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I'm curious, why L2 norm? Each qubit lives in C^2, does it not? I've only ever seen quantum computing formulated over finite dimensional Hilbert spaces (though
by C-x_C-f 3y ago
I'm curious, why L2 norm? Each qubit lives in C^2, does it not? I've only ever seen quantum computing formulated over finite dimensional Hilbert spaces (though to be fair it was only in a math context, no real physics there)
- nh23423fefe 3y agoReal probabilities sum to 1 additively. Complex amplitudes don't. The L2 norm preserves unitarity.
- abdullahkhalids 3y agoWe can't have a why, because the claim that the norm is L2 is axiomatic [1]. However, as the sibling comment notes, we can argue from consistency. Would any other norm give us a sensible theory? Or we can put quantum theory in a larger framework of theories and discuss why the L2 norm makes more sense within that framework. Scott Aaronson discusses some of these idea in his lecture [2]. [1] Feynamn on why https://www.youtube.com/watch?v=36GT2zI8lVA&pp=ygULZmV5bm1hbiB3aHk%3D https://www.youtube.com/watch?v=36GT2zI8lVA&pp=ygULZmV5bm1hb... [2] https://www.scottaaronson.com/democritus/lec9.html https://www.scottaaronson.com/democritus/lec9.html