toqito.states.w_state

Generalized w-state is an entangled quantum state of n qubits.

This state refers to the quantum superposition in which one of the qubits is in an excited state and others are in the ground state.

Module Contents

toqito.states.w_state.w_state(num_qubits, coeff=None)

Produce a W-state [@Dur_2000_ThreeQubits].

Returns the W-state described in [@Dur_2000_ThreeQubits]. The W-state on num_qubits qubits is defined by:

[

|W rangle = frac{1}{sqrt{num_qubits}} left(|100 ldots 0 rangle + |010 ldots 0 rangle + ldots + |000 ldots 1 rangle right).

]

Examples

Using |toqito⟩, we can generate the (3)-qubit W-state

[

|W_3 rangle = frac{1}{sqrt{3}} left( |100rangle + |010 rangle + |001 rangle right)

]

as follows.

`python exec="1" source="above" from toqito.states import w_state print(w_state(3)) `

We may also generate a generalized (W)-state. For instance, here is a (4)-dimensional (W)-state

[

frac{1}{sqrt{30}} left( |1000 rangle + 2|0100 rangle + 3|0010 rangle + 4 |0001 rangle right).

]

We can generate this state in |toqito⟩ as

`python exec="1" source="above" from toqito.states import w_state import numpy as np coeffs = np.array([1, 2, 3, 4]) / np.sqrt(30) print(w_state(4, coeffs)) `

Raises:

ValueError – The number of qubits must be greater than or equal to 1.

Parameters:

• num_qubits (int) – An integer representing the number of qubits.

• coeff (list[int] | None) – default is [1, 1, …, 1]/sqrt(num_qubits): a 1-by-num_qubts vector of coefficients.

Return type:

numpy.ndarray