Abstract
Combinatorial optimization problems are ubiquitous in our modern life. The classic examples include the protein folding in biology and medicine, the frequency assignment in wireless communications, traffic control and routing in air and on surface, microprocessor circuit design, computer vision and graph cut in machine learning, and social network control. They often belong to NP, NP-complete and NP-hard classes, for which modern digital computers and future quantum computers cannot find solutions efficiently, i.e. in polynomial time [1].
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References
M.R. Garey, D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness (W. H. Freeman, New York, 1979)
K. Binder, A.P. Young, Spin glasses: experimental facts, theoretical concepts, and open questions. Rev. Mod. Phys. 58, 801–976 (1986)
E. Ising, Beitrag zur theorie des ferromagnetismus. Z. Phys. 31, 253 (1925)
L. Onsager, Crystal statistics. I. A two-dimensional model with an order-disorder transition. Phys. Rev. 65, 117 (1944)
F. Barahona, On the computational complexity of Ising spin glass models. J. Phys. A Math. Gen. 15, 3241–3253 (1982)
M. Nielson, I. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge/New York, 2000)
T. Kadowaki, H. Nishimori, Quantum annealing in the transverse Ising model. Phys. Rev. E 58, 5355 (1998)
E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lundgren, D. Preda, A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem. Science 292(5516), 472–475 (2001)
S. Utsunomiya, K. Takata, Y. Yamamoto, Mapping of Ising models onto injection-locked laser systems. Opt. Express 19, 18091–18108 (2011)
L.K. Grover, A fast quantum mechanical algorithm for database search, in Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, Philadelphia (1996), p. 212
C.H. Bennett, E. Bernstein, G. Brassard, U.V. Vazirani, Strengths and weaknesses of quantum computing. SIAM J. Comput. 26, 1510 (1997)
J. Roland, N. Cerf, Quantum search by local adiabatic evolution. Phys. Rev. A 65, 042308 (2002)
D. Aharonov, W. van Dam, J. Kempe, Z. Landau, S. Lloyd, O. Regev, Adiabatic quantum computation is equivalent to standard quantum computation. quant-ph/0405098 v2 (2005)
D. Gattesman, The Heisenberg representation of quantum computers. quant-ph/9807006 (1998)
S.D. Bartlett, B.C. Sanders, S.L. Braunstein, K. Nemoto, Efficient classical simulation of continuous variable quantum information processes. quant-ph/0109047 (2001)
L. Gillner, G. Bjork, Y. Yamamoto, Quantum noise properties of an injection-locked laser oscillator with pump-noise suppression and squeezed injection. Phys. Rev. A 41(9), 5053–5065 (1990)
H.A. Haus, Y. Yamamoto, Quantum noise of an injection-locked laser oscillator. Phys. Rev. A 29, 1261–1274 (1984)
M. Surgent, M.O. Scully, W.E. Lamb, Chapter 20, in Laser Physics (Westview Printing, Colorado, 1978), pp. 331–335
H. Haug, Quantum-mechanical rate equations for semiconductor lasers. Phys. Rev. 184, 338–348 (1969)
Y. Yamamoto, S. Machida, O. Neilsson, Amplitude squeezing in a pump-noise-suppressed laser oscillator. Phys. Rev. A 34, 4025–4042 (1986)
M. Yannakakis, Edge-deletion problems. SIAM J. Comput. 10, 297–309 (1981)
R. Greenlaw, R. Pedreschi, Cubic graphs. ACM Comput. Surv. 27, 471–495 (1995)
F. Barahona, M. Grotschel, M. Junger, R. Reinelt, An application of combinatorial optimization to statistical physics and circuit layout design. Oper. Res. 36(3), 493–513 (1988)
A. Galluccio, M. Loebl, J. Vondrak, New algorithm for the Ising problem: partition function for finite lattice graphs. Phys. Rev. Lett. 84, 5924–5927 (2000)
C.W. Gardiner, P. Zoller, Quantum Noise (Springer, Berlin, 1991)
K. Takata, S. Utsunomiya, Y. Yamamoto, Transient time of an Ising machine based on injection-locked laser network. New J. Phys. 14, 013052 (2012)
B.D. McKay, G.F. Royle, Constructing the cubic graphs on up to 20 vertices. Ars Combin. 21, 129–140 (1986)
M.X. Goemans, D.P. Williams, J. ACM 42, 1115 (1995)
S. Saito, O. Nilsson, Y. Yamamoto, Oscillation center frequency tuning, quantum FM noise, and direct frequency characteristics in external grating loaded semiconductor lasers. IEEE J. Quant. Electron. 18, 6 (1982)
H. Nishimori, G. Ortiz, Elements of Phase Transitions and Critical Phenomena (Oxford University Press, Oxford, 2011)
J.A. Acebrón, L.L. Bonilla, C.J.P. Vicente, F. Ritort, R. Spigler, Rev. Mod. Phys. 77, 137 (2005)
A. Gordon, B. Fischer, Phys. Rev. Lett. 89, 103901 (2002)
H. Risken, The Fokker-Planck Equation, 2nd edn. (Springer, Berlin, 1989)
M. Nixon, E. Ronen, A.A. Friedman, N. Davidson, Phys. Rev. Lett. 110, 184192 (2013)
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Utsunomiya, S., Wen, K., Takata, K., Tamate, S., Yamamoto, Y. (2016). Coherent Computing with Injection-Locked Laser Network. In: Yamamoto, Y., Semba, K. (eds) Principles and Methods of Quantum Information Technologies. Lecture Notes in Physics, vol 911. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55756-2_10
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