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Journal of Mathematical Physics / Volume 51 / Issue 6 / ARTICLES / Quantum Information and Computation

J. Math. Phys. 51, 062201 (2010); http://dx.doi.org/10.1063/1.3384661 (21 pages)

Fast universal quantum computation with railroad-switch local Hamiltonians

Daniel Nagaj

Research Center for Quantum Information, Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, 845 11 Bratislava, Slovakia

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(Received 6 October 2009; accepted 16 March 2010; published online 2 June 2010)

We present two universal models of quantum computation with a time-independent, frustration-free Hamiltonian. The first construction uses 3-local (qubit) projectors and the second one requires only 2-local qubit-qutrit projectors. We build on Feynman’s Hamiltonian computer idea [ R. Feynman, Optics News 11, 11 (1985) ] and use a railroad-switch-type clock register. The resources required to simulate a quantum circuit with L gates in this model are O(L) small-dimensional quantum systems (qubits or qutrits), a time-independent Hamiltonian composed of O(L) local, constant norm, projector terms, the possibility to prepare computational basis product states, a running time O(L log2 L), and the possibility to measure a few qubits in the computational basis. Our models also give a simplified proof of the universality of 3-local adiabatic quantum computation.

© 2010 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. FEYNMAN’S COMPUTER AND CLOCK CONSTRUCTIONS
    1. Implementing the clock register
  3. THE RAILROAD SWITCH: A 3-LOCAL GADGET
    1. The dynamics of our model
  4. THE SECOND MODEL: A UNIVERSAL 2-LOCAL QUBIT-QUTRIT HAMILTONIAN
  5. HQC AND AQC
    1. Protecting the computation

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KEYWORDS and PACS

Keywords

quantum computing

PACS

  • 03.67.Lx

    Quantum computation architectures and implementations

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3384661

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    A. M. Childs, D. W. Leung, and M. A. Nielsen, Phys. Rev. A 71, 032318 (2005).

    D. Nagaj and S. Mozes, J. Math. Phys. 48, 072104 (2007)JMAPAQ000048000007072104000001.

    K. G. H. Vollbrecht and J. I. Cirac, Phys. Rev. Lett. 100, 010501 (2008).

    D. Nagaj and P. Wocjan, Phys. Rev. A 78, 032311 (2008).

    A. Mizel, D. A. Lidar, and M. Mitchell, Phys. Rev. Lett. 99, 070502 (2007).

    S. Jordan, E. Farhi, and P. Shor, Phys. Rev. A 74, 052322 (2006).

    D. Lidar, Phys. Rev. Lett. 100, 160506 (2008).

    A. Childs, E. Farhi, and J. Preskill, Phys. Rev. A 65, 012322 (2001).

    J. D. Biamonte and P. J. Love, Phys. Rev. A 78, 012352 (2008).


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