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Abstract The remarkable complexity of a topologically ordered many-body quantum system is encoded in the characteristics of its anyons. Quintessential predictions emanating from this complexity employ the Fibonacci string net condensate (Fib SNC) and its anyons: sampling Fib-SNC would estimate chromatic polynomials while exchanging its anyons would implement universal quantum computation. However, physical realizations remained elusive. We introduce a scalable dynamical string net preparation (DSNP) that constructs Fib SNC and its anyons on reconfigurable graphs suitable for near-term superconducting processors. Coupling the DSNP approach with composite error-mitigation on deep circuits, we create, measure, and braids Fibonacci anyons; charge measurements show 94% accuracy, and exchanging the anyons yields the expected golden ratioϕwith 98% average accuracy. We then sample the Fib SNC to estimate chromatic polynomial atϕ + 2 for several graphs. Our results establish the proof of principle for using Fib-SNC and its anyons for fault-tolerant universal quantum computation and aim at a classically hard problem. 

Abstract Purpose. To investigate the relationship between spatial parotid dose and the risk of xerostomia in patients undergoing head-and-neck cancer radiotherapy, using machine learning (ML) methods.Methods. Prior to conducting voxel-based ML analysis of the spatial dose, two steps were taken: (1) The parotid dose was standardized through deformable image registration to a reference patient; (2) Bilateral parotid doses were regrouped into contralateral and ipsilateral portions depending on their proximity to the gross tumor target. Individual dose voxels were input into six commonly used ML models, which were tuned with ten-fold cross validation: random forest (RF), ridge regression (RR), support vector machine (SVM), extra trees (ET), k-nearest neighbor (kNN), and naïve Bayes (NB). Binary endpoints from 240 patients were used for model training and validation: 0 (N = 119) for xerostomia grades 0 or 1, and 1 (N = 121) for grades 2 or higher. Model performance was evaluated using multiple metrics, including accuracy, F₁score, areas under the receiver operating characteristics curves (auROC), and area under the precision–recall curves (auPRC). Dose voxel importance was assessed to identify local dose patterns associated with xerostomia risk.Results. Four models, including RF, SVM, ET, and NB, yielded average auROCs and auPRCs greater than 0.60 from ten-fold cross-validation on the training data, except for a lower auROC from NB. The first three models, along with kNN, demonstrated higher accuracy and F₁scores. A bootstrapping analysis confirmed test uncertainty. Voxel importance analysis from kNN indicated that the posterior portion of the ipsilateral gland was more predictive of xerostomia, but no clear patterns were identified from the other models.Conclusion. Voxel doses as predictors of xerostomia were confirmed with some ML classifiers, but no clear regional patterns could be established among these classifiers, except kNN. Further research with a larger patient dataset is needed to identify conclusive patterns. 

We study a 2D measurement-only random circuit motivated by the Bacon-Shor error correcting code. We find a rich phase diagram as one varies the relative probabilities of measuring nearest-neighbor Pauli XX and ZZ check operators. In the Bacon-Shor code, these checks commute with a group of stabilizer and logical operators, which therefore represent conserved quantities. Described as a subsystem symmetry, these conservation laws lead to a continuous phase transition between an X-basis and Z-basis spin-glass order. The two phases are separated by a critical point where the entanglement entropy between two halves of an L × L system scales as L ln L, a logarithmic violation of the area law. We generalize to a model where the check operators break the subsystem symmetries (and the Bacon-Shor code structure). In tension with established heuristics, we find that the phase transition is replaced by a smooth crossover, and the X - and Z -basis spin-glass orders spatially coexist. Additionally, if we approach the line of subsystem symmetries away from the critical point in the phase diagram, some spin-glass order parameters jump discontinuously. 

We study the gauging of a global U(1) symmetry in a gapped system in(2+1)d. The gauging procedure has been well-understood for a finiteglobal symmetry group, which leads to a new gapped phase with emergentgauge structure and can be described algebraically using themathematical framework of modular tensor category (MTC). We develop acategorical description of U(1) gauging in a MTC, taking into accountthe dynamics of U(1) gauge field absent in the finite group case. Whenthe ungauged system has a non-zero Hall conductance, the gauged theoryremains gapped and we determine the complete set of anyon data for thegauged theory. On the other hand, when the Hall conductance vanishes, weargue that gauging has the same effect of condensing a special Abeliananyon nucleated by inserting 2\pi 2 π U(1) flux. We apply our procedure to theSU(2) _k k MTCs and derive the full MTC data for the \mathbb{Z}_k ℤ k parafermion MTCs. We also discuss a dual U(1) symmetry that emergesafter the original U(1) symmetry of an MTC is gauged.