Fix single-qubit depolarizing noise channel

[HasanTasdiq]

Summary

Noise.apply_depolarizing_noise (in sequence/utils/noise.py) is documented to support 1 or 2 target qubits, but it hardcodes the Pauli index combinations as 2-qubit tuples:

idx_tuples = [(i, j) for i in range(4) for j in range(4)]

For the single-qubit case (k = 1) only idx_tuple[0] is used, which produces two problems:

• Spurious identity terms: the tuples (0, 1), (0, 2), (0, 3) map the target qubit (and every other qubit) to I, so the full identity operator is added to the Pauli sum three times.
• Wrong normalization: the channel is divided by len(pauli_ops) = 15 instead of 4^1 - 1 = 3.

As a result the single-qubit depolarizing channel is mathematically incorrect. For example, applying p = 0.3 to |0><0|:

	output
current code	diag(0.84, 0.16)
correct channel (1-p)ρ + (p/3)(XρX + YρY + ZρZ)	diag(0.8, 0.2)

Fix

Generate the Pauli index tuples from the actual number of target qubits:

idx_tuples = itertools.product(range(4), repeat=k)

• The two-qubit path is unchanged: 16 tuples, identity excluded → 15 operators (verified identical output to the previous implementation).
• The single-qubit path now yields the correct 3 operators (X, Y, Z) and matches the standard depolarizing channel.

Test plan

• Added test_apply_depolarizing_noise_single_qubit comparing the k=1 output against the standard single-qubit depolarizing channel.
• Confirmed the new test fails on the current code and passes with the fix.
• Existing test_apply_depolarizing_noise (two-qubit) still passes — the two-qubit path is unaffected.

🤖 Generated with Claude Code

[Copilot]

Pull request overview

Fixes Noise.apply_depolarizing_noise so the single-qubit (k=1) depolarizing channel uses the correct set of Pauli operators and normalization, matching the standard definition while keeping the two-qubit (k=2) behavior unchanged.

Changes:

• Generate Pauli index tuples based on the actual number of target qubits via itertools.product(..., repeat=k) (instead of hardcoding 2-qubit tuples).
• Add a regression test verifying the k=1 depolarizing channel matches the standard (1-p)ρ + (p/3)(XρX + YρY + ZρZ) behavior.

Reviewed changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated no comments.

File	Description
sequence/utils/noise.py	Fixes Pauli operator enumeration/normalization for k=1 by generating index tuples with repeat=k.
tests/utils/test_noise.py	Adds a single-qubit depolarizing regression test comparing against a manual reference implementation.

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[caitaozhan]

Looks good!