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Simplifying quantum logic using higher-dimensional Hilbert spaces

Nature Physics volume 5, pages 134–140 (2009)Cite this article

Abstract

Quantum computation promises to solve fundamental, yet otherwise intractable, problems across a range of active fields of research. Recently, universal quantum logic-gate sets—the elemental building blocks for a quantum computer—have been demonstrated in several physical architectures. A serious obstacle to a full-scale implementation is the large number of these gates required to build even small quantum circuits. Here, we present and demonstrate a general technique that harnesses multi-level information carriers to significantly reduce this number, enabling the construction of key quantum circuits with existing technology. We present implementations of two key quantum circuits: the three-qubit Toffoli gate and the general two-qubit controlled-unitary gate. Although our experiment is carried out in a photonic architecture, the technique is independent of the particular physical encoding of quantum information, and has the potential for wider application.

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Figure 1: Simplifying the Toffoli gate.
Figure 2: Simplifying higher-order Toffoli gates.
Figure 3: Simplifying controlled-unitary gates.
Figure 4: Efficiently adding control qubits to an arbitrary controlled circuit.
Figure 5: Toffoli and controlled-unitary experimental layout.
Figure 6: Experimentally constructed Toffoli logical truth table.
Figure 7: Experimentally reconstructed Toffoli output density matrices.
Figure 8: Experimentally reconstructed controlled-unitary gate process matrices.

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Acknowledgements

We acknowledge discussions with W. Munro and D. Kielpinski, and financial support from the Australian Research Council Discovery and Federation Fellow programmes, the DEST Endeavour Europe and International Linkage programmes, and an IARPA-funded US Army Research Office Contract.

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Authors and Affiliations

  1. Department of Physics and Centre for Quantum Computer Technology, University of Queensland, Brisbane 4072, Australia

    Benjamin P. Lanyon, Marco Barbieri, Marcelo P. Almeida, Thomas Jennewein, Timothy C. Ralph, Kevin J. Resch, Geoff J. Pryde, Jeremy L. O’Brien, Alexei Gilchrist & Andrew G. White

  2. Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanng. 3, A-1090 Vienna, Austria

    Thomas Jennewein

  3. Institute for Quantum Computing and Department of Physics & Astronomy, University of Waterloo, N2L 3G1, Canada

    Kevin J. Resch

  4. Centre for Quantum Dynamics, Griffith University, Brisbane 4111, Australia

    Geoff J. Pryde

  5. H. H. Wills Physics Laboratory and Department of Electrical and Electronic Engineering, Centre for Quantum Photonics, University of Bristol, Merchant Venturers Building, Woodland Road, Bristol BS8 1UB, UK

    Jeremy L. O’Brien

  6. Physics Department, Macquarie University, Sydney 2109, Australia

    Alexei Gilchrist

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  1. Benjamin P. Lanyon
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Correspondence to Benjamin P. Lanyon.

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Lanyon, B., Barbieri, M., Almeida, M. et al. Simplifying quantum logic using higher-dimensional Hilbert spaces. Nature Phys 5, 134–140 (2009). https://doi.org/10.1038/nphys1150

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