Quantum

Decoupling Spectral Gaps from Entanglement Complexity in Quantum Annealing

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Based on a feed excerpt; full article content has not been acquired. Source evidence retrieved 07/10/2026, 04:13:25 UTC.

Briefings

A 2026 arXiv preprint argues that exponentially small spectral gaps in quantum annealing do not necessarily require complex entanglement. The authors demonstrate that first-order transitions can close gaps polynomially with bounded Schmidt rank, while continuous transitions close gaps polynomially with logarithmic entanglement growth. Conversely, a mirror-twin manifold model shows exponential gap closure with only logarithmic entanglement. The study derives bounds linking Schmidt rank to Hamming-space geometry, identifying manifold density and connectivity as key factors determining the transition type. This work suggests entanglement complexity alone cannot characterize annealing difficulty, pointing toward a broader search for quantum resources that capture the geometry of state evolution in Hilbert space.

Key points

• The study establishes that exponentially small spectral gaps in quantum annealing do not necessarily require complex entanglement, challenging the assumption that gap scaling and entanglement complexity are linked.
• A mirror-twin manifold model demonstrates exponential gap closure while entanglement entropy grows logarithmically with system size, proving that entanglement complexity alone cannot characterize annealing difficulty.

Context and limitations

The evidence is an arXiv preprint from October 2026, meaning results are subject to revision. The study focuses on specific Ising chain and manifold models and does not provide experimental validation or broader applicability across different quantum systems.

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