Abstract
Distributed quantum computation requires quantum operations to act on logical qubits over a distance. We will develop a formal model for the telegate-based distributive quantum computation. We show that a controlled-controlled-NOT (Toffoli) gate as an elementary gate of the universal quantum computation may be remotely implemented by exploring a high-level quantum system. These remote Toffoli gates cost at most two Einstein-Podolsky-Rosen (EPR) pairs, whereas four or six EPR pairs are required from the teleportation-based quantum computation or the remote CNOT gate, respectively. Thus, the previous Toffoli gate-based circuit synthesis may be used as an elementary subroutine of this distributed quantum computation.
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Feynman, R.: Simulating physics with computers. Int. J. Theoret. Phys. 21(6), 467–488 (1982)
Deutsch, D.: Quantum theory, the Church-Turing principle and the universal quantum computer. Proc. R. Soc. A 400(1818), 97–117 (1985)
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000). pp. 216–271
Barreiro, J.T., Langford, N.K., Peters, N.A., Kwiat, P.G.: Generation of hyperentangled photon pairs. Phys. Rev. Lett. 95, 260501 (2005)
Wang, X.L., et al.: Quantum teleportation of multiple degrees of freedom of a single photon. Nature 518(7540), 516–519 (2015)
Luo, M.X., Wang, X.: Parallel photonic quantum computation assisted by quantum dots in one-side optical microcavities. Sci. Rep. 4, 5732 (2014)
Deutsch, D., Jozsa, R.: Rapid solution of problems by quantum computation. Proc. R. Soc. A 439(1907), 553–558 (1992)
Simon, D.R.: On the power of quantum computation. SIAM J. Comput. 26(5), 116–123 (1997)
Grover, L.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79(2), 325–328 (1997)
Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26(5), 1484–1509 (1997)
Murphy, B., Brent, R.P.: On quadratic polynomials for the number field sieve. Aust. Comput. Sci. Commun. 20, 199–213 (1998)
Rivest, R., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public-key cryptosystems. Commun. ACM 21(6), 120–126 (1978)
Farhi, E., et al.: A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem. Science 292(5516), 472–475 (2001)
Lloyd, S., Mohseni, M., Rebentrost, P.: Quantum principal component analysis. Nat. Phys. 10, 631–633 (2014)
Bishop, C.M.: Pattern Recognition and Machine Learning. Springer, Berlin (2006). pp. 130–211
Gu, B., Sheng, V.S., Wang, Z., Ho, D., Osman, S., Li, S.: Incremental learning for v-support vector regression. Neural Netw. 67, 140–150 (2015)
Chen, B., Shu, H., Coatrieux, G., Chen, G., Sun, X., Coatrieux, J.-L.: Color image analysis by quaternion-type moments. J. Math. Imaging Vis. 51(1), 124–144 (2015)
Xia, Z., Wang, X., Sun, X., Wang, B.: Steganalysis of least significant bit matching using multi-order differences. Sec. Commun. Netw. 7(8), 1283–1291 (2014)
Regev, O.: Quantum computation and lattice problems. SIAM J. Comput. 33(3), 738–760 (2004)
Kuperberg, G.: A subexponential-time quantum algorithm for the dihedral hidden subgroup problem. SIAM J. Comput. 35(1), 170–188 (2005)
Barenco, A., et al.: Elementary gates for quantum computation. Phys. Rev. A 52, 34–57 (1995)
Nielsen, M.A., Dowling, M.R., Gu, M., Doherty, A.C.: Quantum computation as geometry. Science 311, 1133–1135 (2006)
Radhakrishnan, J., Rotteler, M., Sen, P.: Random measurement bases, quantum state distinction and applications to the hidden subgroup problem. Algorithmica 55, 490–516 (2006)
Kawachi, A., Koshiba, T., Nishimura, H., Yamakami, T.: Computational indistinguishability between quantum states and its cryptographic application. J. Cryptol. 25, 528–555 (2009)
Chuang, I.L., Vandersypen, L.M.K., Zhou, X., Leung, D.W., Lloyd, S.: Experimental realization of a quantum algorithm. Nature 393, 143–146 (1998)
Jones, J.A., Mosca, M., Hansen, R.H.: Implementation of a quantum search algorithm on a quantum computer. Nature 393, 344–346 (1998)
Vandersypen, L.M.K., et al.: Experimental realization of Shor’s quantum factoring algorithm using nuclear magnetic resonance. Nature 414, 883–887 (2001)
Lucero, E., et al.: Computing prime factors with a Josephson phase qubit quantum processor. Nat. Phys. 8, 719–723 (2012)
Feng, G., Xu, G., Long, G.: Experimental realization of nonadiabatic holonomic quantum computation. Phys. Rev. Lett. 110, 190501 (2013)
Tame, M.S., Bell, B.A., Di Franco, C., Wadsworth, W.J., Rarity, J.G.: Experimental realization of a one-way quantum computer algorithm solving Simon’s problem. Phys. Rev. Lett. 113, 200501 (2014)
Sun, C.P., Li, Y., Liu, X.F.: Quasi-spin-wave quantum memories with a dynamical symmetry. Phys. Rev. Lett. 91, 147903 (2003)
Simon, J., Haruka, T., Ghosh, S., Vuleti, V.: Single-photon bus connecting spin-wave quantum memories. Nat. Phys. 3, 765–769 (2007)
Reim, K.F., et al.: Towards high-speed optical quantum memories. Nat. Photon. 4, 218–221 (2010)
Diniz, I., et al.: Strongly coupling a cavity to inhomogeneous ensembles of emitters: potential for long-lived solid-state quantum memories. Phys. Rev. A 84, 063810 (2011)
George, C., Dollimore, J., Kindberg, T., Blair, G.: Distributed Systems: Concepts and Design. Addison-Wesley, Reading (2011). pp. 230–312
Gottesman, D., Chuang, I.L.: Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations. Nature 402, 390–393 (1999)
Cirac, J.I., Ekert, A., Huelga, S.F., Macchiavello, C.: Distributed quantum computation over noisy channels. Phys. Rev. A 59, 42–49 (1999)
Meter, R.V., Munro, W.J., Nemoto, K., Itoh, K.M.: Arithmetic on a distributed-memory quantum multicomputer. ACM J. Emerg. Tech. Comput. Syst. 3, 1–23 (2008)
Spiller, T.P., et al.: Quantum computation by communication. New J. Phys. 8, 30 (2006)
Danos, V., D’Hondt, E., Kashefi, E., Panangaden, P.: Distributed measurement-based quantum computation. Elect. Notes Theoret. Comput. Sci. 170, 73–94 (2007)
Love, P.J., Boghosian, B.M.: Type II quantum algorithms. Phys. A 362(1), 210–214 (2006)
Yimsiriwattana, A., Lomonaco Jr., S.J.: Distributed quantum computing: a distributed Shor algorithm (2004). arXiv:quant-ph/0403146
Huang, Y.F., Ren, X.F., Zhang, Y.S., Duan, L.M., Guo, G.C.: Experimental teleportation of a quantum controlled-NOT gate. Phys. Rev. Lett. 93, 240501 (2004)
Meter, R.V., Nemoto, K., Munro, W.: Communication links for distributed quantum computation. IEEE Trans. Comput. 56(12), 1643–1653 (2007)
Ying, M., Feng, Y.: An algebraic language for distributed quantum computing. IEEE Trans. Comput. 58(6), 728–743 (2009)
Wang, H.F., Zhu, A.D., Zhang, S., Yeon, K.H.: Optically controlled phase gate and teleportation of a controlled-NOT gate for spin qubits in quantum dot-microcavity coupled system. Phys. Rev. A 87, 062337 (2013)
Luo, M.X., Li, H.R., Wang, X.: Teleportation of a controlled-Not gate for photon and electron-spin qubits assisted by the nitrogen-vacancy center. Quantum Inf. Comput. 15(15), 1397–1419 (2015)
Luo, M.X., Wang, X.: Universal remote quantum computation assisted by the cavity input-output process. Proc. R. Soc. A 471(2184), 20150274 (2015)
Bennett, C.H., et al.: Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70, 1895 (1993)
Toffoli, T.: Reversible computing. In: de Bakker, J., van Leeuwen, J. (eds.) Automata, Languages and Programming. LNCS, vol. 85, pp. 632–644. Springer, Berlin (2005)
Shor, P.W.: Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52, R2493(R) (1995)
Calderbank, A., Rains, E., Shor, P.W., Sloane, N.: Quantum error correction via codes over GF(4). IEEE Trans. Inf. Theor. 44, 1369–1387 (1998)
Calderbank, A.R., Shor, P.W.: Good quantum error-correcting codes exist. Phys. Rev. A 54, 1098–1105 (1996)
Knill, E., Laflamme, R., Martinez, R., Negrevergne, C.: Benchmarking quantum computers: the five-qubit error correcting code. Phys. Rev. Lett. 86, 5811–5814 (2001)
Steane, A.M.: Error correcting codes in quantum theory. Phys. Rev. Lett. 77, 793–797 (1996)
Shi, Y.: Both Toffoli and controlled-NOT need little help to do universal quantum computation. Quantum Inf. Comput. 3(1), 84–92 (2003)
Yu, N., Duan, R., Ying, R.: Five two-qubit gates are necessary for implementing the Toffoli gate. Phys. Rev. A 88, 010304(R) (2013)
Lanyon, B.P., et al.: Simplifying quantum logic using higher-dimensional Hilbert spaces. Nat. Phys. 5, 134–140 (2008)
Luo, M.X., Ma, S.Y., Chen, X.B., Wang, X.: Hybrid Toffoli gate on photons and quantum spins. Sci. Rep. 5, 16716 (2015)
Acknowledgements
This work is supported by the National Natural Science Foundation of China (No. 61303039), Chuying Fellowship, CSC Fund, and Open Foundation of China-USA Computer Science Research Center (Nanjing University of Information Science and Technology) (No. KJR16132).
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Luo, MX., Li, HR. (2016). Distributed Quantum Computation Assisted by Remote Toffoli Gate. In: Sun, X., Liu, A., Chao, HC., Bertino, E. (eds) Cloud Computing and Security. ICCCS 2016. Lecture Notes in Computer Science(), vol 10039. Springer, Cham. https://doi.org/10.1007/978-3-319-48671-0_42
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DOI: https://doi.org/10.1007/978-3-319-48671-0_42
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