2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/89857Nielsen [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.Results and discussed expanded, simple discrete universal sets of measurements presentedQuantum Physicstext