  Nielsen [quant-ph/0108020] showed that universal quantum computation is
possible given quantum memory and the ability to perform projective
measurements on up to 4-qubits. We describe an improved method that requires
only 2-qubit measurements, which are both sufficient and necessary. We present
a method to partially collapse the $C_k$-hierarchy in the indirect construction
of unitary gates [Gottesman and Chuang, Nature, {\bf 402} 309 (1999)], and
apply the method to find discrete universal sets of 2-qubit measurements.
