Symmetry-protected self-correcting quantum memories

A self-correcting quantum memory can store and protect quantum information for a time that increases without bound with the system size and without the need for active error correction. We demonstrate that symmetry can lead to self-correction in 3D spin-lattice models. In particular, we investigate codes given by 2D symmetry-enriched topological (SET) phases that appear naturally on the boundary of 3D symmetry-protected topological (SPT) phases. We find that while conventional on-site symmetries are not sufficient to allow for self-correction in commuting Hamiltonian models of this form, a generalized type of symmetry known as a 1-form symmetry is enough to guarantee self-correction. We illustrate this fact with the 3D "cluster-state" model from the theory of quantum computing. This model is a self-correcting memory, where information is encoded in a 2D SET-ordered phase on the boundary that is protected by the thermally stable SPT ordering of the bulk. We also investigate the gauge color code in this context. Finally, noting that a 1-form symmetry is a very strong constraint, we argue that topologically ordered systems can possess emergent 1-form symmetries, i.e., models where the symmetry appears naturally, without needing to be enforced externally.Comment: 39 pages, 16 figures, comments welcome; v2 includes much more explicit detail on the main example model, including boundary conditions and implementations of logical operators through local moves; v3 published versio

Beyond Keeping the Peace: Can Peacekeepers Reduce Ethnic Divisions After Violence?

Existing research suggests that international peacekeeping contributes to conflict resolution and helps sustain peace, often in locations with hostile ethnic divisions. However, it is unclear whether the presence of peacekeepers actually reduces underlying ethnocentric views and parochial behaviors that sustain those divisions. We examine the effects of NATO peacekeeper deployments on ethnocentrism in postwar Bosnia. While peacekeepers were not randomly deployed in Bosnia, we find that highly ethnocentric attitudes were common across Bosnia at the onset of peacekeeper deployments, reducing endogeneity concerns. To measure ethnocentrism, we employ a variety of survey instruments as well as a behavioral experiment (the dictator game) with ethnic treatments across time. We find that regions with peacekeepers exhibit lower levels of ethnocentrism in comparison to regions without peacekeepers, and this effect persists even after peacekeepers have departed. The peacekeeping effect is also robust to a sub-sample of ethnic Bosnian Serbs, suggesting that peacekeeper deployments can have positive effects on diminishing ethnocentrism, even when local communities are especially hostile to their presence. Our results speak to the potential long-term role of peacekeepers in reducing tensions among groups in conflict

The 2-generalized knot group determines the knot

Generalized knot groups $G_n(K)$ were introduced independently by Kelly (1991) and Wada (1992). We prove that $G_2(K)$ determines the unoriented knot type and sketch a proof of the same for $G_n(K)$ for $n>2$.Comment: 4 page

Resonating Valence Bond Quantum Monte Carlo: Application to the ozone molecule

We study the potential energy surface of the ozone molecule by means of Quantum Monte Carlo simulations based on the resonating valence bond concept. The trial wave function consists of an antisymmetrized geminal power arranged in a single-determinant that is multiplied by a Jastrow correlation factor. Whereas the determinantal part incorporates static correlation effects, the augmented real-space correlation factor accounts for the dynamics electron correlation. The accuracy of this approach is demonstrated by computing the potential energy surface for the ozone molecule in three vibrational states: symmetric, asymmetric and scissoring. We find that the employed wave function provides a detailed description of rather strongly-correlated multi-reference systems, which is in quantitative agreement with experiment.Comment: 5 page, 3 figure