pdft.bases.DCT4Basis

class pdft.bases.DCT4Basis(m, n, tensors=None, code=None, inv_code=None, parametrization='o4')

Bases: object

DCT-IV tensor-network basis: the real-orthogonal, ancilla-free analogue of QFTBasis.

Mirrors QFTBasis (one tensor list; inverse_transform applies conj(tensors) through inv_code). The gates are emitted by pdft.bases.circuit.dct4.dct4_code(); at initialization the forward operator is the bit-reversed orthonormal DCT-IV per dimension, and — since DCT-IV is self-inverse — the basis reconstructs exactly. tensors holds every gate — the affine R_y rotation layer, the branch Hadamards, the mirror-Q CNOT permutations and the Delta sign — each a learnable leaf on its auto-selected Riemannian manifold (O(2) / O(4) / phase). The gate tensors are real-valued (stored complex128, zero imaginary), so the unitary manifold trains the real-orthogonal subset under a real objective: exact DCT-IV at init, then relaxed, just as QFT relaxes within U.

Pytree contract:

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

Parameters:

• m (int)

• n (int)

• tensors (list[Array])

• code (object)

• inv_code (object)

• parametrization (str)

__init__(m, n, tensors=None, code=None, inv_code=None, parametrization='o4')

Parameters:

• m (int)

• n (int)

• tensors (Sequence[Array] | None)

• code (object | None)

• inv_code (object | None)

• parametrization (str)

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