发表机构
Indian Institute of Technology Bhubaneswar; University College London（印度技术学院布巴内斯瓦尔分校; 伦敦大学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究证明量子退火中谱隙标度与纠缠复杂性可解耦，通过反转传统相变中的配对关系，指出纠缠复杂性不足以衡量退火难度，需探索捕捉希尔伯特空间几何的量子资源。
AI 中文摘要
指数级小的谱隙是绝热量子退火的主要障碍，然而这些瓶颈是否必然要求相应复杂的纠缠仍不清楚。我们证明谱隙的标度行为与纠缠复杂性无需相互关联。传统的一阶相变将指数级小的谱隙与有界的$O(1)$二分施密特秩相结合，即使临界态保留全局多体关联，而连续相变则将多项式闭合的谱隙与对数增长的纠缠相结合。我们表明每种配对也可以反转：在交错场反铁磁伊辛链中已知的一阶相变中，尽管施密特秩有界，谱隙仍多项式闭合，而我们构建了一个镜像孪生流形模型，其谱隙指数闭合，同时纠缠熵随系统大小对数增长。我们推导了将施密特秩与汉明空间几何联系起来的界限，并确定流形密度和连通性是决定出现哪种组合的关键因素。这些结果表明，仅凭纠缠复杂性无法表征退火难度，并指向更广泛地寻找能够捕捉希尔伯特空间中态演化几何的量子资源。
英文摘要
Exponentially small spectral gaps are the central obstacle to adiabatic quantum annealing, yet whether such bottlenecks demand correspondingly complex entanglement remains unclear. We show that gap scaling and entanglement complexity need not be linked. Conventional first-order transitions combine exponentially small gaps with bounded $O(1)$ bipartite Schmidt rank, even though the critical states retain global multipartite correlations, while continuous transitions combine polynomially closing gaps with logarithmically growing entanglement. We show that each pairing can also be inverted: in a known first-order transition in a staggered-field antiferromagnetic Ising chain the gap closes polynomially despite bounded Schmidt rank, while we construct a mirror-twin manifold model whose gap closes exponentially even as its entanglement entropy grows logarithmically with system size. We derive bounds connecting Schmidt rank to Hamming-space geometry, and identify manifold density and connectivity as the ingredients that determine which combination occurs. These results show that entanglement complexity alone cannot characterize annealing difficulty, and point toward a broader search for quantum resources that capture the geometry of state evolution in Hilbert space.
Comments18 pages 5 figures
