# Timeline for What is the most economical and preferred basis for the qudit?

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Feb 10 '21 at 6:58 history edited
deleted 1 character in body; edited tags
Dec 13 '18 at 19:42 history edited
edited tags
S Apr 11 '18 at 8:52 history
Fixed grammar and improved Formatting
Apr 11 '18 at 8:48 answer timeline score: 3
Apr 11 '18 at 7:06 review
S Apr 11 '18 at 8:52
Apr 10 '18 at 20:56 history reopened
Apr 7 '18 at 18:15 history edited
Stripped to just one question.
Apr 7 '18 at 18:10 comment @Mithrandir24601 - I'll remove the radix from this one. Thanks for taking the time to re-review the question.
Apr 7 '18 at 17:21 comment There are now clear questions here. However, there are two distinct questions, so would you be able to split this into two separate posts with one question each in order to potentially get better answers for the individual questions? Thanks
Apr 7 '18 at 16:02 review
Apr 10 '18 at 20:56
Apr 7 '18 at 15:44 history edited
Apr 6 '18 at 20:02 history closed Needs details or clarity
Apr 6 '18 at 15:41 comment @gIS - Thanks, I will incorporate that into the answer I am writing for this question.
Apr 6 '18 at 9:23 comment Each physical system has a different "preferred basis", which depends on the system as well as on our capabilities to control the system in said basis. There is no univocal way to say that a basis is better than another in this sense, it all just depends on what do you want to do and what you are capable of doing.
Apr 5 '18 at 22:36 history edited
Expanded upon the last section, one more edit to go.
Apr 5 '18 at 18:41 comment @Rob: In many circumstances it is better to carry more than just apples: it depends on what you want to do with the apples. Even if all you want is apples, what variety of apple also matters, not everyone likes to eat Granny Smith, for example. Sheer number is not what is important --- suitability for a given purpose is a higher consideration. The dimensionality of the qudit is just one factor for that purpose.
Apr 5 '18 at 18:24 history edited
Approximately 3/4 the way through editing, then a proofreading.
Apr 5 '18 at 17:23 comment @Rob: Higher dimensions are not necessarily useful. It is more important to have the dynamics that you want, to perform the applications that you want, than to have high dimension. That motivates concerning yourself not with wondering what "the right dimension of qudit to use", but "what systems seem practical to control, and what dimensions of qudits are natural for that system". That is, you put the system first, and then ask questions about the qudits relative to that choice of system. Doing it in the opposite order is like asking what is the best number of apples.
Apr 5 '18 at 13:59 comment @Rob: that helps, but I'm still confused. Are you asking "what dimension of qudit would be most effective to compute with", as a theoretical optimum, in some sense analogous to the efficiency of a radix (motivated similarly, though perhaps taking into account more than just the typical efficiency of expressing integers)? Are you interested in choices motivated by a specific model of computation (your reference to anyons)? Or are you interested in practical issues related to what is possible due to decoherence in some architecture (your other references)?
Apr 5 '18 at 13:34 history edited
Clairified one point without changing the meaning of the content or invalidating the answer currently offered.
Apr 5 '18 at 11:40 answer timeline score: 4
Apr 5 '18 at 10:20 comment Can you explain why you expect the radix economy to be different in the quantum case? You encode the digits x into $|x\rangle$, so I don't see why it should be different. Or are you thinking of a different representation of the numbers?
Apr 5 '18 at 9:43 review
Apr 6 '18 at 20:04
Apr 5 '18 at 9:27 comment There's a lot going on here; it's a bit difficult to sift through. Note that in your remarks on radix economy, the result that the most economical integer base is ternary is a mathematical result: it's difficult to see what you are getting at when you ask about "what radix to use" for qubits, which would seem to bake in the radix of 2. I also don't see what any of your linked references have to do with the question, with the (possible?) exception of the one on Fibonacci anyons, depending on what exactly you are trying to find out. Could you clarify what precisely you would like to know?
Apr 5 '18 at 8:32 history edited
deleted 10 characters in body; edited tags
Apr 5 '18 at 7:54 history asked