizerness, whereas the pairing phase shows substantial multipartite entanglement and non-stabilizerness. The research proposes a classically scalable method using stabilizer-state expansion and variational basis optimization to describe the phase diagram, identifying graph states as relevant stabilizer states.

Key points

• The deformed phase of the fermionic system exhibits high entanglement coexisting with low non-stabilizerness.
• The superfluid pairing phase is characterized by substantial multipartite entanglement and non-stabilizerness alongside maximal fermionic anti-flatness.

Context

This research addresses a central challenge in many-body physics by investigating how collective phenomena like pairing and deformation emerge in interacting fermionic systems, focusing on the correlations that shape simulation resources.

Limitations

The study covers only two main forms of collectivity (deformation and pairing) and uses entanglement, non-stabilizerness, and fermionic non-Gaussianity as metrics. It does not provide data on system size scaling for the pairing phase beyond noting exponential growth, nor does it offer experimental validation or specific numerical results for the Hamiltonian decomposition.

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