Abstract
In previous chapters we have seen that quantum mechanics permits strong nonlocal correlations which are classically forbidden. It turns out that this makes it very difficult to engineer a classical digital computer to mimic the behaviour of quantum systems—it seems very likely that the general problem is classically intractable. However, we have good reason to believe that a quantum computer should be able to efficiently simulate most quantum systems of interest.
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Notes
- 1.
Note that this question is related to the Extended Church-Turing Thesis, discussed in Sect. 6.3.2 of this thesis.
References
S. Michael, D. Auld, C. Klumpp, A. Jadhav, W. Zheng, N. Thorne, C.P. Austin, J. Inglese, A. Simeonov, A robotic platform for quantitative high-throughput screening. Assay. Drug. Dev. Technol. 5, 637–657 (2008)
R.P. Feynman, Simulating physics with computers. Int. J. Theor. Phy. Theor. Phy. 21, 467–488 (1982)
P.W. Shor, Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer (1995). arXiv:quant-ph/9508027
R. Babbush, A. Perdomo-Ortiz, B. O’Gorman, W. Macready, A. Aspuru-Guzik, Construction of Energy Functions for Lattice Heteropolymer Models: A Case Study in Constraint Satisfaction Programming and Adiabatic Quantum Optimization (2012). arXiv:1211.3422
G.J. Halász, A. Perveaux, B. Lasorne, M.A. Robb, F. Gatti, Á. Vibók, Simulation of laser-induced quantum dynamics of the electronic and nuclear motion in the ozone molecule on the attosecond time scale. Phys. Rev. A 86, 043–426 (2012)
P.W. Anderson, The resonating valence bond state in la2cuo4 and superconductivity. Science 235(4793), 1196–1198 (1987)
R. Moessner, S.L. Sondhi, P. Chandra, Two-dimensional periodic frustrated ising models in a transverse field. Phys. Rev. Lett. 84, 4457–4460 (2000). May
J.W. Britton, B.C. Sawyer, A.C. Keith, C.-C.J. Wang, J.K. Freericks, H. Uys, M.J. Biercuk, J.J. Bollinger, Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins. Nature 484, 489–492 (2012). April
M. Sarovar, A. Ishizaki, G.R. Fleming, K.B. Whaley, Quantum entanglement in photosynthetic light-harvesting complexes. Nat. Phys. 6, 462–467 (2010). June
Dirac. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, vol. 123, 714–733 (1929)
L. Pauling, The nature of the chemical bond, vol. 2 (Univ. Press, New York, addison-wesley edition, Cornell, 1939)
M. Born, J. Robert Oppenheimer, On the quantum theory of molecules. Ann. Phys. 389, 457–484 (1927)
I. Kassal, J.D. Whitfield, A. Perdomo-Ortiz, M.-H. Yung, A. Aspuru-Guzik, Simulating chemistry using quantum computers. Ann. Rev. Phys. Chem. 62, 185–207 (2011)
J.C. Slater, The theory of complex spectra. Phys. Rev. 34, 1293–1322 (1929)
I. Shavitt, R.J Bartlett, Many-Body Methods in Chemistry and Physics: MBPT and Coupled-Cluster Theory. Cambridge (2009)
W. Koch, M.C. Holthausen, A Chemist’s Guide to Density Functional Theory, 2nd Edition. Wiley (2001)
T. Fukuhara, P. Schauß, M. Endres, S. Hild, M. Cheneau, I. Bloch, C. Gross, MicroscopiC Observation Of Magnon Bound States And Their Dynamics (2013). arXiv:1305.6598
M.A Nielsen, The fermionic canonical commutation relations and the jordan-wigner transform (2005)
P. Jordan, E. Wigner, über das paulische äquivalenzverbot. Z. Phys. 47(9–10), 631–651 (1928)
G. Ortiz, J.E. Gubernatis, E. Knill, R. Laflamme, Quantum algorithms for fermionic simulations. Phys. Rev. A 64, 022319 (2001)
R. Somma, G. Ortiz, J.E. Gubernatis, E. Knill, R. Laflamme, Simulating physical phenomena by quantum networks. Phys. Rev. A 65(4), 042323 (2002)
D.S. Abrams, S. Lloyd, Simulation of many-body fermi systems on a universal quantum computer. Phys. Rev. Lett. 79, 2586–2589 (1997)
A.Y. Kitaev, A.H. Shen, M.N. Vyalyi, Classical and Quantum Computation. Amer Mathematical Society (2002)
Michael A. Nielsen and Isaac L. Chuang. Quantum Computation and Quantum Information (Cambridge Series on Information and the Natural Sciences). Cambridge University Press, 1 edition (2004)
J. Whitfield, J. Biamonte, A. Aspuru-Guzik, Simulation of electronic structure Hamiltonians using quantum computers. Mol. Phys. 109, 735–750 (2011). March
D. Wecker, B. Bauer, B.K. Clark, M.B. Hastings, M. Troyer, Can quantum chemistry be performed on a small quantum computer? ( 2013). arXiv:1312.1695
O. Johnston, The Illusion of Life: Disney Animation. Disney Editions (1981)
Alán Aspuru-Guzik, Anthony D. Dutoi, Peter J. Love, Martin Head-Gordon, Simulated quantum computation of molecular energies. Science 309(5741), 1704–1707 (2005)
B.P. Lanyon, J.D. Whitfield, G.G. Gillett, M.E. Goggin, M.P. Almeida, I. Kassal, J.D. Biamonte, M. Mohseni, B.J. Powell, M. Barbieri, A. Aspuru-Guzik, A.G. White, Towards quantum chemistry on a quantum computer. Nat. Chem. 2, 106–111 (2010)
S. Lloyd, Universal quantum simulators. Science 273, 1073–1078 (1996)
J. Kempe, A. Kitaev, O. Regev, The Complexity of the Local Hamiltonian Problem. arXiv:quant-ph/0406180
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Shadbolt, P. (2016). Quantum Chemistry on a Photonic Chip. In: Complexity and Control in Quantum Photonics. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-21518-1_5
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