A quantum computer is said to be “universally programmable” if it accepts “quantum programs” given as a quantum state and can execute any unitary operation specified by the program. The idea has been around at least as early as 1997, which is actually a “no-go” result. Since then, our understanding on universal programmability has improved, especially on “how many copies of a quantum program is required”. On the other hand, these results typically assume that a quantum computer accepting the program is already a fault-tolerant quantum computer, capable of executing any quantum operation allowed by the axioms of quantum theory. In this talk, I’ll cover some of the important background on universal programmability and discuss our recent result on the simplification of the executing quantum computer.