quairkit.database.state¶
The library of common quantum states.
-
quairkit.database.state.zero_state(num_systems, system_dim=
2)¶ The function to generate a zero state.
-
quairkit.database.state.one_state(num_systems, system_dim=
2)¶ The function to generate a one state.
-
quairkit.database.state.computational_state(num_systems, index, system_dim=
2)¶ Generate a computational state \(|e_{i}\rangle\) , whose i-th element is 1 and all the other elements are 0.
- Parameters:¶
- num_systems : int¶
number of systems in this state. Alias of
num_qubits.- index : int¶
Index \(i\) of the computational basis state :math`|e_{i}rangle` .
- system_dim : List[int] | int¶
dimension of systems. Can be a list of system dimensions or an int representing the dimension of all systems. Defaults to be qubit case.
- Returns:¶
The generated quantum state.
- Return type:¶
State
-
quairkit.database.state.bell_state(num_systems, system_dim=
2)¶ Generate a bell state.
Its matrix form is:
\[|\Phi_{D}\rangle=\frac{1}{\sqrt{D}} \sum_{j=0}^{D-1}|j\rangle_{A}|j\rangle_{B}\]
- quairkit.database.state.bell_diagonal_state(prob)¶
Generate a bell diagonal state.
Its matrix form is:
\[p_{1}|\Phi^{+}\rangle\langle\Phi^{+}|+p_{2}| \Psi^{+}\rangle\langle\Psi^{+}|+p_{3}| \Phi^{-}\rangle\langle\Phi^{-}| + p_{4}|\Psi^{-}\rangle\langle\Psi^{-}|\]
- quairkit.database.state.w_state(num_qubits)¶
Generate a W-state.
- quairkit.database.state.ghz_state(num_qubits)¶
Generate a GHZ-state.
- quairkit.database.state.completely_mixed_computational(num_qubits)¶
Generate the density matrix of the completely mixed state.
- quairkit.database.state.r_state(prob)¶
Generate an R-state.
Its matrix form is:
\[p|\Psi^{+}\rangle\langle\Psi^{+}| + (1 - p)|11\rangle\langle11|\]- 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
- quairkit.database.state.s_state(prob)¶
Generate the S-state.
Its matrix form is:
\[p|\Phi^{+}\rangle\langle\Phi^{+}| + (1 - p)|00\rangle\langle00|\]- 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
- quairkit.database.state.isotropic_state(num_qubits, prob)¶
Generate the isotropic state.
Its matrix form is:
\[p(\frac{1}{\sqrt{D}} \sum_{j=0}^{D-1}|j\rangle_{A}|j\rangle_{B}) + (1 - p)\frac{I}{2^n}\]