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.
 Z. Jiang, K. J. Sung, K. Kechedzhi, V. N. Smelyanskiy and S. Boixo, Phys. Rev. Appl. 9, 044036 (2018).
 B. Kraus, Phys. Rev. Lett. 107, 250503 (2011).
 A. J. Ferris, Phys. Rev. Lett. 113, 010401 (2014).
 Device specifications: https://github.com/Qiskit/qiskit-backend-information/tree/master/backends.
 Official announce of IBM ``Teach Me QISKit" award winnerhttps://www.ibm.com/blogs/research/2018/06/teach-qiskit-winner/.
 Francesco Tacchino, Alessandro Chiesa, Stefano Carretta, and Dario Gerace, "Quantum Computers as Universal Quantum Simulators: State‐of‐the‐Art and Perspectives", Advanced Quantum Technologies 3 3, 1900052 (2020).
 Cristina Cîrstoiu, Zoë Holmes, Joseph Iosue, Lukasz Cincio, Patrick J. Coles, and Andrew Sornborger, "Variational fast forwarding for quantum simulation beyond the coherence time", npj Quantum Information 6 1, 82 (2020).
 Alba Cervera-Lierta, José Ignacio Latorre, and Dardo Goyeneche, "Quantum circuits for maximally entangled states", Physical Review A 100 2, 022342 (2019).
 P M Q Cruz, G Catarina, R Gautier, and J Fernández-Rossier, "Optimizing quantum phase estimation for the simulation of Hamiltonian eigenstates", Quantum Science and Technology 5 4, 044005 (2020).
 Konrad Jałowiecki, Andrzej Więckowski, Piotr Gawron, and Bartłomiej Gardas, "Parallel in time dynamics with quantum annealers", Scientific Reports 10 1, 13534 (2020).
 Marcello Calvanese Strinati, Leon Bello, Avi Pe'er, and Emanuele G. Dalla Torre, "Theory of coupled parametric oscillators beyond coupled Ising spins", Physical Review A 100 2, 023835 (2019).
 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 states", Quantum Information Processing 18 7, 218 (2019).
 Aydin Deger and Tzu-Chieh Wei, "Geometric entanglement and quantum phase transition in generalized cluster-XY models", Quantum Information Processing 18 10, 326 (2019).
 Kishore S. Shenoy, Dev Y. Sheth, Bikash K. Behera, and Prasanta K. Panigrahi, "Demonstration of a measurement-based adaptation protocol with quantum reinforcement learning on the IBM Q experience platform", Quantum Information Processing 19 5, 161 (2020).
 Adam Smith, M. S. Kim, Frank Pollmann, and Johannes Knolle, "Simulating quantum many-body dynamics on a current digital quantum computer", npj Quantum Information 5 1, 106 (2019).
 Leon Bello, Marcello Calvanese Strinati, Emanuele G. Dalla Torre, and Avi Pe’er, "Persistent Coherent Beating in Coupled Parametric Oscillators", Physical Review Letters 123 8, 083901 (2019).
 Jason P. Terry, Prosper D. Akrobotu, Christian F. A. Negre, Susan M. Mniszewski, and Itay Hen, "Quantum isomer search", PLOS ONE 15 1, e0226787 (2020).
 Lindsay Bassman, Kuang Liu, Aravind Krishnamoorthy, Thomas Linker, Yifan Geng, Daniel Shebib, Shogo Fukushima, Fuyuki Shimojo, Rajiv K. Kalia, Aiichiro Nakano, and Priya Vashishta, "Towards simulation of the dynamics of materials on quantum computers", Physical Review B 101 18, 184305 (2020).
 Bartłomiej Gardas, Marek M. Rams, and Jacek Dziarmaga, "Quantum neural networks to simulate many-body quantum systems", Physical Review B 98 18, 184304 (2018).
 K. M. Anandu, Muhammad Shaharukh, Bikash K. Behera, and Prasanta K. Panigrahi, "Demonstration of teleportation-based error correction in the IBM quantum computer", arXiv:1902.01692.
 Amandeep Singh Bhatia and Mandeep Kaur Saggi, "Implementing Entangled States on a Quantum Computer", arXiv:1811.09833.
 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.
 Alakesh Baishya, Lingraj Kumar, Bikash K. Behera, and Prasanta K. Panigrahi, "Experimental Demonstration of Force Driven Quantum Harmonic Oscillator in IBM Quantum Computer", arXiv:1906.01436.
 Ashley Montanaro and Stasja Stanisic, "Compressed variational quantum eigensolver for the Fermi-Hubbard model", arXiv:2006.01179.
 Bhupesh Bishnoi, "Quantum-Computation and Applications", arXiv:2006.02799.
 Rafael I. Nepomechie, "Bethe ansatz on a quantum computer?", arXiv:2010.01609.
The above citations are from Crossref's cited-by service (last updated successfully 2020-10-20 19:44:56) and SAO/NASA ADS (last updated successfully 2020-10-20 19:44:56). The list may be incomplete as not all publishers provide suitable and complete citation data.
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.