pdft.bases.RichBasis

class pdft.bases.RichBasis(m, n, tensors=None, code=None, inv_code=None)

Bases: object

QFT topology with H + learnable U(4) gates instead of H + CP.

Parameter count at m=n=3 (within an 8x8 block):

• 3 H gates per dim × 3 free real params (SU(2)) = 9

• 3 U(4) gates per dim × 15 free real params (SU(4)) = 45

• total per dim: 54 (BELOW the 63-dim of SU(8) — meaningful structure)

Initialised so the circuit is BIT-IDENTICAL to QFTBasis at training step 0 (each U(4) starts at the 4×4 controlled-phase diag(1, 1, 1, exp(iφ)) of its corresponding QFT slot). Adam can then deform the U(4) gates into any 4×4 unitary, but the family is a strict 54-dim submanifold of SU(8) and does NOT contain 8×8 DCT exactly (empirically: fit_to_dct plateaus at Frobenius² ≈ 63.7).

Pytree contract:

leaves = tensors (one list) aux data = (m, n, len(tensors), code, inv_code)

Parameters:

• m (int)

• n (int)

• tensors (list[Array])

• code (object)

• inv_code (object)

__init__(m, n, tensors=None, code=None, inv_code=None)

Parameters:

• m (int)

• n (int)

• tensors (Sequence[Array] | None)

• code (object | None)

• inv_code (object | None)

Methods

__init__(m, n[, tensors, code, inv_code])
forward_transform(pic)
inverse_transform(pic)

Attributes

image_size
inv_tensors
num_parameters
m
n
tensors
code
inv_code

m: int

n: int

tensors: list[Array]

code: object

inv_code: object

property inv_tensors: list[Array]

property image_size: tuple[int, int]

property num_parameters: int

forward_transform(pic)

Parameters:

pic (Array)

Return type:

Array

inverse_transform(pic)

Parameters:

pic (Array)

Return type:

Array