Abstract
Quantum technology based on photons has emerged as one of the most promising platforms for quantum information processing, having already been used in proof-of-principle demonstrations of quantum communication and quantum computation. However, the scalability of this technology depends on the successful integration of experimentally feasible devices in an architecture that tolerates realistic errors and imperfections. Here, we analyse an atom-optical architecture for quantum computation designed to meet the requirements of scalability. The architecture is based on a modular atom-cavity device that provides an effective photon-photon interaction, allowing for the rapid, deterministic preparation of a large class of entangled states. We begin our analysis at the physical level, where we outline the experimental cavity quantum electrodynamics requirements of the basic device. Then, we describe how a scalable network of these devices can be used to prepare a three-dimensional topological cluster state, sufficient for universal fault-tolerant quantum computation. We conclude at the application level, where we estimate the system-level requirements of the architecture executing an algorithm compiled for compatibility with the topological cluster state.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
ARDA, Quantum information science and technology roadmap project (2004), http://qist.lanl.gov
R. Barends, J. Kelly, A. Megrant, A. Veitia, D. Sank, E. Jeffrey, T. White, J. Mutus, A. Fowler, B. Campbell, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, C. Neill, P. O‘Malley, P. Roushan, A. Vainsencher, J. Wenner, A. Korotkov, A. Cleland, J. Martinis, Logic gates at the surface code threshold: superconducting qubits poised for fault-tolerant quantum computing. Nature 508, 500–503 (2014)
S. Barrett, T. Stace, Fault tolerant quantum computation with very high threshold for loss errors. Phys. Rev. Lett. 105, 200,502 (2010)
J. Benhelm, G. Kirchmair, C. Roos, R. Blatt, Towards fault-tolerant quantum computing with trapped ions. Nat. Phys. 4, 463 (2008)
C. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, W. Wooters, Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70, 1895 (1993)
B.B. Blinov, D.L. Moehring, L.M. Duan, C. Monroe, Observation of entanglement between a single trapped atom and a single photon. Nature 428(6979), 153–157 (2004). http://dx.doi.org/10.1038/nature02377
H. Bombin, M. Martin-Delgato, Topological quantum distillation. Phys. Rev. Lett. 97, 180,501 (2006)
H. Bombin, M. Martin-Delgato, Topological computation without braiding. Phys. Rev. Lett. 98, 160,502 (2007)
S. Bravyi, A. Kitaev, Quantum codes on a lattice with boundary (1998). quant-ph/9811052
S. Bravyi, A. Kitaev, Universal quantum computation with ideal clifford gates and noisy ancillas. Phys. Rev. A 71, 022,316 (2005)
J. Cirac, P. Zoller, Quantum computations with cold trapped ions. Phys. Rev. Lett. 74, 4091 (1995)
D. Cory, A. Fahmy, T. Havel, Ensemble quantum computing by NMR spectroscopy. Proc. Natl. Acad. Sci. 94, 1634–1639 (1997)
E. Dennis, A. Kitaev, A. Landahl, J. Preskill, Topological quantum memory. J. Math. Phys. 43, 4452 (2002)
D. Deutsch, Quantum computational networks. Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci. 425, 73 (1989)
S. Devitt, K. Nemoto, Programming a topological quantum computer, in 2012 IEEE 21st Asian Test Symposium (ATS), Niigatta (2012), pp. 55–60
S. Devitt, A. Greentree, R. Ionicioiu, J. O’Brien, W. Munro, L. Hollenberg, The photonic module: an on-demand resource for photonic entanglement. Phys. Rev. A 76, 052312 (2007)
S. Devitt, A. Fowler, A. Stephens, A. Greentree, L. Hollenberg, W. Munro, K. Nemoto, Architectural design for a topological cluster state quantum computer. New. J. Phys. 11, 083,032 (2009)
S. Devitt, A. Stephens, W. Munro, K. Nemoto, Integration of highly probabilistic sources into optical quantum architectures: perpetual quantum computation. New J. Phys. 13, 095,001 (2011)
S. Devitt, W. Munro, K. Nemoto, Quantum error correction for beginners. Rep. Prog. Phys. 76, 076,001 (2013)
S. Devitt, A. Stephens, W. Munro, K. Nemoto, Requirements for fault-tolerant factoring on an atom-optics quantum computer. Nat. Commun. 4, 2524 (2013)
D. DiVincenzo, Topics in quantum computers. in Mesoscopic Electron Transport, ed. by L. Kowenhoven, G. Schon, L. Sohn. NATO ASI Series E (Kluwer Academic, Dordrecht, 1997)
D. DiVincenzo, The physical implementation of quantum computation. Fortschr. Phys. 48, 771 (2000)
J. Dowling, G. Milburn, Quantum technology: the second quantum revolution (2002). quant-ph/0206091
G. Duclos-Cianci, D. Poulin, Fault-tolerant renormalization group decoded for Abelian topological codes. Quantum Inf. Comput. 14, 0721 (2014)
J. Edmonds, Paths, trees, and flowers. Can. J. Math. 17, 449 (1965)
A. Ekert, Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661 (1991)
R. Feynman, Simulating physics with computers. Int. J. Theor. Phys. 21, 467 (1982)
A. Fowler, Low overhead surface code logical H. Quantum Inf. Comput. 12, 970 (2012)
A. Fowler, S. Devitt, A bridge to lower overhead quantum computation (2012). arXiv:1209.0510
A. Fowler, K. Goyal, Topological cluster state quantum computing. Quantum Inf. Comput. 9, 721 (2009)
A. Fowler, S. Devitt, L. Hollenberg, Implementation of Shor’s algorithm on a linear nearest neighbour qubit array. Quantum Inf. Comput. 4, 237–251 (2004)
A. Fowler, A. Stephens, P. Groszkowski, High threshold universal quantum computation on the surface code. Phys. Rev. A 80, 052,312 (2009)
A. Fowler, M. Mariantoni, J. Martinis, A. Cleland, Surface codes: towards practical large-scale quantum computation. Phys. Rev. A 86, 032,324 (2012)
A. Fowler, S. Devitt, C. Jones, Surface code implementation of block code state distillation. Sci. Rep. 3, 1939 (2013)
M. Freedman, D.A. Meyer, Projective plane and planar quantum codes. Found. Comput. Math. 1, 325 (2001)
C.W. Gardiner, P. Zoller, Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics. Springer Series in Synergetics (Springer, Berlin/Heidelberg, 2004)
C. Gerry, P.L. Knight, Introductory Quantum Optics (Cambridge University Press, Cambridge, 2004)
N. Gershenfeld, I. Chuang, Bulk spin resonance quantum computing. Science 275, 350 (1997)
B. Giles, P. Selinger, Exact synthesis of multiqubit Clifford+T circuits. Phys. Rev. A 87, 032,332 (2013)
N. Gisin, G. Ribordy, W. Tittel, H. Zbinden, Quantum cryptography. Rev. Mod. Phys. 74, 145 (2002)
L. Grover, Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79, 325 (1997)
T. Harty, D. Allcock, C. Ballance, L. Guidoni, H. Janacek, N. Linke, D. Stacey, D. Lucas, High-fidelity preparation, gates, memory and readout of a trapped-ion quantum bit (2014). arXiv:1403.1524
C.K. Hong, Z.Y. Ou, L. Mandel, Measurement of subpicosecond time intervals between two photons by interference. Phys. Rev. Lett. 59(18), 2044–2046 (1987)
C. Hu, A. Young, J. O’Brien, W. Munro, J. Rarity, Giant optical Faraday rotation induced by a single-electron spin in a quantum dot: applications to entangling remote spins via a single photon. Phys. Rev. B 78, 085,307 (2008)
C. Hu, W. Munro, J. O’Brien, J. Rarity, Proposed entanglement beam splitter using a quantum-dot spin in a double-sided optical microcavity. Phys. Rev. B 80, 025,326 (2009)
N.C. Jones, R.V. Meter, A. Fowler, P. McMahon, J. Kim, T. Ladd, Y. Yamamoto, A layered architecture for quantum computing using quantum dots. Phys. Rev. X 2, 031,007 (2012)
B. Kane, A silicon-based nuclear spin quantum computer. Nature (London) 393, 133 (1998)
A. Kitaev, Quantum computations: algorithms and error correction. Russ. Math. Serv. 52, 1191 (1997)
A. Kitaev, Fault-tolerant quantum computation by anyons. Ann. Phys. 303, 2 (2003)
T. Kleinjung, K. Aoki, J. Franke, A.K. Lenstra, E. Thomé, J.W. Bos, P. Gaudry, A. Kruppa, P.L. Montgomery, D.A. Osvik, H. te Riele, A. Timofeev, P. Zimmermann, Factorization of a 768-bit RSA modulus, in Advances in Cryptology – CRYPTO 2010, ed. by T. Rabin. IACR International Association for Cryptologic Research (Springer, Berlin, 2010), pp. 333–350
V. Kliuchnikov, D. Maslov, M. Mosca, Asymptotically optimal approximation of single qubit unitaries by Clifford and T circuits using a constant number of ancillary qubits. Phys. Rev. Lett. 110, 190,502 (2013)
E. Knill, R. Laflamme, G. Milburn, A scheme for efficient quantum computation with linear optics. Nature (London) 409, 46 (2001)
V. Kolmogorov, Blossom V: a new implementation of a minimum cost perfect matching algorithm. Math. Program. Comput. 1, 43 (2009)
H.K. Lo, S. Popescu, T. Spiller (eds.), Introduction To Quantum Computation and Information (World Scientific, Singapore, 1998)
C. Lorenz, R. Ziff, Precise determination of the bond percolation thresholds and finite-size scaling corrections for the sc, fcc, and bcc lattices. Phys. Rev. E. 57, 230 (1998)
D. Loss, D. DiVincenzo, Quantum computation with quantum dots. Phys. Rev. A 57, 120 (1998)
R.V. Meter, T. Ladd, A. Fowler, Y. Yamamoto, Distributed quantum computation architecture using semiconductor nanophotonics. Int. J. Quantum Inf. 8, 295 (2010)
C. Monroe, R. Raussendorf, A. Ruthven, K. Brown, P. Maunz, L.M. Duan, J. Kim, Large scale modular quantum computer architecture with atomic memory and photonic interconnects. Phys. Rev. A 89, 022,317 (2014)
J. Mooij, T. Orlando, L. Levitov, L. Tian, C. van der Wal, S. Lloyd, Josephson persistent-current qubit. Science 285, 1096–1039 (1999)
Y. Nakamura, Y.A. Pashkin, J. Tsai, Coherent control of macroscopic quantum states in a cooper-pair box. Nature (London) 398, 786 (1999)
K. Nemoto, M. Trupke, S. Devitt, A. Stephens, K. Buczak, T. Nobauer, M. Everitt, J. Schmiedmayer, W. Munro, Photonic architecture for scalable quantum information processing in NV-diamond. arXiv:1309.4277 (2013)
M. Nielsen, Optical quantum computation using cluster states. Phys. Rev. Lett. 93, 040,503 (2004)
M. Nielsen, I. Chuang, Quantum Computation and Information, 2nd edn. (Cambridge University Press, Cambridge/New York, 2000)
T. Ohno, G. Arakawa, I. Ichinose, T. Matsui, Phase structure of the random-plaquette image gauge model: accuracy threshold for a toric quantum memory. Nucl. Phys. B 697, 462 (2004)
A. Paetznick, A. Fowler, Quantum circuit optimization by topological compaction in the surface code (2013). arXiv:1304.2807
S.J.D. Phoenix, P.L. Knight, Establishment of an entangled atom-field state in the jaynes-cummings model. Phys. Rev. A 44, 6023–6029 (1991). doi:10.1103/PhysRevA.44.6023. http://link.aps.org/doi/10.1103/PhysRevA.44.6023
R. Raussendorf, H.J. Briegel, A one way quantum computer. Phys. Rev. Lett. 86, 5188 (2001)
R. Raussendorf, J. Harrington, Fault-tolerant quantum computation with high threshold in two dimensions. Phys. Rev. Lett. 98, 190,504 (2007)
R. Raussendorf, J. Harrington, K. Goyal, A fault-tolerant one way quantum computer. Ann. Phys. 321, 2242 (2006)
R. Raussendorf, J. Harrington, K. Goyal, Topological fault-tolerance in cluster state quantum computation. New J. Phys. 9, 199 (2007)
N. Ross, P. Selinger, Optimal ancilla-free Clifford+T approximation of z-rotations (2014). arXiv:1403.2975
C. Ryan, M. Laforest, R. Laflamme, Randomized benchmarking of single-and multi-qubit control in liquid-state NMR quantum information processing. New J. Phys. 11, 013,034 (2009)
C. Santori, D. Fattal, Y. Yamamoto, Single-Photon Devices and Applications (Whiley-VCH, Weinheim, 2010)
P. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Sci. Statist. Comput. 26, 1484 (1997)
T. Spiller, W. Munro, Towards a quantum information technology industry. J. Phys.: Condens. Matter 18, 1–10 (2006)
T. Spiller, W. Munro, S. Barrett, P. Kok, An introduction to quantum information processing: applications and realizations. Contemp. Phys. 46, 407 (2005)
T.P. Spiller, K. Nemoto, S.L. Braunstein, W. Munro, P. van Loock, G.J. Milburn, Quantum computation by communication. New J. Phys. 8, 30 (2006)
A. Stephens, Fault-tolerant thresholds for quantum error correction with the surface code. Phys. Rev. A 89, 022,321 (2014)
A. Stephens, Z. Evans, S. Devitt, A. Greentree, A. Fowler, W. Munro, J. O’Brien, K. Nemoto, L. Hollenberg, Deterministic optical quantum computer using photonic modules. Phys. Rev. A 78, 032,318 (2008)
A. Stephens, W. Munro, K. Nemoto, High-threshold topological quantum error correction against biased noise. Phys. Rev. A 88, 060,301(R) (2013)
R. Stock, D. James, A scalable, high-speed measurement based quantum computer using trapped ions. Phys. Rev. Lett. 102, 170,501 (2009)
E. Togan, Y. Chu, A.S. Trifonov, L. Jiang, J. Maze, L. Childress, M.V.G. Dutt, A.S. Sorensen, P.R. Hemmer, A.S. Zibrov, M.D. Lukin, Quantum entanglement between an optical photon and a solid-state spin qubit. Nature 466(7307), 730–734 (2010). http://dx.doi.org/10.1038/nature09256
E. Waks, J. Vuckovic, Dipole induced transparency in drop-filter cavity-waveguide systems. Phys. Rev. Lett. 96, 153,601 (2006)
D. Walls, G. Milburn, Quantum Optics (Springer, Berlin, 1994)
C. Wang, J. Harrington, J. Preskill, Confinement-Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory. Ann. Phys. 303, 31 (2003)
D. Wang, A. Fowler, A. Stephens, L. Hollenberg, Threshold error rates for the toric and surface codes. Quantum Inf. Comput. 10, 456 (2010)
T. Wilk, S.C. Webster, A. Kuhn, G. Rempe, Single-atom single-photon quantum interface. Science 317(5837), 488–490 (2007). doi:10.1126/science.1143835. http://www.sciencemag.org/content/317/5837/488.abstract
N. Yao, L. Jiang, A. Gorshkov, P. Maurer, G. Giedke, J. Cirac, M. Lukin, Scalable architecture for a room temperature solid-state quantum information processor. Nat. Commun. 3, 800 (2012)
A. Young, C. Hu, L. Marseglia, J. Harrington, J. O’Brien, J. Rarity, Deterministic photon entangler using a charged quantum dot inside a microcavity. Phys. Rev. B 78, 125,318 (2008)
S.B. Zheng, G.C. Guo, Efficient scheme for two-atom entanglement and quantum information processing in cavity qed. Phys. Rev. Lett. 85, 2392–2395 (2000). doi:10.1103/PhysRevLett.85.2392. http://link.aps.org/doi/10.1103/PhysRevLett.85.2392
Acknowledgements
This work was supported by the Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST Program), a Scientific Research of Specially Promoted Research (grant no.18001002) by MEXT and a Quantum Cybernetics grant.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer Japan
About this chapter
Cite this chapter
Devitt, S.J., Stephens, A.M., Munro, W.J., Nemoto, K. (2016). Analysis of an Atom-Optical Architecture for Quantum Computation. 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_19
Download citation
DOI: https://doi.org/10.1007/978-4-431-55756-2_19
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-55755-5
Online ISBN: 978-4-431-55756-2
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)