  Classical data encoding is usually treated as a black-box in the oracle-based
quantum algorithms. On the other hand, their constructions are crucial for
practical algorithm implementations. Here, we open the black-boxes of data
encoding and study the Clifford$+T$ complexity of constructing some typical
quantum access models. For general matrices, we show that both sparse-access
input models and block-encoding require nearly linear circuit complexities
relative to the matrix dimension, even if matrices are sparse. We also gives
construction protocols achieving near-optimal gate complexities. On the other
hand, the construction becomes efficient with respect to the data qubit when
the matrix is the linear combination polynomial terms of efficient unitaries.
As a typical example, we propose improved block encoding when these unitaries
are Pauli strings. Our protocols are built upon improved quantum state
preparation and a selective oracle for Pauli strings, which hold independent
value. Our access model constructions offer considerable flexibility, allowing
for tunable ancillary qubit number and offers corresponding space-time
trade-offs.
