Exact Ising model simulation on a quantum computer

Abstract

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 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.

arXiv commentThe program used for this work for the IBM quantum devices was awarded with the IBM "Teach Me QISKit" award. Accepted in Quantum journal (2018-12-18)

References in corpus (18)

• Elementary gates for quantum computation
• Efficient classical simulation of slightly entangled quantum computations
• The Physical Implementation of Quantum Computation
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Quantum Algorithms for Fermionic Simulations
• Solving strongly correlated electron models on a quantum computer
• Quantum circuits for strongly correlated quantum systems
• Quantum algorithms to simulate many-body physics of correlated fermions
• Performing Quantum Computing Experiments in the Cloud
• Experimental test of Mermin inequalities on a 5-qubit quantum computer
• 16-qubit IBM universal quantum computer can be fully entangled
• Density matrix quantum Monte Carlo
• Fourier transform of fermionic systems and the spectral tensor network
• Numerical Contraction of the Tensor Network generated by the Algebraic Bethe Ansatz
• The Algebraic Bethe Ansatz and Tensor Networks
• Compressed quantum computation using the IBM Quantum Experience
• Compressed quantum simulation of the Ising model
• Kitaev honeycomb tensor networks: exact unitary circuits and applications

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