Exact Ising model simulation on a quantum computer

Alba Cervera-Lierta

Barcelona Supercomputing Center (BSC), Barcelona, Spain
Institut de Ciències del Cosmos, Universitat de Barcelona, Barcelona, Spain

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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.

In this work, it is presented a quantum circuit that diagonalizes exactly the 1D antiferromagnetic Ising Hamiltonian. With this circuit, it is possible to simulate time and temperature evolution since we have access to the whole model spectrum by just preparing a product state. As an example, it is provided an explicit circuit for four spins which is run in IBM's and Rigetti's quantum devices. As the Ising model can be solved analitically and this circuit can be extenend to higher number of qubits, it can also be used to benchmark quantum computers.

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