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Can we think of Quantum Circuits as another representation to describe the dynamics of a system other than its Hamiltonian? How can we go from the spin Hamiltonian version (for eg: SSH Model Hamiltonian) to quantum circuits (It would be of great help if someone can suggest resources on how to get started with this, analytically without using user-friendly software packages) including how to come with relevant initial ansatz? Since the circuits are dimensionless quantities which I think seem to make sense to me as any observable quantity has physical significance only if they are dimensionless.

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