Some question about multiplication depth and security parameter

FHE Use Cases
1

Question 1, I would like to ask how to reduce the multiplication depth. Initially, I set the multiplication depth to 30 because it is necessary to perform Chebyshev approximation and ciphertext comparison (CKKS → FHEW) on the ciphertext.

Question 2, I want to use a 128-bit security level, but under the condition of a multiplication depth of 30, the recommended ring size is very large. Is there any way to reduce the ring size? What are the recommended parameters for using a 128-bit security level in CKKS, such as scaleModSize, firstModSize, and multiplication depth?

Question 3, Can I initially set a smaller multiplication depth and then automatically increase the multiplication depth during the calculation process for operations such as comparing ciphertexts or computing some operations of the Chebyshev approximation?

Question Four, what is the difference between HEStd_128_quantum and HEStd_128_classic? Do they choose different ring dimensions?

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Do you solve your questions?

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These questions are too open-ended and not well-defined. I can point to introductory material on FHE, papers, or tutorials if this helps. I also suggest asking one question at a time (with a concrete description of the example/application).