Experimental demonstration of a compiled version of Shor's algorithm with quantum entanglement.

@article{Lanyon2007ExperimentalDO,
  title={Experimental demonstration of a compiled version of Shor's algorithm with quantum entanglement.},
  author={Ben P. Lanyon and Till Weinhold and Nathan K Langford and Marco Barbieri and Daniel F. V. James and Alexei Gilchrist and A. G. White},
  journal={Physical review letters},
  year={2007},
  volume={99 25},
  pages={
          250505
        }
}
Shor's powerful quantum algorithm for factoring represents a major challenge in quantum computation. Here, we implement a compiled version in a photonic system. For the first time, we demonstrate the core processes, coherent control, and resultant entangled states required in a full-scale implementation. These are necessary steps on the path towards scalable quantum computing. Our results highlight that the algorithm performance is not the same as that of the underlying quantum circuit and… 

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References

SHOWING 1-10 OF 20 REFERENCES

Figure 1(e) is equivalent to the order-4 C ˆ 7 circuit in Ref. [14]: CSWAP is equivalent to a Toffoli and CNOTS

  • Figure 1(e) is equivalent to the order-4 C ˆ 7 circuit in Ref. [14]: CSWAP is equivalent to a Toffoli and CNOTS

Phys. Rev. Lett

  • Phys. Rev. Lett
  • 2002

Phys. Rev. Lett

  • Phys. Rev. Lett
  • 2005

Phys. Rev. A

  • Phys. Rev. A
  • 2001

Phys. Rev. Lett

  • Phys. Rev. Lett
  • 1999

E-PRLTAO-99-020750 for supplementary information. For more information on EPAPS

  • E-PRLTAO-99-020750 for supplementary information. For more information on EPAPS

We use convex optimization tomography

  • We use convex optimization tomography

Phys. Rev. Lett

  • Phys. Rev. Lett
  • 2005

Proc. 35th Ann. Symp. Found. Comp. Sci

  • Proc. 35th Ann. Symp. Found. Comp. Sci
  • 1994

Phys. Rev. Lett

  • Phys. Rev. Lett
  • 1997