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arXiv · 2508.02468

Measured dynamics of an XXZ quantum simulator in a highly symmetrical double-ringed geometry

D. J. Papoular
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Abstract

We theoretically identify observable consequences of spatial and spin symmetries on the dynamics of a small XXZ quantum simulator. Our proposed protocol relies on the choice of suitable initial states, and involves the measurement scheme whose experimental implementation is the simplest. We analyze a system of $N=2n=6$ to $12$ particles, trapped in a planar geometry comprised of two rings which exhibits point group symmetry $D_{nh}$. The particles represent effective spins whose interaction is described by the XXZ or Heisenberg Hamiltonian. The system is prepared in an initial state which is sitewise-factorized and invariant under all spatial symmetries, it evolves for a given time, after which the $z$-components of all $N$ spins are measured. We show that symmetries dictate (i) the qualitative behaviour of the measurement probabilities as a function of the evolution time, and (ii) the number of measurement results with different probabilities. We highlight the role of a twofold rotation of all spins. We also demonstrate that, in larger systems, the collapse of the initial state may be observed.

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D. J. Papoular. 2025-08-04. Measured dynamics of an XXZ quantum simulator in a highly symmetrical double-ringed geometry. https://arxiv.org/abs/2508.02468

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