I What Is the Difference Between Loss and Cost Functions in Quantum Computing?

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The discussion centers on the distinction between loss and cost functions in the context of variational quantum algorithms. While both terms are often used interchangeably, some sources suggest they may have subtle differences based on context. Participants express a need for clarity and examples to better understand these concepts. The conversation highlights the ambiguity in definitions found in literature, with many treating them as synonyms unless explicitly differentiated. Overall, the need for more precise definitions and context in quantum computing discussions is emphasized.
SaschaSIGI
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Hello,
Im currently hearing a module about quantum computing and Im wondering what is the difference of a loss and cost function for variational quantum algortihms? Both functions also can be presented into a loss/cost landscape? Are they the same ?

Already a big thank you for all the upcoming answers!
 
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Hello, and :welcome: !

No answers in three weeks, so there must be something missing in this post.
Perhaps you can provide some context, examples, references ? Be more specific ?

Would be good to read the guidelines even though this isn't homework.

##\ ##
 
BvU said:
No answers in three weeks, so there must be something missing in this post.
Perhaps you can provide some context, examples, references ? Be more specific ?
I don't think so, the problem is rather that https://en.wikipedia.org/wiki/Loss_function and other sources write
a loss function or cost function (sometimes also called an error function)
And even so there is the feeling that they really are used for the same thing but in slightly different contexts, it is hard to pin this down.
 
I always treat loss/cost/objective function as synonyms until a reference uses both and gives a definition of both that clarifies the distinction.
 
For the quantum state ##|l,m\rangle= |2,0\rangle## the z-component of angular momentum is zero and ##|L^2|=6 \hbar^2##. According to uncertainty it is impossible to determine the values of ##L_x, L_y, L_z## simultaneously. However, we know that ##L_x## and ## L_y##, like ##L_z##, get the values ##(-2,-1,0,1,2) \hbar##. In other words, for the state ##|2,0\rangle## we have ##\vec{L}=(L_x, L_y,0)## with ##L_x## and ## L_y## one of the values ##(-2,-1,0,1,2) \hbar##. But none of these...

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