Bases

Trainable sparsifying bases. Circuit bases (QFT, entangled QFT, TEBD, MERA, Rich, RealRich, DCT-IV) act on a whole 2^m x 2^n image; BlockedBasis tiles an inner basis over image blocks. The *_code and *_mat helpers build the underlying einsum circuits and reference DFT matrices.

Sparse-basis subpackage.

Two families:

• bases.circuit — full circuit topologies (QFT, EntangledQFT, TEBD, MERA), comparable to FFT/DCT.

• bases.block — BlockedBasis over arbitrary block partitions (Rich/RealRich are re-exported here for back-compat; they live in circuit).

The abstract base class and bases_allclose helper live in bases.base.

Contents

QFTBasis	QFT tensor-network basis.
EntangledQFTBasis	QFT + appended entanglement layer on min(m, n) row/col qubit pairs.
TEBDBasis	2D TEBD basis with row + column rings of controlled-phase gates.
MERABasis	2D MERA basis.
DCT4Basis	DCT-IV tensor-network basis: the real-orthogonal, ancilla-free analogue of QFTBasis.
RichBasis	QFT topology with H + learnable U(4) gates instead of H + CP.
RealRichBasis	QFT topology with H + real-orthogonal 2-qubit gates.
BlockedBasis	Wraps an inner parametric basis as a within-block transform.
AbstractSparseBasis	Structural interface shared by every basis: an image_size, a num_parameters count, and forward_transform / inverse_transform on a 2^m x 2^n image.
freeze_as_blocked	Return (basis_copy_with_identity_outer_gates, frozen_indices).
fit_to_dct	Fit a parametric basis so its forward circuit ≈ DCT_2D.
bases_allclose	Semantic equality across any of the registered basis types.
qft_code	Return (einsum_fn, initial_tensors) for 2D QFT on (2^m, 2^n) images.
entangled_qft_code	Return (einsum_fn, initial_tensors, n_entangle) for entangled 2D QFT.
tebd_code	Return (einsum_fn, initial_tensors, n_row_gates, n_col_gates).
mera_code	Return (einsum_fn, initial_tensors, n_row_gates, n_col_gates).
ft_mat	Apply 2D QFT circuit to a (2^m, 2^n) image.
ift_mat	Apply 2D inverse QFT circuit.