Two dimenstional Heisenberg Hamiltonian for spin 1/2 system

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SUMMARY

Noora is seeking assistance in transforming a one-dimensional Heisenberg Hamiltonian for a system of seven qubits into a two-dimensional representation. The discussion highlights the need for clarity on the arrangement of qubits in two dimensions, which is crucial for the correct formulation of the Hamiltonian. Participants are encouraged to provide insights on the necessary modifications to achieve this transformation.

PREREQUISITES
  • Understanding of Heisenberg Hamiltonian
  • Familiarity with qubit systems and quantum mechanics
  • Knowledge of quantum state representation in multiple dimensions
  • Experience with Hamiltonian dynamics in quantum systems
NEXT STEPS
  • Research the arrangement of qubits in a two-dimensional lattice
  • Explore modifications to the Heisenberg Hamiltonian for 2D systems
  • Study quantum mechanics principles related to multi-qubit interactions
  • Investigate computational tools for simulating two-dimensional quantum systems
USEFUL FOR

Quantum physicists, researchers in quantum computing, and students studying multi-qubit systems will benefit from this discussion.

Noora Alameri
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Hey everybody,

I am trying to expand a system of seven qubits from one dimensional Hamiltonian to the two dimensional representation.

I have the one dimensional representation and I don't know what to add to transform it from 1D to 2D representation.

I would really appreciate your help and guidance.

Here is my !D Hamiltonian:

152157332685491.png
Thank You,
Noora
 

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How are the cubits arranged in 2D?
 

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