states.dicke¶
Dicke states are an equal-weight superposition of all n-qubit states with Hamming Weight k.
Functions¶
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Produce a Dicke state with specified excitations. |
Module Contents¶
- states.dicke.dicke(num_qubit, num_excited, return_dm=False)¶
Produce a Dicke state with specified excitations.
The Dicke state is a quantum state with a fixed number of excitations (i.e., num_excited) distributed across the given number of qubits (i.e., num_qubit). It is symmetric and represents an equal superposition of all possible states with the specified number of excited qubits.
Example
Consider generating a Dicke state with 3 qubits and 1 excitation:
>>> from toqito.states import dicke >>> dicke(3, 1) array([0. , 0.57735027, 0.57735027, 0. , 0.57735027, 0. , 0. , 0. ])
If we request the density matrix for this state, the return value is:
>>> from toqito.states import dicke >>> dicke(3, 1, return_dm=True) array([[0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ], [0. , 0.33333333, 0.33333333, 0. , 0.33333333, 0. , 0. , 0. ], [0. , 0.33333333, 0.33333333, 0. , 0.33333333, 0. , 0. , 0. ], [0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ], [0. , 0.33333333, 0.33333333, 0. , 0.33333333, 0. , 0. , 0. ], [0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ], [0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ], [0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ]])
References
- Raises:
ValueError – If the number of excitations exceeds the number of qubits.
- Parameters:
num_qubit (int) – The total number of qubits in the system.
num_excited (int) – The number of qubits that are in the excited state.
return_dm (bool) – If True, returns the state as a density matrix (default is False).
- Returns:
The Dicke state vector or density matrix as a NumPy array.
- Return type:
numpy.ndarray