# Why is it impossible to work with polylog length encoding schemes for quantum circuits?

I am going through Quantum Computational Complexity by John Watrous. On page $12$, he said:

The encoding disallows compression: it is not possible to work with encoding schemes that allow for extremely short (e.g., polylogarithmic-length) encodings of circuits; so for simplicity it is assumed that the length of every encoding of a quantum circuit is at least the size of the circuit.

My question:

Why is it impossible to work with polylogarithmic-length encoding schemes for quantum circuits?

But in context the author is in the middle of explaining the complexity class BQP (bounded-probability quantum polynomial-time). I think they're just making sure that you don't sneak non-polynomial amounts of work into the encoding. You don't want "repeat the diffusion operator $\sqrt{2}^n$ times" to count as being in BQP with respect to $n$.