Quantum computation: a universal set of quantum gates Two noncomputable One nontrivial two-qubit gate single-qubit gates U Ux()=exp(ir, o, /2) If lwm)is a product state U2(y)=ex(-iy2a:/2) out) is an entangled state then u is nontrivial a general U can be decomposed into single-qubit rotations and a nontrivial two-qubit gate5 Quantum computation: a universal set of quantum gates • Two noncommutable single-qubit gates • • • One nontrivial two-qubit gate If is a product state is an entangled state then U is nontrivial •A general U can be decomposed into single-qubit rotations and a nontrivial two-qubit gate U ( ) exp( / 2) X x x x U  = −i  ( ) exp( / 2) Z z z z U  = −i  U C T  in  out