Classical simulation of a quantum system is a hard problem. It’s known that these problems can be solved efficiently by using quantum computers. This study demonstrates the simulation of the molecular Hamiltonian of 2p-π electrons of ethylene in order to calculate the ground state energy. The ground state energy is estimated by an iterative phase estimation algorithm. The ground state is prepared by the adiabatic state preparation and the implementation of the procedure is carried out by numerical simulation of two-qubit NMR quantum simulator. The readout scheme of the simulator is performed by extracting binary bits via NMR interferometer.
M. A. Nielsen and I. L. Chuang, “Quantum Computation and Quantum Information,” Cambridge University Press, Cambridge, 2000.
P. D. Jonathan and J. M. Gerard, “Quantum Technology: The Second Quantum Revolution,” Philosophical Transactions of the Royal Society A, Vol. 361, 2011, pp. 1655-1674.
R. P. Feynman, “Simulating Physics with Computers,” International Journal of Theoretical Physics, Vol. 21, No. 6-7, 1982, pp. 467-488. doi:10.1007/BF02650179
D. Deutsch, “Quantum Theory the Church Turing Principle and Universal Quantum Computer,” Proceedings of the Royal Society A, Vol. 400, No. 1818, 1985, pp. 97- 117.
P. W. Shor, “Polynomial Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer,” SIAM Review, Vol. 41, No. 2, 1999, pp. 303-332. doi:10.1137/S0036144598347011
L. K. Grover, “Quantum Mechanics Helps in Searching a Needle in a Haystack,” Physical Review Letters, Vol. 79, No. 2, 1997, pp. 325-328. doi:10.1103/PhysRevLett.79.325
S. Lloyd, “Universal Quantum Simulators,” Science, Vol. 273, No. 5278, 1996, pp. 1073-1078. doi:10.1126/science.273.5278.1073
K. L. Brown, W. J. Munro and V. M. Kendon, “Using Quantum Computers for Quantum Simulation,” Entropy, Vol. 12, No. 11, 2010, pp. 2268-2307. doi:10.3390/e12112268
S. Somaroo, T. F. Havel, R. Laflamme, et al., “Quantum Simulations on a Quantum Computer,” Physical Review Letters, Vol. 82, No. 26, 1999, pp. 5381-5384. doi:10.1103/PhysRevLett.82.5381
S. Somaroo, T. F. Havel, R. Laflamme, et al., “Quantum Simulation of a Three Body Interaction Hamiltonian on an NMR Quantum Computer,” Physical Review A, Vol. 61, No.1, 1999, Article ID: 012302. doi:10.1103/PhysRevA.61.012302
A. K. Krithin and B. M. Fung, “NMR Simulation of an Eight State Quantum System,” Physical Review A, Vol. 64, No. 3, 2001, Article ID: 032306. doi:10.1103/PhysRevA.64.032306
G. Ortiz, E. Knill, R. Laflamme, et al., “Liquid State NMR Simulations of Quantum Many Body Problems,” Physical Review A, Vol. 71, No. 3, 2005, Article ID: 032 344. doi:10.1103/PhysRevA.71.032344
X. Peng , J. Du and D. Suter, “Quantum Phase Transition of Ground State Entanglement in a Heisenberg Spin Chain Simulated in an NMR Quantum Computer,” Physical Review A, Vol. 71, No. 1, 2005, Article ID: 012307. doi:10.1103/PhysRevA.71.012307
D. S. Abrams and S. Lloyd, “Quantum Algorithm Providing Exponantial Speed Increase for Finding Eigenvalues and Eigenvectors,” Physical Review Letters, Vol. 83, No. 24, 1999, pp. 5162-5165. doi:10.1103/PhysRevLett.83.5162
R. Cleve, A. Ekert, M. Mosca, et al., “Quantum Algorithms Revisited,” Proceedings of the Royal Society of London A, Vol. 454, No. 1969, 1998, pp. 339-354.
A. A. Guzik, A. D. Dutoi, P. J. Love, et al., “Simulated Quantum Computation of Molecular Energies,” Science, Vol. 309, No. 5741, 2005, pp. 1704-1707. doi:10.1126/science.1113479
A. Messiah, “Quantum Mechanics,” Wiley, New York, 1976.
I. Kassal, M. Mohseni, A. A. Guzik, et al., “Polynomial-Time Quantum Algorithm for the Simulation of Chemical Dynamics,” PNAS, Vol. 105, No. 48, 2008, pp. 18681-18686. doi:10.1073/pnas.0808245105
I. Kassal, A. P. Ortiz, A. A. Guzik, et al., “Simulating Chemistry Using Quantum Computers,” Annual Review of Physical Chemistry, Vol. 62, No. 1, 2011, pp. 185-207. doi:10.1146/annurev-physchem-032210-103512
B. P. Lanyon, I. Kassal, A. A. Guzik, et al., “Towards Quantum Chemistry on a Quantum Computer,” Nature Chemistry, Vol. 2, No. 2, 2010, pp. 106-111. doi:10.1038/nchem.483
J. Du, X. Peng, D. Lu, et al., “NMR Implementation of a Molecular Hydrogen Simulation with Adiabatic State Preparation,” Physical Review Letters, Vol. 104, No. 3, 2010, Article ID: 030520. doi:10.1103/PhysRevLett.104.030502
J. D. Whitfield, J. Biamonte and A. A. Guzik, “Simulation of Electronic Structure Hamiltonians Using Quantum Computers,” Molecular Physics, Vol. 109, No. 5, 2011, pp. 735-750. doi:10.1080/00268976.2011.552441
Z. Li , X. Peng, A. A. Guzik, et al., “Solving Ground State Problems with Nuclear Magnetic Resonance,” Scientific Reports, Vol. 1, No. 88, 2011, pp. 1-7.
M. Dobsicek, G. Johansson, G. Wendin, et al., “Arbitrary Accuracy Iterative Quantum Phase Estimation Algorithm Using a Single Ancillary Qubit: A Two-Qubit Benchmark,” Physical Review A, Vol. 76, No. 3, 2007, Article ID: 030306. doi:10.1103/PhysRevA.76.030306
M. Steffen, W. V. Dam, I. Chuang, et al., “Experimental Implementation of an Adiabatic Optimization Algorithm,” Physical Review Letters, Vol. 90, No. 6, 2003, Article ID: 067903. doi:10.1103/PhysRevLett.90.067903
A. Szabo and N. S. Ostlund, “Modern Quantum Chemistry,” Dover Publications Inc., New York, 1996.
R. G. Parr, “The Quantum Theory Molecular Electronic Structure,” W.A. Benjamin Inc., New York, 1963.
R. Laflamme, D. G. Cory, T. F. Havel, et al., “NMR and Quantum Information Processing,” Los Alamos Science, Vol. 27, 2002, pp. 227-259.
J. A. Jones, “Quantum Computing with NMR,” Progress in Nuclear Magnetic Resonance Spectroscopy, Vol. 59, No. 2, 2011, pp. 91-120. doi:10.1016/j.pnmrs.2010.11.001
M. H. Levitt, “Spin Dynamics,” John Wiley & Sons, Chichester, 2001.
M. D. Price, S. S. Somaroo, T. F. Havel, et al., “Construction and Implementation of NMR Quantum Logic Gates for Two Spin Systems,” Journal of Magnetic Resonance,Vol. 140, No. 2, 1999, pp. 371-378.
X. Peng, D. Suter, K. Gao, et al., “Quantification of Complementarity in Multiqubitsystems,” Physical Review A, Vol. 72, No. 5, 2005, Article ID: 052109. doi:10.1103/PhysRevA.72.052109
K. R. Brown, R. J. Clark and I. L. Chuang, “Limitations of Quantum Simulation Examined by Simulating a Pairing Hamiltonian Using Nuclear Magnetic Resonance,” Physical Review Letters, Vol. 97, No. 5, 2006, Article ID: 050504. doi:10.1103/PhysRevLett.97.050504