The problem of efficiently simulating a Hamiltonian is one of the long standing problems in computational physics. Today, the problem of Hamiltonian simulation stands as one of the most impacting and significant contribution of quantum computers. Furthermore since it is a BQP-complete problem, devising any efficient classical algorithm for the same is believed to be intractable.
We simulated the Hamiltonian of the Heisenberg Spin Chain model using topologically optimized Trotterisation on a 7-qubit IBM quantum computer. We then compare the results of this simulation with purely-classical Hamiltonian simulation and classically Trotterised Hamiltonian simulation.
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