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>