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1. Generation of genuine all-way entanglement in defect-nuclear spin systems through dynamical decoupling sequences

   https://doi.org/10.22331/q-2024-03-28-1304  

   Takou, Evangelia; Barnes, Edwin; Economou, Sophia E (March 2024, Quantum)

   Multipartite entangled states are an essential resource for sensing, quantum error correction, and cryptography. Color centers in solids are one of the leading platforms for quantum networking due to the availability of a nuclear spin memory that can be entangled with the optically active electronic spin through dynamical decoupling sequences. Creating electron-nuclear entangled states in these systems is a difficult task as the always-on hyperfine interactions prohibit complete isolation of the target dynamics from the unwanted spin bath. While this emergent cross-talk can be alleviated by prolonging the entanglement generation, the gate durations quickly exceed coherence times. Here we show how to prepare high-quality GHZ ${}_M$-like states with minimal cross-talk. We introduce the $M$-tangling power of an evolution operator, which allows us to verify genuine all-way correlations. Using experimentally measured hyperfine parameters of an NV center spin in diamond coupled to carbon-13 lattice spins, we show how to use sequential or single-shot entangling operations to prepare GHZ ${}_M$-like states of up to $M=10$qubits within time constraints that saturate bounds on $M$-way correlations. We study the entanglement of mixed electron-nuclear states and develop a non-unitary $M$-tangling power which additionally captures correlations arising from all unwanted nuclear spins. We further derive a non-unitary $M$-tangling power which incorporates the impact of electronic dephasing errors on the $M$-way correlations. Finally, we inspect the performance of our protocols in the presence of experimentally reported pulse errors, finding that XY decoupling sequences can lead to high-fidelity GHZ state preparation. 

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2. Digital quantum simulation of Floquet symmetry-protected topological phases

   https://doi.org/10.1038/s41586-022-04854-3  

   Zhang, Xu; Jiang, Wenjie; Deng, Jinfeng; Wang, Ke; Chen, Jiachen; Zhang, Pengfei; Ren, Wenhui; Dong, Hang; Xu, Shibo; Gao, Yu; et al (July 2022, Nature)

   Abstract Quantum many-body systems away from equilibrium host a rich variety of exotic phenomena that are forbidden by equilibrium thermodynamics. A prominent example is that of discrete time crystals 1–8 , in which time-translational symmetry is spontaneously broken in periodically driven systems. Pioneering experiments have observed signatures of time crystalline phases with trapped ions 9,10 , solid-state spin systems 11–15 , ultracold atoms 16,17 and superconducting qubits 18–20 . Here we report the observation of a distinct type of non-equilibrium state of matter, Floquet symmetry-protected topological phases, which are implemented through digital quantum simulation with an array of programmable superconducting qubits. We observe robust long-lived temporal correlations and subharmonic temporal response for the edge spins over up to 40 driving cycles using a circuit of depth exceeding 240 and acting on 26 qubits. We demonstrate that the subharmonic response is independent of the initial state, and experimentally map out a phase boundary between the Floquet symmetry-protected topological and thermal phases. Our results establish a versatile digital simulation approach to exploring exotic non-equilibrium phases of matter with current noisy intermediate-scale quantum processors 21 . 

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3. Dynamics and Persistence of a Generalized Multi-strain SIS Model

   https://doi.org/10.1007/s11538-025-01516-z  

   Greenhalgh, Scott; Henriquez, Tabitha; Frutschy, Michael; Leonard, Rebecah (September 2025, Bulletin of Mathematical Biology)

   Abstract Autonomous differential equation compartmental models hold broad utility in epidemiology and public health. However, these models typically cannot account explicitly for myriad factors that affect the trajectory of infectious diseases, with seasonal variations in host behavior and environmental conditions as noteworthy examples. Fortunately, using non-autonomous differential equation compartmental models can mitigate some of these deficiencies, as the inclusion of time-varying parameters can account for temporally varying factors. The inclusion of these temporally varying factors does come at a cost though, as many analysis techniques, such as the use of Poincaré maps and Floquet theory, on non-autonomous differential equation compartmental models are typically only tractable numerically. Here, we illustrate a rare$$n$$ $n$-strain generalized Susceptible-Infectious-Susceptible (SIS) compartmental model, with a general time-varying recovery rate, which features Floquet exponents that are algebraic expressions. We completely characterize the persistence and stability properties of our$$n$$ $n$-strain generalized SIS model for$$n\ge 1$$ $n\ge 1$. We also derive a closed-form solution in terms of elementary functions for the single-strain SIS model, which is capable of incorporating almost any infectious period distribution. Finally, to demonstrate the applicability of our work, we apply it to recent syphilis incidence data from the United States, utilizing Akaike Information Criteria and Forecast Skill Scores to inform on the model’s goodness of fit relative to complexity and the model’s capacity to predict future trends. 

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4. Measurements of polarization and spin correlation and observation of entanglement in top quark pairs using $\mathrm{lepton}+\text{jets}$ events from proton-proton collisions at $\sqrt{s}=13\mathrm{TeV}$

   https://doi.org/10.1103/PhysRevD.110.112016  

   Hayrapetyan, A; Tumasyan, A; Adam, W; Andrejkovic, J W; Benato, L; Bergauer, T; Chatterjee, S; Damanakis, K; Dragicevic, M; Hussain, P S; et al (December 2024, Physical Review D)

   Measurements of the polarization and spin correlation in top quark pairs ( $t\overline{t}$) are presented using events with a single electron or muon and jets in the final state. The measurements are based on proton-proton collision data from the LHC at $\sqrt{s}=13\mathrm{TeV}$collected by the CMS experiment, corresponding to an integrated luminosity of $138{\mathrm{fb}}^{-1}$. All coefficients of the polarization vectors and the spin correlation matrix are extracted simultaneously by performing a binned likelihood fit to the data. The measurement is performed inclusively and in bins of additional observables, such as the mass of the $t\overline{t}$system and the top quark scattering angle in the $t\overline{t}$rest frame. The measured polarization and spin correlation are in agreement with the standard model. From the measured spin correlation, conclusions on the $t\overline{t}$spin entanglement are drawn by applying the Peres-Horodecki criterion. The standard model predicts entangled spins for $t\overline{t}$states at the production threshold and at high masses of the $t\overline{t}$system. Entanglement is observed for the first time in events at high $t\overline{t}$mass, where a large fraction of the $t\overline{t}$decays are spacelike separated, with an expected and observed significance of above 5 standard deviations. © 2024 CERN, for the CMS Collaboration2024CERN 

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5. Nonlinear Dynamics for the Ising Model

   https://doi.org/10.1007/s00220-024-05129-w  

   Caputo, Pietro; Sinclair, Alistair (November 2024, Communications in Mathematical Physics)

   Abstract We introduce and analyze a natural class of nonlinear dynamics for spin systems such as the Ising model. This class of dynamics is based on the framework of mass action kinetics, which models the evolution of systems of entities under pairwise interactions, and captures a number of important nonlinear models from various fields, including chemical reaction networks, Boltzmann’s model of an ideal gas, recombination in population genetics and genetic algorithms. In the context of spin systems, it is a natural generalization of linear dynamics based on Markov chains, such as Glauber dynamics and block dynamics, which are by now well understood. However, the inherent nonlinearity makes the dynamics much harder to analyze, and rigorous quantitative results so far are limited to processes which converge to essentially trivial stationary distributions that are product measures. In this paper we provide the first quantitative convergence analysis for natural nonlinear dynamics in a combinatorial setting where the stationary distribution contains non-trivial correlations, namely spin systems at high temperatures. We prove that nonlinear versions of both the Glauber dynamics and the block dynamics converge to the Gibbs distribution of the Ising model (with given external fields) in times$$O(n\log n)$$ $O(nlogn)$and$$O(\log n)$$ $O(logn)$respectively, wherenis the size of the underlying graph (number of spins). Given the lack of general analytical methods for such nonlinear systems, our analysis is unconventional, and combines tools such as information percolation (due in the linear setting to Lubetzky and Sly), a novel coupling of the Ising model with Erdős-Rényi random graphs, and non-traditional branching processes augmented by a “fragmentation” process. Our results extend immediately to any spin system with a finite number of spins and bounded interactions. 

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