Embeddings

class tn4ml.embeddings.Embedding

Data embedding (feature map) class.

dtype

Data Type

Type:

numpy.dtype

__init__(dtype=<class 'numpy.float32'>)

__new__(**kwargs)

Trigonometric

class tn4ml.embeddings.trigonometric

Trigonometric feature map.

\(\phi(x_\textit{j}) = \left[ cos(\frac{\pi}{2}x_\textit{j}), sin(\frac{\pi}{2}x_\textit{j}) \right]\)

k

Custom parameter = dim/2.

Type:

int

__init__(k=1, **kwargs)

Parameters:

k (int)

property dim: int

Mapping dimension

property input_dim: int

Dimensionality of input feature. 1 = number, 2 = vector

Fourier

class tn4ml.embeddings.fourier

Fourier feature map. \(\phi(x_\textit{j}) = \frac{1}{\sqrt{k}}\left[ cos(\frac{\pi x_\textit{j}}{2}), sin(\frac{\pi x_\textit{j}}{2}), ..., cos(\frac{\pi x_\textit{j}}{2^k}), sin(\frac{\pi x_\textit{j}}{2^k})\right]\)

p

Mapping dimension.

Type:

int

__init__(p=2, **kwargs)

Parameters:

p (int)

property dim: int

Mapping dimension

property input_dim: int

Dimensionality of input feature. 1 = number, 2 = vector

Linear Complement

class tn4ml.embeddings.linear_complement_map

Feature map \([x, 1-x]\) or \([1, x, 1-x]\) where x = feature in range [0,1].

p

Mapping dimension.

Type:

int

__init__(p=2, **kwargs)

Parameters:

p (int)

property dim: int

Mapping dimension

property input_dim: int

Dimensionality of input feature. 1 = number, 2 = vector

Gaussian RBF

class tn4ml.embeddings.gaussian_rbf

Gaussian Radial Basis Function.

centers

Gaussian centers.

Type:

numpy.ndarray

gamma

Scaling factor \(\gamma=\frac{1}{2\sigma^2}\)

Type:

float

__init__(centers=None, gamma=None, **kwargs)

Parameters:

• centers (ndarray)

• gamma (float)

property dim: int

Mapping dimension

property input_dim: int

Dimensionality of input feature. 1 = number

Polynomial

class tn4ml.embeddings.polynomial

Polynomial feature map

degree

Degree of polynomial.

Type:

int

n

Number of features.

Type:

int

include_bias

Include bias term.

Type:

bool

__init__(degree, n, include_bias=False, **kwargs)

Parameters:

• degree (int)

• n (int)

• include_bias (bool)

property dim: int

Mapping dimension

property input_dim: int

Dimensionality of input feature

Jax Arrays

class tn4ml.embeddings.jax_arrays

Input arrays to JAX arrays. No embedding. Optional: adding one to the input array.

add_bias

Add bias term (1.0)

Type:

bool

__init__(dim=None, add_bias=False, **kwargs)

Parameters:

• dim (int)

• add_bias (bool)

property dim: int

Mapping dimension

Patch Embedding

class tn4ml.embeddings.PatchEmbedding

__init__(k=2, **kwargs)

Initialize the PatchedEmbedding class.

Parameters:

k (int) – The kernel size of the patch window kxk.

Return type:

None

property dims: list

Dimensions of mps arrays

pad_or_truncate_statevector(statevector, target_size)

Pad or truncate the statevector to a target size.

Parameters:

• statevector (jax.numpy.ndarray) – The input statevector.

• target_size (int) – The desired size of the statevector.

Returns:

A statevector of the target size.

Return type:

jax.numpy.ndarray

create_statevector(x)

Create a statevector representation of an input array (vector like).

Parameters:

x (jax.numpy.ndarray) – An array of patch pixel intensities flattened from original patch k x k.

Returns:

A statevector representation of the input array.

Return type:

jax.numpy.ndarray

flatten_snake(image)

Flatten an image in a snake-like fashion.

Parameters:

image (jax.numpy.ndarray) – A 2D array of pixel intensities.

Returns:

A 1D array of pixel intensities in snake-like order.

Return type:

jax.numpy.ndarray

combine_mps_patches(mps_patches, n_qubits)

Combine arrays of each MPS patch into a single MPS.

Parameters:

• mps_patches (numpy.ndarray) – List of MPS patches (nested lists of arrays).

• n_qubits (int) – Number of qubits.

Returns:

A list of arrays for combined MPS.

Return type:

jax.numpy.ndarray

Embed Function

tn4ml.embeddings.embed(x, phi, **mps_opts)

Creates a product state from a vector of features x. Works only if features are separated and not correlated (this check you need to do yourself).

Parameters:

• x (numpy.ndarray) – Vector or Matrix of features.

• phi (tn4ml.embeddings.Embedding or tn4ml.embeddings.ComplexEmbedding or tn4ml.embeddings.StateVectorToMPSEmbedding) – Feature map for each feature.

• mps_opts (Optional parameters.) – Additional arguments passed to MatrixProductState class.