Quantum Computing Using Optics
Definition of the Subject
Quantum computation is a new approach to information processing based on physical devices that operate according to the quantum principles ofsuperposition and unitary evolution [5,9]. This enablesmore efficient algorithms than are available for a computer operating according to classical principles, the most significant of which is Shor'sefficient algorithm for finding the prime factors of a large integer [51]. There is no knownefficient algorithm for this task on conventional computing hardware.
Optical implementations of quantum computing have largely focused on encoding quantum information using single photon states of light. For example,a single photon could be excited to one of two carefully defined orthogonal mode functions of the field with different momentum directions. However,as optical photons do not interact with each other directly, physical devices that enable one encoded bit of information to unitarily change another arehard to implement. In...
Bibliography
- 1.Beckman D, Chari AN, Devabhaktuni S, Preskill J (1996) Phys RevA 54:1034MathSciNetADSGoogle Scholar
- 2.Braunstein SL et al (1999) Phys Rev Lett 83:1054MathSciNetADSGoogle Scholar
- 3.Cleve R, Ekert A, Henderson L, Macchiavello C, Mosca M (1999) On quantumalgorithms. LANL quant-ph/9903061Google Scholar
- 4.Darquie B, Jones MPA, Dingjan J, Beugnon J, Bergamini S, Sortais Y, Messin G,Browaeys A, Grangier P (2005) Science 309:454ADSGoogle Scholar
- 5.Deutsch D (1985) Quantum‐theory, the Church–Turing principle and theuniversal quantum computer. Proc R Soc Lond A 400:97–117MathSciNetADSMATHGoogle Scholar
- 6.Duan L-M, Lukin MD, Cirac JI, Zoller P (2001) Nature414:413ADSGoogle Scholar
- 7.Einstein A (1905) On a Heuristic Point of View about the Creation andConversion of Light? Ann Physik 17:132ADSMATHGoogle Scholar
- 8.Eisaman MD, Fleischhauer M, Lukin MD, Zibrov AS (2006) Toward quantum control ofsingle photons. Opt Photonics News 17:22–27ADSGoogle Scholar
- 9.Feynman RP (1982) Simulating physics with computers. Int J Theor Phys21:467MathSciNetGoogle Scholar
- 10.Gasparoni S et al (2004) Phys Rev Lett 93:020504ADSGoogle Scholar
- 11.Gilchrist A, Langford NK, Nielsen MA (2005) Distance measures to compare realand ideal quantum processes. Phys Rev A 71:062310ADSGoogle Scholar
- 12.Gottesman D, Chuang IL (1999) Demonstrating the viability of universal quantumcomputation using teleportation and single‐qubit operations. Nature 402:390–393ADSGoogle Scholar
- 13.Hennrich M, Legero T, Kuhn A, Rempe G (2004) Photon statistics ofa non‐stationary periodically driven single‐photon source. New J Phys 6:86Google Scholar
- 14.Hofmann H, Takeuchi S (2002) Phys RevA 66:024308ADSGoogle Scholar
- 15.Hong CK, Ou ZY, Mandel L (1987) Measurement of subpicosecond time intervalsbetween two photons by interference. Phys Rev Lett 59:2044ADSGoogle Scholar
- 16.Hutchinson GD, Milburn GJ (2004) Nonlinear quantum optical computing viameasurement. J Modern Opt 51:1211–1222MathSciNetADSMATHGoogle Scholar
- 17.James DFV, Kwiat PG, Munro WJ, White AG (2001) Measurement of qubits. Phys RevA 64:052312ADSGoogle Scholar
- 18.Jiang L, Taylor JM, Khaneja N, Lukin MD (2007) Optimal approach to quantumcommunication using dynamic programming. arXiv:quant-ph/0710.5808
- 19.Keller M, Lange B, Hayasaka K, Lange W, Walther H (2003) Continuous generationof single photons with controlled waveform in an ion-trap cavity system. Nature 431:1075ADSGoogle Scholar
- 20.Kieling K, Rudolph T, Eisert J (2007) Percolation, renormalization, and quantumcomputing with nondeterministic gates. Phys Rev Lett 99:130501MathSciNetADSGoogle Scholar
- 21.Kiesel N, Schmid C, Weber U, Ursin R, Weinfurter H (2007) Phys Rev Lett99:250505Google Scholar
- 22.Knill E (2002) Phys Rev A 66:052306MathSciNetADSGoogle Scholar
- 23.Knill E (2005) Quantum computing with realistically noisy devices. Nature434:39–44ADSGoogle Scholar
- 24.Knill E, Laflamme R, Milburn GJ (2001) Efficient linear optical quantumcomputation. Nature 409:46ADSGoogle Scholar
- 25.Kok P, Lee H, Dowling JP (2002) Phys RevA 66:063814ADSGoogle Scholar
- 26.Kok P, Munro WJ, Nemoto K, Ralph TC, Dowling JP, Milburn GJ (2007) Linearoptical quantum computing. Rev Mod Phys 79:135ADSGoogle Scholar
- 27.Langford NK, Weinhold TJ, Prevedel R, Gilchrist A, O'Brien JL, Pryde GJ, WhiteAG (2005) Phys Rev Lett 95:210504ADSGoogle Scholar
- 28.Lanyon BP, Barbieri M, Almeida MP, Jennewein T, Ralph TC, Resch KJ, Pryde G,O'Brien JL, Gilchrist A, White AG (2007) Quantum computing using shortcuts through higher dimensions. appear in Nat PhysGoogle Scholar
- 29.Lanyon BP, Weinhold TJ, Langford NK, Barbieri M, James DFV, Gilchrist A, WhiteAG (2007) Phys Rev Lett 99:250505ADSGoogle Scholar
- 30.Lu C-Y, Browne DE, Yang T, Pan J-W (2007) Phys Rev Lett99:250504ADSGoogle Scholar
- 31.Lu C-Y, Zhou X-Q, Gühne O, Gao W-B, Zhang J, Yuan Z-S, Goebel A, Yang T, Pan J-W(2007) Experimental entanglement of six photons in graph states. Nature Phys 3:91Google Scholar
- 32.Menicucci NC et al (2002) Phys Rev Lett 88:167901ADSGoogle Scholar
- 33.Migdall A et al (2002) Phys RevA 66:053805ADSGoogle Scholar
- 34.Milburn GJ (1989) A quantum optical fredkin gate. Phys Rev Lett62:2124–2127ADSGoogle Scholar
- 35.Mishina OS, Kupriyanov DV, Muller JH, Polzik ES (2007) Spectral theory ofquantum memory and entanglement via Raman scattering of light by an atomic ensemble. Phys Rev A 75:042326ADSGoogle Scholar
- 36.Neergaard‐Nielsen JS, Melholt Nielsen B, Takahashi H, Vistnes AI, PolzikES (2007) High purity bright single photon source. Opt Express 15:7940Google Scholar
- 37.Nielsen MA (2004) Optical quantum computation using cluster states. Phys RevLett 93:040503ADSGoogle Scholar
- 38.O'Brien JL et al (2004) Phys Rev Lett 93:080502ADSGoogle Scholar
- 39.O'Brien JL, Pryde GJ, White AG, Ralph TC Branning D(2003) Demonstration of an all‐optical quantum controlled‐NOT gate. Nature 426:264ADSGoogle Scholar
- 40.Okamoto R, Hofmann HF, Takeuchi S, Sasaki K (2007) Phys Rev Lett99:250506Google Scholar
- 41.Pittman TB, Jacobs BC, Franson JD (2001) Probabilistic quantum logic operationsusing polarizing beam splitters. Phys Rev A 64:062311ADSGoogle Scholar
- 42.Pittman TB, Jacobs BC, Franson JD (2002) Phys Rev Lett88:257902ADSGoogle Scholar
- 43.Pittman TB, Fitch MJ, Jacobs BC, Franson JD (2003) Experimentalcontrolled‐NOT logic gate for single photons in the coincidence basis. Phys Rev A 68:032316ADSGoogle Scholar
- 44.Popescu S (2006) KLM quantum computation as a measurement basedcomputation. arXiv:quant-ph/0610025
- 45.Prevedel R et al (2007) Nature 445:65ADSGoogle Scholar
- 46.Ralph TC, White AG, Munro WJ, Milburn GJ (2001) Simple scheme for efficientlinear optics quantum gates. Phys Rev A 65:012314ADSGoogle Scholar
- 47.Ralph TC, Langford NK, Bell TB, White AG (2002) Linear opticalcontrolled‐NOT gate in the coincidence basis. Phys Rev A 65:062324ADSGoogle Scholar
- 48.Raussendorf R, Briegel HJ (2001) A one-way quantum computer. Phys Rev Lett86:5188ADSGoogle Scholar
- 49.Rhode PP, Ralph TC (2005) Phys Rev A 71:032320ADSGoogle Scholar
- 50.Sangouard N, Simon C, Minar J, Zbinden H, de Riedmatten H, Gisin N (2007)Long‐distance entanglement distribution with single‐photon sources. arXiv:quant-ph/0706.1924v1
- 51.Shor P (1994) Algorithms for quantum computation: Discrete logarithms andfactoring. Proc 35th annual symposium on foundations of computer science. See also LANL preprint quant-ph/9508027Google Scholar
- 52.Simon C et al (2007) Phys Rev Lett 98:190503ADSGoogle Scholar
- 53.Special Issue on Single photon Sources (2004) Single photon Sources51(9–10)Google Scholar
- 54.U'Ren AB, Mukamel E, Banaszek K, Walmsley IA (2003) Phil Trans Roy SocA 361:1471Google Scholar
- 55.Van Meter R, Ladd TD, Munro WJ, Nemoto K (2007) System Design fora Long-Line Quantum Repeater. arXiv:quant-ph/0705.4128v1
- 56.Vandersypen LMK et al (2001) Nature 414:883ADSGoogle Scholar
- 57.Walls DF, Milburn GJ (2008) Quantum Optics, 2nd edn. Springer, BerlinMATHGoogle Scholar
- 58.Walther P, Resch KJ, Rudolph T, Schenck E, Weinfurter H, Vedral V, Aspelmeyer M,Zeilinger A (2005) Experimental one-way quantum computing. Nature 434:169ADSGoogle Scholar
- 59.Weinhold TJ, Gilchrist A, Resch KJ, Doherty AC, O'Brien JL, Pryde GJ, White AG (2008) Understanding photonic quantum-logic gates: The road to fault tolerance. arxiv 0808.0794Google Scholar
- 60.White AG et al (2007) Measuring two-qubit gates. J Opt Soc Am B24:172–183ADSGoogle Scholar
- 61.Yamamoto Y, Kitagawa M, Igeta K (1988) Proc 3rd Asia‐Pacific phys conf779. World Scientific, SingaporeGoogle Scholar