toqito.matrix_ops.tensor_unravel

Generate the 1D contraint.

Module Contents

toqito.matrix_ops.tensor_unravel.tensor_unravel(constraint_tensor)[source]

Decode a clause tensor (indicator tensor) into its raw 1D representation.

In binary constraint system (BCS) games, parity constraints can be encoded as clause tensors — n-dimensional NumPy arrays of shape (2, 2, …, 2), filled with a constant background value (e.g., (-1)**b[i]) except for a single unique entry that marks the satisfying assignment.

This function unravels such a tensor by:

  1. Locating the unique element (the one appearing exactly once).

  2. Extracting its multi-dimensional index (i1, i2, …, in).

  3. Returning a 1D NumPy array [i1, i2, …, in, value], where the first n entries are the coordinates and the last entry is the unique value (±1).

Conceptually, this is a form of structured tensor decoding, closely related to:

  • Indicator (Kronecker delta) tensors in multilinear algebra refer to [@Kolda_2009_Tensor].

  • The matrix vec-operator for flattening matrices refer to [@Horn_1985_Matrix].

  • Parity-projector encodings in linear-system games refer to [@Cleve_2016_Perfect].

The tensor-form constraint representation is commonly used in implementations of binary constraint system (BCS) games. For background on BCS games, refer to [@Cleve_2014_Characterization].

Examples

```python exec=”1” source=”above” import numpy as np from toqito.matrix_ops import tensor_unravel

tensor_constraint = np.array([[-1, -1], [-1, 1]]) print(tensor_unravel(tensor_constraint)) ```

Parameters:

  • constraint_tensor (numpy.ndarray) – An n-dimensional tensor with shape (2,)*n, where each element is either -1 or +1.

  • assignment. (All entries should be equal except for one unique position that marks the satisfying)

Returns:

A 1D numpy array of length (n+1) where the first (n) elements are the coordinates (indices), and the last element is the unique constant (rhs).

Return type:

numpy.ndarray