Efficient linear optics quantum computation with Bell States
by
Dan Browne
Imperial College
Coauthors: Dan Browne and Terry Rudolph

We present a novel optical quantum computation scheme [1] which utilises, as its basic resource, maximally polarisation entangled photon pairs (Bell states). The scheme operates in the “cluster state” approach to quantum computation [2]. Cluster states are a class of entangled multi-qubit states with many interesting properties [3]. In particular, by measuring the individual qubits of a cluster state of sufficient size in particular eigenbases and in a particular order, any quantum network can be efficiently simulated and thus universal quantum computation can be achieved [2]. We will describe how cluster states can be generated from Bell states non deterministically with linear optical elements and photo-detection. The quantum computation is then implemented, in a deterministic step, by polarisation measurements on individual photons. The resources required to generate the cluster state in our scheme scale linearly with its size. The scheme which we describe has several attractive features. Firstly, it avoids the need for the concatenation of large numbers of beam-splitters, which is necessary in standard linear optics quantum computation proposals [4] and which places extremely high demands on the degrees of mode-matching required in their experimental implementation. Additionally, its resource requirements are much more favourable than the original linear optics quantum computation proposal [4], and also improve on more recent schemes such as [5] and the cluster-state based approach in [6].

References

[1] D.E. Browne and T. Rudolph, quant-ph/0405157.

[2] R. Raussendorf and H. J. Briegel, Phys. Rev. Lett. 86, 5188-5191 (2001); R. Raussendorf, D.E. Browne and H.J. Briegel, Phys. Rev. A 68, 022312 (2003).

[3] H.J. Briegel and R. Raussendorf, Phys. Rev. Lett. 86, 910-913 (2001).

[4] E. Knill, R. Laflamme, and G. Milburn, Nature 409, 46 (2001).

[5] N. Yoran and B. Reznik, Phys. Rev. Lett. 91, 037903 (2003).

[6] M.A. Nielsen, quant-ph/0402005.

Paper reference: arXiv:quant-ph/0405157

Date received: April 1, 2004