We present an exact simulation of a one-dimensional transverse Ising spin chain with a quantum computer. We construct an efficient quantum circuit that diagonalizes the Ising Hamiltonian and allows to obtain all eigenstates of the model by just preparing the computational basis states. With an explicit example of that circuit for $n=4$ spins, we compute the expected value of the ground state transverse magnetization, the time evolution simulation and provide a method to also simulate thermal evolution. All circuits are run in IBM and Rigetti quantum devices to test and compare them qualitatively.
 Device specifications: https://github.com/Qiskit/qiskit-backend-information/tree/master/backend.
 Official announce of IBM ``Teach Me QISKit" award winnerhttps://www.ibm.com/blogs/research/2018/06/teach-qiskit-winner/.
 Manoranjan Swain, Amit Rai, Bikash K. Behera, and Prasanta K. Panigrahi, "Experimental demonstration of the violations of Mermin's and Svetlichny's inequalities for W- and GHZ-class of states", arXiv:1810.00874 (2018).
 Bartłomiej Gardas, Marek M. Rams, and Jacek Dziarmaga, "Quantum neural networks to simulate many-body quantum systems", Physical Review B 98 18, 184304 (2018).
 Harshavardhan Reddy Nareddula, Bikash K. Behera, and Prasanta K. Panigrahi, "Quantum Cost Efficient Scheme for Violating the Holevo Bound and Cloning in the Presence of Deutschian Closed Timelike Curves", arXiv:1901.00379 (2018).
 Amandeep Singh Bhatia and Mandeep Kaur Saggi, "Simulation of Matrix Product State on a Quantum Computer", arXiv:1811.09833 (2018).
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This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.