We calculate the critical temperature of the Ising model on a set of graphs representing a concatenated three-bit error-correction code. The graphs are derived from the stabilizer formalism used in quantum error correction. The stabilizer for a subspace is defined as the group of Pauli operators whose eigenvalues are +1 on the subspace. The group can be generated by a subset of operators in the stabilizer, and the choice of generators determines the structure of the graph. The Wolff algorithm, together with the histogram method and finite-size scaling, is used to calculate both the critical temperature and the critical exponents of each structure. The simulations show that the choice of stabilizer generators, both the number and the geometry, has a large effect on the critical temperature.
Ground states of quantum many-body systems are both entangled and possess a kind of quantum complexity as their preparation requires universal resources that go beyond the Clifford group and stabilizer states. These resources - sometimes described as magic - are also the crucial ingredient for quantum advantage. We study the behavior of the stabilizer Rényi entropy in the integrable transverse field Ising spin chain. We show that the locality of interactions results in a localized stabilizer Rényi entropy in the gapped phase thus making this quantity computable in terms of local quantities in …
Stabilizer code quantum Hamiltonians have been introduced with the intention of physically realizing a quantum memory because of their resilience to decoherence. In order to analyze their finite temperature thermodynamics, we show how to generically solve their partition function using duality techniques. By unveiling each model's universality class and effective dimension, insights may be gained on their finite temperature dynamics and robustness. Our technique is demonstrated in particular on the 4D Toric Code and Haah's Code -- we find that the former falls into the 4D Ising universality cl…
Selected Stabilizer Subspaces for Compact Many-Body Wave Functions
Yusuf Hamied Department of Chemistry, University of Cambridge（剑桥大学尤素夫·哈米德化学系）；Department of Physics and Thomas Young Centre, King’s College London（伦敦国王学院物理系及托马斯·杨中心）
Stabilizer-Rényi Microscopy of Critical Correlations in Interacting Fermions
School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学李政道研究所）；Hefei National Laboratory（合肥国家实验室）
Interplay of entanglement structures and stabilizer entropy in spin models
Università di Napoli Federico II（那不勒斯费德里科二世大学）；The Abdus Salam International Center for Theoretical Physics (ICTP)（阿卜杜斯·萨拉姆国际理论物理中心）；INFN, Sezione di Napoli（意大利国家核物理研究院那不勒斯分部）；Scuola Superiore Meridionale（南方高等学院）
Classical Root Systems Reveal Defect-Junction Data in Stabilizer Renyi Entropy
Instituto de Física, Universidade Federal Fluminense（弗鲁米嫩塞联邦大学物理研究所）；Theoretical Physics III, Center for Electronic Correlations and Magnetism, Institute of Physics, University of Augsburg（奥格斯堡大学物理研究所电子关联与磁学中心理论物理第三系）
The sign structure of quantum states is closely connected to quantum phases of matter, yet detecting such fine-grained properties of amplitudes is subtle. Here we employ as a diagnostic measurement-induced entanglement (MIE): the average entanglement generated between two parties after measuring the rest of the system. We propose that for a sign-free state, the MIE upon measuring in the sign-free basis decays no slower than correlations in the state before measurement. Concretely, we prove that MIE is upper bounded by mutual information for sign-free stabilizer states (essentially CSS codes), …
