Noise

class sequence.utils.noise.Noise

Provides static methods to simulate common quantum noise processes on circuits and density matrices.

Supported noise models include: - Single-qubit depolarizing noise - Two-qubit depolarizing noise (standalone or full density matrix injection) - Measurement bit-flip errors - Noisy two-qubit gate application in circuits

These methods support both circuit-level (via SeQUeNCe Circuit objects) and density-matrix-level simulations, enabling realistic modeling of quantum errors for testing protocols like quantum error correction or entanglement generation.

All methods are stateless and can be used independently within simulation pipelines.

static apply_depolarizing_noise(rho: ndarray, p: float, qubits: list[int], keys: list[int]) → ndarray

Apply depolarizing noise to selected qubits in an n-qubit density matrix.

This function simulates the depolarizing channel:

(rho) → (1 - p) * (rho) + (p / (4^k - 1)) * Σ_i P_i * (rho) * P_i†

where:

• k = len(qubits), the number of qubits affected (must be 1 or 2),

• {P_i} is the set of all non-identity Pauli operators on those k qubits,

• Each P_i is extended (lifted) to act on the full n-qubit system.

The result is a noisy version of the original state, mixing in random Pauli errors on the selected qubits. This function returns a new density matrix that reflects this transformation.

Parameters:

• rho (np.ndarray) – A (2^n x 2^n) density matrix representing an n-qubit state. The qubit ordering is determined by the keys list.

• p (float) – Depolarizing probability (0 ≤ p ≤ 1). - p = 0: state remains unchanged, - p = 1: selected qubits become maximally mixed.

• qubits (List[int]) – One or two qubit indices to apply noise to. These must appear in the keys list.

• keys (List[int]) –

  A permutation of [0, 1, …, n-1] defining the tensor product order of qubits in rho.

  Each key corresponds to a qubit managed by QuantumManagerDensity. For example, keys = [3, 7, 1] means qubit 3 is treated as the first subsystem (most significant), 7 as second, and 1 as third.

  This lets rho represent entangled states with flexible qubit ordering. The function uses this list to locate where each target qubit appears in the tensor product and apply noise accordingly.

Returns:

The updated (2^n x 2^n) density matrix with depolarizing noise on the given qubits.

Return type:

np.ndarray

Raises:

ValueError – If p is not in [0, 1], if rho has the wrong shape, if qubits has length not in {1, 2}, or if any target qubit is missing from keys.

Notes

• After applying noise, update the simulation manually using: quantum_manager.set(keys, new_rho). This function does not modify global state.

• The function returns a new density matrix (does not mutate rho in-place) because noise channels are CPTP maps that return fresh quantum states.

• The code finds each qubit’s position in the tensor product using keys, and applies Pauli operators using Kronecker products to avoid reshuffling the full matrix.

static apply_measurement_noise(circuit: Circuit, meas_error_rate: float, qubit_index: int = 0)

Applies classical measurement noise by flipping the qubit with probability η.

With probability meas_error_rate, an X gate is applied to the specified qubit to simulate a bit-flip error in the measurement result.

Parameters:

• circuit (Circuit) – The quantum circuit to modify. This function mutates the circuit in place by appending an X gate if a flip occurs.

• meas_error_rate (float) – Probability η (between 0 and 1) that the measurement result is incorrect.

• qubit_index (int, optional) – Index of the qubit to apply noise to (default is 0).

Returns:

This function does not return anything. It modifies the input circuit directly.

Return type:

None

Notes

• Used to simulate classical readout errors after measurement.

• The circuit is directly updated — no new object is returned.