toqito.matrix_ops.tensor_comb

Compute tensor combination of list of vectors.

Module Contents

toqito.matrix_ops.tensor_comb.tensor_comb(states, k, mode='injective', density_matrix=True)[source]

Generate all possible tensor product combinations of quantum states (vectors).

This function creates a tensor product of quantum state vectors by generating all possible sequences of length k from a given list of quantum states, and computing the tensor product for each sequence.

Given n quantum states, this function generates (n^k) combinations of sequences of length k, computes the tensor product for each sequence, and converts each tensor product to its corresponding density matrix.

For one definition and usage of a quantum sequence, refer to [@Gupta_2024_Optimal].

Examples

Consider the following basis vectors for a 2-dimensional quantum system.

[

e_0 = left[1, 0 right]^{text{T}}, e_1 = left[0, 1 right]^{text{T}}.

]

We can generate all possible tensor products for sequences of length 2.

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

e_0 = np.array([1, 0]) e_1 = np.array([0, 1])

result = tensor_comb([e_0, e_1], 2, mode=”injective”, density_matrix=True)

for key, mat in result.items():

print(f”tensor_comb{key} =n{mat}n”)

```

Raises:

ValueError – If the input list of states is empty.

Parameters:

  • states (list[numpy.ndarray]) – A list of state vectors.

  • k (int) – The length of the sequence.

  • mode (str) – Determines the type of sequences. Default is “injective”. non-injective will allow repetitions in

  • sequences (no repetitions)

  • injective (injective will ensures sequences are)

  • indices (sequences with repeated)

  • density_matrix (bool) – Determines whether the return is a density matrix or a ket. Default is True.

Returns:

A dictionary where keys are tuples representing sequences of state indices, and values are density matrices of the tensor products of the corresponding state vectors or tensor products of the corresponding state vectors based on input density_matrix being either True or False.

Return type:

dict[tuple[int, Ellipsis], numpy.ndarray]