paddle_quantum.state.common

The common function of the quantum state.

paddle_quantum.state.common.to_state(data, num_qubits=None, backend=None, dtype=None)

The function to generate a specified state instance.

Parameters:

data (Tensor | ndarray | QEnv) – The analytical form of quantum state.
num_qubits (int | None) – The number of qubits contained in the quantum state. Defaults to None, which means it will be inferred by the data.
backend (Backend | None) – Used to specify the backend used. Defaults to None, which means to use the default backend.
dtype (str | None) – Used to specify the data dtype of the data. Defaults to None, which means to use the default data type.

Returns:

The generated quantum state.

Return type:

State

paddle_quantum.state.common.zero_state(num_qubits, backend=None, dtype=None)

The function to generate a zero state.

Parameters:

num_qubits (int) – The number of qubits contained in the quantum state.
backend (Backend | None) – Used to specify the backend used. Defaults to None, which means to use the default backend.
dtype (str | None) – Used to specify the data dtype of the data. Defaults to None, which means to use the default data type.

Raises:

NotImplementedError – If the backend is wrong or not implemented.

Returns:

The generated quantum state.

Return type:

State

paddle_quantum.state.common.computational_basis(num_qubits, index, backend=None, dtype=None)

Generate a computational basis state $| e_{i} ⟩$ , whose i-th element is 1 and all the other elements are 0.

Parameters:

num_qubits (int) – The number of qubits contained in the quantum state.
index (int) – Index $i$ of the computational basis state :math`|e_{i}rangle` .
backend (Backend | None) – Used to specify the backend used. Defaults to None, which means to use the default backend.
dtype (str | None) – Used to specify the data dtype of the data. Defaults to None, which means to use the default data type.

Raises:

NotImplementedError – If the backend is wrong or not implemented.

Returns:

The generated quantum state.

Return type:

State

paddle_quantum.state.common.bell_state(num_qubits, backend=None)

Generate a bell state.

Its matrix form is:

| Φ_{D} ⟩ = \frac{1}{\sqrt{D}} \sum_{j = 0}^{D - 1} | j ⟩_{A} | j ⟩_{B}

Parameters:

num_qubits (int) – The number of qubits contained in the quantum state.
backend (Backend | None) – Used to specify the backend used. Defaults to None, which means to use the default backend.

Raises:

NotImplementedError – If the backend is wrong or not implemented.

Returns:

The generated quantum state.

Return type:

State

paddle_quantum.state.common.bell_diagonal_state(prob)

Generate a bell diagonal state.

Its matrix form is:

p_{1} | Φ^{+} ⟩ ⟨ Φ^{+} | + p_{2} | Ψ^{+} ⟩ ⟨ Ψ^{+} | + p_{3} | Φ^{-} ⟩ ⟨ Φ^{-} | + p_{4} | Ψ^{-} ⟩ ⟨ Ψ^{-} |

Parameters:

prob (List[float]) – The prob of each bell state.

Raises:

Exception – The state should be a pure state if the backend is state_vector.
NotImplementedError – If the backend is wrong or not implemented.

Returns:

The generated quantum state.

Return type:

State

paddle_quantum.state.common.random_state(num_qubits, is_real=False, rank=None)

Generate a random quantum state.

Parameters:

num_qubits (int) – The number of qubits contained in the quantum state.
is_real (bool | None) – If the quantum state only contains the real number. Defaults to False.
rank (int | None) – The rank of the density matrix. Defaults to None which means full rank.

Raises:

NotImplementedError – If the backend is wrong or not implemented.

Returns:

The generated quantum state.

Return type:

State

paddle_quantum.state.common.w_state(num_qubits)

Generate a W-state.

Parameters:: num_qubits (int) – The number of qubits contained in the quantum state.
Raises:: NotImplementedError – If the backend is wrong or not implemented.
Returns:: The generated quantum state.
Return type:: State

paddle_quantum.state.common.ghz_state(num_qubits)

Generate a GHZ-state.

Parameters:: num_qubits (int) – The number of qubits contained in the quantum state.
Raises:: NotImplementedError – If the backend is wrong or not implemented.
Returns:: The generated quantum state.
Return type:: State

paddle_quantum.state.common.completely_mixed_computational(num_qubits)

Generate the density matrix of the completely mixed state.

Parameters:

num_qubits (int) – The number of qubits contained in the quantum state.

Raises:

Exception – The state should be a pure state if the backend is state_vector.
NotImplementedError – If the backend is wrong or not implemented.

Returns:

The generated quantum state.

Return type:

State

paddle_quantum.state.common.r_state(prob)

Generate an R-state.

Its matrix form is:

p | Ψ^{+} ⟩ ⟨ Ψ^{+} | + (1 - p) | 11 ⟩ ⟨ 11 |

Parameters:

prob (float) – The parameter of the R-state to be generated. It should be in $[0, 1]$ .

Raises:

Exception – The state should be a pure state if the backend is state_vector.
NotImplementedError – If the backend is wrong or not implemented.

Returns:

The generated quantum state.

Return type:

State

paddle_quantum.state.common.s_state(prob)

Generate the S-state.

Its matrix form is:

p | Φ^{+} ⟩ ⟨ Φ^{+} | + (1 - p) | 00 ⟩ ⟨ 00 |

Parameters:

prob (float) – The parameter of the S-state to be generated. It should be in $[0, 1]$ .

Raises:

Exception – The state should be a pure state if the backend is state_vector.
NotImplementedError – If the backend is wrong or not implemented.

Returns:

The generated quantum state.

Return type:

State

paddle_quantum.state.common.isotropic_state(num_qubits, prob)

Generate the isotropic state.

Its matrix form is:

p (\frac{1}{\sqrt{D}} \sum_{j = 0}^{D - 1} | j ⟩_{A} | j ⟩_{B}) + (1 - p) \frac{I}{2^{n}}

Parameters:

num_qubits (int) – The number of qubits contained in the quantum state.
prob (float) – The parameter of the isotropic state to be generated. It should be in $[0, 1]$ .

Raises:

Exception – The state should be a pure state if the backend is state_vector.
NotImplementedError – If the backend is wrong or not implemented.

Returns:

The generated quantum state.

Return type:

State