[Feature Request]: Generalization of `PhaseDamping` Channel to Support Qudits

[evmckinney9]

Feature Description

The PhaseDamping channel currently only supports qubits. To enhance our quantum simulations, we aim to generalize this channel for higher-dimensional systems (qudits), such as qutrits.

Rationale for Generalization

• Broader Simulation Scope: Extending to qudits enables simulations of more complex systems.
• Research Alignment: This aligns with current research trends in quantum computing.
• Consistency: Follows the precedent set by AmplitudeDamping for qudits.

Technical Challenges

• New Definitions Required: Phase damping in qudits needs new mathematical definitions and Kraus operators.
• Complexity in Formulation: The formulation for qudits involves more intricate structures compared to qubits.

Current Implementation for Qubits

class PhaseDamping(Channel):
    """Phase damping channel for qubits."""

    def __init__(self, T2, num_qubits=1, hilbert_space_dim=2):
        """Initialize with a given T2 dephasing time and number of qubits."""
        self.T2 = T2
        self.num_qubits = num_qubits
        self.hilbert_space_dim = hilbert_space_dim
        super().__init__(dims=hilbert_space_dim**num_qubits)

    def _create_single_qubit_operators(self):
        """Create single-qubit Kraus operators for phase damping."""
        if self.hilbert_space_dim == 2:  # standard qubit case
            _gamma = 1 - np.exp(-self._trotter_dt / self.T2)
            E0_single = np.array([[1, 0], [0, np.sqrt(1 - _gamma)]])
            E1_single = np.array([[0, 0], [0, np.sqrt(_gamma)]])
            return [E0_single, E1_single]

        else:
            raise NotImplementedError("Unsupported Hilbert space dimension.")

Proposed Changes

• [x] Research and develop phase damping models for qudits.
• [x] Update PhaseDamping to support these higher-dimensional systems.
• [x] Maintain compatibility with the existing framework and error channels.

Additional Resources

• Further resources for mathematical modeling of qudit phase damping are to be identified.

Testing

• [x] Create tests for the extended functionality.
• [x] Validate against current qubit models for accuracy.