Criteria for Exact Qudit Universality

Details Criteria for Exact Qudit Universality Criteria for Exact Qudit Universality

2004-07-28

arxiv.org/abs/quant-ph/0407223v1

Physical Review A 71, 052318 (2005).

Physics

Quantum Physics

7 pages, 1 figure

Scientific paper

10.1103/PhysRevA.71.052318

We describe criteria for implementation of quantum computation in qudits. A qudit is a d-dimensional system whose Hilbert space is spanned by states |0>, |1>,... |d-1>. An important earlier work of Mathukrishnan and Stroud [1] describes how to exactly simulate an arbitrary unitary on multiple qudits using a 2d-1 parameter family of single qudit and two qudit gates. Their technique is based on the spectral decomposition of unitaries. Here we generalize this argument to show that exact universality follows given a discrete set of single qudit Hamiltonians and one two-qudit Hamiltonian. The technique is related to the QR-matrix decomposition of numerical linear algebra. We consider a generic physical system in which the single qudit Hamiltonians are a small collection of H_{jk}^x=\hbar\Omega (|k>k iff H_{jk}^{x,y} are allowed Hamiltonians. One qudit exact universality follows iff this graph is connected, and complete universality results if the two-qudit Hamiltonian H=-\hbar\Omega |d-1,d-1>

Affiliated with

Also associated with

No associations

Rating

Criteria for Exact Qudit Universality does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Criteria for Exact Qudit Universality, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Criteria for Exact Qudit Universality will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-623704