Timeline for How is the set of states $Q$ logically replaced by a Hilbert space?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 9, 2020 at 11:57 | vote | accept | Jack Rock | ||
| Dec 9, 2020 at 11:57 | comment | added | Jack Rock | Thank you. I read here. Maybe I want to find inverse point of view, "How to interpret a matrix as a quantum circuit?" because I prefer represent mathematical structures with quantum logical gates instead to represent quantum gates with matrices. | |
| Dec 8, 2020 at 21:41 | comment | added | psitae | There's a correspondence between kets and vectors. $|0\rangle$ is [1,0] and $|1\rangle$ is [0,1]. From there, you can use matrix representation of the gates to calculate the result of the computation. | |
| Dec 8, 2020 at 21:39 | comment | added | Jack Rock | ok, I remember that bras and kets are typical representations for Hilbert space. But, electronically speking, how bras and kets are realized with digital/quantum (gate) circuits? Do they use Controlled NOT gate, Hadamard (H) gate? I take a look here now to understand better en.wikipedia.org/wiki/Quantum_logic_gate#Hadamard_(H)_gate | |
| Dec 8, 2020 at 21:20 | comment | added | psitae | Maybe you're familiar with Cartesian space. There are many ways to represent elements of that space: "origin", "(0,0)", even a picture will do. If you want to get crazy, you can even bijectively map the 1D real number line onto Cartesian space. Then "0" would be a representation of the origin. This is called representation theory. Representations are not unique. For Hilbert spaces in QM, bras and kets are typical representations, as are square matrices. Note that the term 'vector' is being used here in a much more general way than what you learned pre-calc. | |
| Dec 8, 2020 at 20:48 | comment | added | Jack Rock | Thank you for your answer. When you say "elements" of the "Hilbert space" you say they are some numbers of some matrix representation that we can call 'vectors' and 'Hilbert space'? I ask this because logically representation of same concept is not easy to figure out. | |
| Dec 8, 2020 at 20:32 | history | answered | psitae | CC BY-SA 4.0 |