References

  1. Scott Aaronson & Alex Arkhipov (2013): The Computational Complexity of Linear Optics. Theory of Computing 9(4), pp. 143–252, doi:10.4086/toc.2013.v009a004.
  2. Dorit Aharonov, Wim van Dam, Julia Kempe, Zeph Landau, Seth Lloyd & Oded Regev (2007): Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation. SIAM Journal on Computing 37, pp. 166–194, doi:10.1137/S0097539705447323.
  3. C. Bennett, E. Bernstein, G. Brassard & U. Vazirani (1997): Strengths and Weaknesses of Quantum Computing. SIAM Journal on Computing 26(5), pp. 1510–1523, doi:10.1137/S0097539796300933.
  4. Robin Blume-Kohout, Carlton M. Caves & Ivan H. Deutsch (2002): Climbing Mount Scalable: Physical Resource Requirements for a Scalable Quantum Computer. Found. Phys. 32(11), pp. 1641–1670, doi:10.1023/A:1021471621587.
  5. Hamza Bougroura, Habib Aissaoui, Nicholas Chancellor & Viv Kendon (2016): Quantum-walk transport properties on graphene structures. Phys. Rev. A 94, pp. 062331, doi:10.1103/PhysRevA.94.062331.
  6. M. A. Broome, A. Fedrizzi, B. P. Lanyon, I. Kassal, A. Aspuru-Guzik & A. G. White (2010): Discrete single-photon quantum walks with tunable decoherence. Phys. Rev. Lett. 104, pp. 153602, doi:10.1103/PhysRevLett.104.153602.
  7. K. L. Brown, W. J. Munro & V. M. Kendon (2010): Using Quantum Computers for Quantum Simulation. Entropy 12(11), pp. 2268–2307, doi:10.3390/e12112268.
  8. A Callison, N Chancellor, F Mintert & V Kendon (2019): Finding spin glass ground states using quantum walks. New J. Phys. 21, pp. 123022, doi:10.1088/1367-2630/ab5ca2.
  9. N. Chancellor (2017): Modernizing Quantum Annealing II: Genetic algorithms with the Inference Primitive Formalism. Available at https://arxiv.org/abs/1609.05875. ArXiv:1609.05875.
  10. N. Chancellor (2017): Modernizing Quantum Annealing using Local Searches. New J. Phys. 19(2), pp. 023024, doi:10.1088/1367-2630/aa59c4.
  11. Andrew M. Childs (2009): Universal computation by quantum walk. Phys. Rev. Lett. 102, pp. 180501, doi:10.1103/PhysRevLett.102.180501.
  12. Andrew M. Childs, Richard Cleve, Enrico Deotto, Edward Farhi, Sam Gutmann & Daniel A. Spielman (2003): Exponential algorithmic speedup by a quantum walk. In: Proc. 35th Annual ACM Symposium on Theory of Computing (STOC 2003). Assoc. for Comp. Machinery, New York, pp. 59–68, doi:10.1145/780542.780552.
  13. Andrew M. Childs, Edward Farhi & John Preskill (2001): Robustness of adiabatic quantum computation. Physical Review A 65(1), pp. 012322, doi:10.1103/PhysRevA.65.012322.
  14. Andrew M. Childs & Jeffrey Goldstone (2004): Spatial search by quantum walk. Physical Review A 70(2), pp. 022314, doi:10.1103/PhysRevA.70.022314.
  15. Andrew M. Childs, David Gosset & Zak Webb (2013): Universal computation by multi-particle quantum walk. Science 339, pp. 791–794, doi:10.1126/science.1229957.
  16. Vicky Choi (2010): Adiabatic quantum algorithms for the NP-complete Maximum-Weight Independent set, Exact Cover and 3SAT problems. Available at https://arxiv.org/abs/1004.2226. ArXiv:1004.2226.
  17. A. Ben Dodds, Viv Kendon, Charles S. Adams & Nicholas Chancellor (2019): Practical designs for permutation-symmetric problem Hamiltonians on hypercubes. Phys. Rev. A 100, pp. 032320, doi:10.1103/PhysRevA.100.032320.
  18. A Ekert & J Jozsa (1998): Quantum algorithms: entanglement–enhanced information processing. Phil. Trans. Royal Soc. A 356, pp. 1769–82, doi:10.1098/rsta.1998.0248.
  19. E. Farhi, J. Goldstone, S. Gutmann & M. Sipser (2000): Quantum Computation by Adiabatic Evolution. Available at http://arxiv.org/quant-ph/abs/0001106. ArXiv:quant-ph/0001106.
  20. E Farhi & S Gutmann (1998): Quantum computation and decison trees. Phys. Rev. A 58, pp. 915–928, doi:10.1103/PhysRevA.58.915.
  21. A. B. Finilla, M. A. Gomez, C. Sebenik & J. D. Doll (1994): Quantum annealing: A new method for minimizing multidimensional functions. Chem. Phys. Lett. 219, pp. 343, doi:10.1016/0009-2614(94)00117-0.
  22. Lucien Hardy (2001): Quantum theory from five reasonable axioms. Available at http://arxiv.org/quant-ph/abs/0101012. ArXiv:quant-ph/0101012.
  23. A. Hartwig, F. Daske & S. Kobe (1984): A recursive branch-and-bound algorithm for the exact ground state of Ising spin-glass models. Computer Physics Communications 32(2), pp. 133 – 138, doi:10.1016/0010-4655(84)90066-3.
  24. C. Horsman, S. Stepney, R. C. Wagner & V. Kendon (2014): When does a Physical System Compute?. Proc. Roy. Soc. A 470(2169), pp. 20140182, doi:10.1098/rspa.2014.0182.
  25. D Horsman, V Kendon, S Stepney & P Young (2017): Abstraction and representation in living organisms: when does a biological system compute?. In: Giovagnoli R Dodig-Crnkovic G: Representation and Reality in Humans, Other Living Organisms and Intelligent Machines, Studies in Applied Philosophy, Epistemology and Rational Ethics 28. Springer, pp. 91–116, doi:10.1007/978-3-319-43784-2_6.
  26. Richard I. G. Hughes (1997): Models and representation. Philosophy of science 64, pp. S325–S336, doi:10.1086/392611.
  27. T. Kadowaki & H. Nishimori (1998): Quantum annealing in the transverse Ising model. Phys. Rev. E 58, pp. 5355, doi:10.1103/PhysRevE.58.5355.
  28. Michal Karski, Leonid Forster, Jai-Min Choi, Andreas Steffen, Wolfgang Alt, Dieter Meschede & Artur Widera (2009): Quantum Walk in Position Space with Single Optically Trapped Atoms. Science 325(5937), pp. 174–177, doi:10.1126/science.1174436.
  29. Kempe, Kitaev & Regev (2004): The Complexity of the Local Hamiltonian Problem. In: K. Lodaya & M. Mahajan: Proc. 24th FSTTCS, LNCS 3328. Springer, pp. 372–383, doi:10.1007/978-3-540-30538-5_31.
  30. V. Kendon, A. Sebald, S. Stepney, M. Bechmann, P. Hines & R. C. Wagner (2011): Heterotic computing. In: C.S. Calude, J. Kari, I. Petre & G. Rozenberg: Unconventional Computation, LNCS 6714. Springer, Berlin, Heidelberg, pp. 113–124, doi:10.1007/978-3-642-21341-0_16.
  31. V Kendon, A Siebald & S Stepney (2015): Heterotic computing: exploiting hybrid computational devices. Phil. Trans. Royal Soc. A 373. Royal Society, London, UK, doi:10.1098/rsta.2015.0091.
  32. Viv Kendon (2020): How to compute using quantum walks, doi:10.24350/CIRM.V.19600203. CIRM. Audiovisual resource..
  33. Daniel Lidar (2019): Arbitrary-time error suppression for Markovian adiabatic quantum computing using stabilizer subspace codes. Available at http://arxiv.org/abs/1904.12028.
  34. Bas Lodewijks (2019): Mapping NP-hard and NP-complete optimisation problems to Quadratic Unconstrained Binary Optimisation problems. Available at http://arxiv.org/abs/1911.08043.
  35. N. B. Lovett, S. Cooper, M. S. Everitt, M. Trevers & V. Kendon (2010): Universal quantum computation using the discrete time quantum walk. Phys. Rev. A 81, pp. 042330, doi:10.1103/PhysRevA.81.042330.
  36. M. Mohseni, P. Rebentrost, S. Lloyd & A. Aspuru-Guzik (2008): Environment-assisted quantum walks in photosynthetic energy transfer. J. Chem. Phys. 129, pp. 174106, doi:10.1063/1.3002335.
  37. Ashley Montanaro (2018): Quantum-Walk Speedup of Backtracking Algorithms. Theory of Computing 14(15), pp. 1–24, doi:10.4086/toc.2018.v014a015.
  38. Ashley Montanaro (2019): Quantum speedup of branch-and-bound algorithms. Available at http://arxiv.org/abs/1906.10375. ArXiv:1906.10375.
  39. JG Morley, N Chancellor, S Bose & V Kendon (2019): Quantum search with hybrid adiabatic-quantum walk algorithms and realistic noise. Phys. Rev. A 99, pp. 022339, doi:10.1103/PhysRevA.99.022339.
  40. Hagai B. Perets, Yoav Lahini, Francesca Pozzi, Marc Sorel, Roberto Morandotti & Yaron Silberberg (2008): Realization of quantum walks with negligible decoherence in waveguide lattices. Phys. Rev. Lett. 100, pp. 170506, doi:10.1103/PhysRevLett.100.170506.
  41. Gualtiero Piccinini (2017): Computation in Physical Systems. In: Edward N. Zalta: The Stanford Encyclopedia of Philosophy, Summer 2017 edition. Stanford University Press. Available at http://plato.stanford.edu/archives/sum2017/entries/computation-physicalsystems/.
  42. Hilary Putnam (1988): Representation and Reality. MIT Press, Cambridge, MA. Available at https://mitpress.mit.edu/books/representation-and-reality. ISBN: 9780262161084.
  43. Jérémie Roland & Nicolas J. Cerf (2002): Quantum search by local adiabatic evolution. Phys. Rev. A 65, pp. 042308, doi:10.1103/PhysRevA.65.042308.
  44. C. A. Ryan, M. Laforest, J. C. Boileau & R. Laflamme (2005): Experimental implementation of discrete time quantum random walk on an NMR quantum information processor. Phys. Rev. A 72, pp. 062317, doi:10.1103/PhysRevA.72.062317.
  45. A. Schreiber, K. N. Cassemiro, V. Potoček, A. Gábris, I. Jex & Ch. Silberhorn (2011): Decoherence and disorder in quantum walks: From ballistic spread to localization. Phys. Rev. Lett. 106, pp. 180403, doi:10.1103/PhysRevLett.106.180403.
  46. Neil Shenvi, Julia Kempe & K Birgitta Whaley (2003): A quantum random walk search algorithm. Phys. Rev. A 67, pp. 052307, doi:10.1103/PhysRevA.67.052307.
  47. Steffen, vanDam, Hogg, Breyta & Chuang (2003): Experimental implementation of an adiabatic quantum optimization algorithm. Phys. Rev. Lett. 90(6), pp. 067903, doi:10.1103/PhysRevLett.90.067903.
  48. S. Stepney & V. Kendon (2019): The role of the representational entity in physical computing. In: UCNC 2019, Tokyo, Japan, June 2019, LNCS 11493. Springer, pp. 219–231, doi:10.1007/978-3-030-19311-9_18.
  49. K. Wiesner (2009): Quantum Cellular Automata. In: Robert A. Meyers: Springer Encyclopedia of Complexity and System Science, chapter Cellular Automata, Mathematical Basis of, Ed. Andy Adamatzky. Springer, pp. 00105, doi:10.1007/978-0-387-30440-3_426. or http://arxiv.org/abs/0808.0679.
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