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?