So I was working on a project with qudits (specifically d = 4) and came across a problem. How do I generate gates for these? I can construct Hadamard and X gates for these, but how does one approach other gates, like S and P?

  • 2
    $\begingroup$ That depends what you want to do. Do you simply want to construct a universal gate set, or are you somewhat interested in an intrinsic stabilizer formalism for $d=4$? For the first goal: You can simply embed $d=2$ gates into $\mathbb C^4$ and tensor copies thereof. What I'm saying is that $n$ ququarts have a Hilbert space which is isomorphic to the one of $2n$ qubits. Hence, you can just use normal gate sets and you'll be universal for $U(4^n)\simeq U(2^{2n})$. $\endgroup$ May 4 at 6:57
  • $\begingroup$ WHat do you mean by "generate"? Areyou talking about some sort of physical action, or merely "define"? $\endgroup$
    – DaftWullie
    May 4 at 10:34
  • $\begingroup$ Yes I meant define, really sorry about being unclear, however MarkusHeinrich figured out what I was trying to achieve, however can you expand on embedding matrixes? I assume you dont mean expanding a to [a,a,a,a]. Thanks! $\endgroup$
    – Random
    May 4 at 16:31


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