A variational eigenvalue solver on a photonic quantum processor
10.1038/ncomms5213
Crossref journal-article
Springer Science and Business Media LLC
Nature Communications (297)
Bibliography

Peruzzo, A., McClean, J., Shadbolt, P., Yung, M.-H., Zhou, X.-Q., Love, P. J., Aspuru-Guzik, A., & O’Brien, J. L. (2014). A variational eigenvalue solver on a photonic quantum processor. Nature Communications, 5(1).

Authors 8
  1. Alberto Peruzzo (first)
  2. Jarrod McClean (additional)
  3. Peter Shadbolt (additional)
  4. Man-Hong Yung (additional)
  5. Xiao-Qi Zhou (additional)
  6. Peter J. Love (additional)
  7. Alán Aspuru-Guzik (additional)
  8. Jeremy L. O’Brien (additional)
References 37 Referenced 3,146
  1. Thogersen, L. & Olsen, J. A coupled cluster and full configuration interaction study of cn and cn-. Chem. Phys. Lett. 393, 36–43 (2004). (10.1016/j.cplett.2004.06.001) / Chem. Phys. Lett. by L Thogersen (2004)
  2. Helgaker, T., Jorgensen, P. & Olsen, J. Mol. Electronic Struct. Theory Wiley, Sussex (2002).
  3. Saad, Y. Numerical Methods for Large Eigenvalue Problems Vol. 158, (SIAM (1992).
  4. Page, L., Brin, S., Motwani, R. & Winograd, T. The Pagerank Citation Ranking: Bringing Order to the Web. Technical Report 1999-66 (Stanford InfoLab, (1999).
  5. Golub, G. H. & van der Vorst, H. A. Eigenvalue computation in the 20th century. J. Comput. Appl. Math. 123, 35–65 (2000). (10.1016/S0377-0427(00)00413-1) / J. Comput. Appl. Math. by GH Golub (2000)
  6. Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information Cambridge University Press (2000).
  7. Kitaev, A. Quantum measurements and the Abelian stabilizer problem. Electronic Colloquium on Computational Complexity (ECCC) 3 (1996).
  8. Griffiths, R. B. & Niu, C.-S. Semiclassical fourier transform for quantum computation. Phys. Rev. Lett. 76, 3228–3231 (1996). (10.1103/PhysRevLett.76.3228) / Phys. Rev. Lett. by RB Griffiths (1996)
  9. Neven, H., Rose, G. & Macready, W. G. Image recognition with an adiabatic quantum computer I. Mapping to quadratic unconstrained binary optimization. Preprint at http://arxiv.org/abs/0804.4457 (2008).
  10. Harrow, A., Hassidim, A. & Lloyd, S. Quantum algorithm for linear systems of equations. Phys. Rev. Lett. 103, 150502 (2009). (10.1103/PhysRevLett.103.150502) / Phys. Rev. Lett. by A Harrow (2009)
  11. Berry, D. W. High-order quantum algorithm for solving linear differential equations. J. Phys. A 47, 105301 (2014). (10.1088/1751-8113/47/10/105301) / J. Phys. A by DW Berry (2014)
  12. Garnerone, S., Zanardi, P. & Lidar, D. A. Adiabatic quantum algorithm for search engine ranking. Phys. Rev. Lett. 108, 230506 (2012). (10.1103/PhysRevLett.108.230506) / Phys. Rev. Lett. by S Garnerone (2012)
  13. Abrams, D. S. & Lloyd, S. Simulation of many-body fermi systems on a universal quantum computer. Phys. Rev. Lett. 79, 2586–2589 (1997). (10.1103/PhysRevLett.79.2586) / Phys. Rev. Lett. by DS Abrams (1997)
  14. Abrams, D. S. & Lloyd, S. Quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors. Phys. Rev. Lett. 83, 5162–5165 (1999). (10.1103/PhysRevLett.83.5162) / Phys. Rev. Lett. by DS Abrams (1999)
  15. Aspuru-Guzik, A., Dutoi, A. D., Love, P. J. & Head-Gordon, M. Simulated quantum computation of molecular energies. Science 309, 1704–1707 (2005). (10.1126/science.1113479) / Science by A Aspuru-Guzik (2005)
  16. Lanyon, B. P. et al. Towards quantum chemistry on a quantum computer. Nat. Chem. 2, 106–111 (2010). (10.1038/nchem.483) / Nat. Chem. by BP Lanyon (2010)
  17. Whitfield, J. D., Biamonte, J. & Aspuru-Guzik, A. Simulation of electronic structure hamiltonians using quantum computers. Mol. Phys. 109, 735–750 (2011). (10.1080/00268976.2011.552441) / Mol. Phys. by JD Whitfield (2011)
  18. Aspuru-Guzik, A. & Walther, P. Photonic quantum simulators. Nat. Phys. 8, 285–291 (2012). (10.1038/nphys2253) / Nat. Phys. by A Aspuru-Guzik (2012)
  19. Jones, N. C. et al. Faster quantum chemistry simulation on fault-tolerant quantum computers. New J. Phys. 14, 115023 (2012). (10.1088/1367-2630/14/11/115023) / New J. Phys. by NC Jones (2012)
  20. Lloyd, S. Computational capacity of the universe. Phys. Rev. Lett. 88, 237901 (2002). (10.1103/PhysRevLett.88.237901) / Phys. Rev. Lett. by S Lloyd (2002)
  21. Ma, X.-s., Dakic, B., Naylor, W., Zeilinger, A. & Walther, P. Quantum simulation of the wavefunction to probe frustrated Heisenberg spin systems. Nat. Phys. 7, 399–405 (2011). (10.1038/nphys1919) / Nat. Phys. by X-s Ma (2011)
  22. Oseledets, I. Approximation of 2d × 2d matrices using tensor decomposition. SIAM J. Matrix Anal. A 31, 2130–2145 (2010). (10.1137/090757861) / SIAM J. Matrix Anal. A by I Oseledets (2010)
  23. Ortiz, G., Gubernatis, J. E., Knill, E. & Laflamme, R. Quantum algorithms for fermionic simulations. Phys. Rev. A 64, 022319 (2001). (10.1103/PhysRevA.64.022319) / Phys. Rev. A by G Ortiz (2001)
  24. Liu, Y.-K., Christandl, M. & Verstraete, F. Quantum computational complexity of the n-representability problem: Qma complete. Phys. Rev. Lett. 98, 110503 (2007). (10.1103/PhysRevLett.98.110503) / Phys. Rev. Lett. by Y-K Liu (2007)
  25. Temme, K., Osborne, T. J., Vollbrecht, K. G., Poulin, D. & Verstraete, F. Quantum Metropolis sampling. Nature 471, 87–90 (2011). (10.1038/nature09770) / Nature by K Temme (2011)
  26. Yung, M.-H. & Aspuru-Guzik, A. A quantum-quantum Metropolis algorithm. Proc. Natl Acad. Sci. USA 109, 754–759 (2012). (10.1073/pnas.1111758109) / Proc. Natl Acad. Sci. USA by M-H Yung (2012)
  27. Rayleigh, J. W. In finding the correction for the open end of an organ-pipe. Phil. Trans. 161, 77 (1870). / Phil. Trans. by JW Rayleigh (1870)
  28. Ritz, W. Über eine neue Methode zur Lösung gewisser variationsprobleme der mathematischen physik. J. Reine Angew. Math. 135, 1–61 (1908). / J. Reine Angew. Math. by W Ritz (1908)
  29. Taube, A. G. & Bartlett, R. J. New perspectives on unitary coupled-cluster theory. Int. J. Quant. Chem. 106, 3393–3401 (2006). (10.1002/qua.21198) / Int. J. Quant. Chem. by AG Taube (2006)
  30. O'Brien, J. L., Furusawa, A. & Vuckovic, J. Photonic quantum technologies. Nat. Photon. 3, 687–695 (2009). (10.1038/nphoton.2009.229) / Nat. Photon. by JL O'Brien (2009)
  31. Shadbolt, P. et al. Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit. Nat. Photon. 6, 45–49 (2011). (10.1038/nphoton.2011.283) / Nat. Photon. by P Shadbolt (2011)
  32. Crawford, T. D. et al. Psi3: an open-source ab initio electronic structure package. J. Comp. Chem. 28, 1610–1616 (2007). (10.1002/jcc.20573) / J. Comp. Chem. by TD Crawford (2007)
  33. Szarek, S. J. Volume of separable states is super-doubly-exponentially small in the number of qubits. Phys. Rev. A 72, 032304 (2005). (10.1103/PhysRevA.72.032304) / Phys. Rev. A by SJ Szarek (2005)
  34. Zhou, X.-Q. et al. Adding control to arbitrary unknown quantum operations. Nat. Commun. 2, 413 (2011). (10.1038/ncomms1392) / Nat. Commun. by X-Q Zhou (2011)
  35. Kempe, J., Kitaev, A. & Regev, O. The complexity of the local hamiltonian problem. SIAM J. Comput. 35, 1070–1097 (2006). (10.1137/S0097539704445226) / SIAM J. Comput. by J Kempe (2006)
  36. Nelder, J. A. & Mead, R. A simplex method for function minimization. Comput. J. 7, 308–313 (1965). (10.1093/comjnl/7.4.308) / Comput. J. by JA Nelder (1965)
  37. Conn, A. R., Gould, N. I. & Toint, P. L. Trust Region Methods Vol. 1 (, Society for Industrial Mathematics (1987).
Dates
Type When
Created 11 years, 1 month ago (July 23, 2014, 5:45 a.m.)
Deposited 2 years, 7 months ago (Jan. 5, 2023, 5:31 p.m.)
Indexed 7 hours, 44 minutes ago (Aug. 24, 2025, 6:52 p.m.)
Issued 11 years, 1 month ago (July 23, 2014)
Published 11 years, 1 month ago (July 23, 2014)
Published Online 11 years, 1 month ago (July 23, 2014)
Funders 0

None

@article{Peruzzo_2014, title={A variational eigenvalue solver on a photonic quantum processor}, volume={5}, ISSN={2041-1723}, url={http://dx.doi.org/10.1038/ncomms5213}, DOI={10.1038/ncomms5213}, number={1}, journal={Nature Communications}, publisher={Springer Science and Business Media LLC}, author={Peruzzo, Alberto and McClean, Jarrod and Shadbolt, Peter and Yung, Man-Hong and Zhou, Xiao-Qi and Love, Peter J. and Aspuru-Guzik, Alán and O’Brien, Jeremy L.}, year={2014}, month=jul }