Measured dynamics of an XXZ quantum simulator in a highly symmetrical double-ringed geometry
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 behavior 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.
Related
BibTeX
@article{papoular2026measured,
title = {{Measured dynamics of an XXZ quantum simulator in a highly symmetrical double-ringed geometry}},
author = {David Papoular},
journal = {Journal of Physics A: Mathematical and Theoretical},
year = {2026},
month = oct,
doi = {10.1088/1751-8121/aeae7b},
url = {https://hal.science/hal-05803311v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Measured dynamics of an XXZ quantum simulator in a highly symmetrical double-ringed geometry
AU - David Papoular
PY - 2026
DA - 2026/10/13
JO - Journal of Physics A: Mathematical and Theoretical
DO - 10.1088/1751-8121/aeae7b
UR - https://hal.science/hal-05803311v1
AB - 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 behavior 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.
SN - 1751-8113
SN - 1751-8121
ER -