Enable pulling through Clifford operations, also add an option of only applying dd to single qubit gate moments

[babacry]

Enable adding dynamical decoupling in single qubit gate moments only.

Adding mechanism is described in the code. In short:

For each qubit:
      For moments in (first_active_moment, last_active_single_qubit_moment):
            Insert
      Absorb the inverse to the last_active_single_qubit_moment

2 test cases added for single qubit gates moments insertion mode:

Test case 1: add dd preserves the circuit.

0: ───────────────────────────────H───@───
                                      │
1: ───────────────────────H───@───H───X───
                              │
2: ───────────────H───@───H───X───────────
                      │
3: ───H───────@───H───X───────────────────
              │
4: ───H───@───X───────────────────────────
          │
5: ───H───X───────H───@───────────────────
                      │
6: ───────────────H───X───H───@───────────
                              │
7: ───────────────────────H───X───H───@───
                                      │
8: ───────────────────────────────H───X───

Test case 2:

input_circuit's diagram is:

0: ───────────────────────────────H───@───H───
                                      │
1: ───────────────────────H───@───H───X───H───
                              │
2: ───────────────H───@───H───X───────────H───
                      │
3: ───H───────@───H───X───────────────────H───
              │
4: ───H───@───X───────────────────────────H───
          │
5: ───H───X───────H───@───────────────────H───
                      │
6: ───────────────H───X───H───@───────────H───
                              │
7: ───────────────────────H───X───H───@───H───
                                      │
8: ───────────────────────────────H───X───H───

output diagram is

0: ───────────────────────────────H───@───H────────────────────────
                                      │
1: ───────────────────────H───@───H───@───H────────────────────────
                              │
2: ───────────────H───@───H───@───X───────PhXZ(a=-0.5,x=0.5,z=0)───
                      │
3: ───H───────@───H───@───X───────X───────H────────────────────────
              │
4: ───H───@───@───X───────X───────X───────PhXZ(a=-0.5,x=0.5,z=0)───
          │
5: ───H───@───────H───@───X───────X───────H────────────────────────
                      │
6: ───────────────H───@───H───@───X───────PhXZ(a=-0.5,x=0.5,z=0)───
                              │
7: ───────────────────────H───@───H───@───H────────────────────────
                                      │
8: ───────────────────────────────H───@───H────────────────────────

[codecov[bot]]

Codecov Report

All modified and coverable lines are covered by tests :white_check_mark:

Project coverage is 97.83%. Comparing base (e2e8aef) to head (74305a0). Report is 2 commits behind head on main.

Additional details and impacted files

```diff @@ Coverage Diff @@ ## main #6675 +/- ## ======================================== Coverage 97.83% 97.83% ======================================== Files 1075 1077 +2 Lines 92325 92493 +168 ======================================== + Hits 90324 90492 +168 Misses 2001 2001 ```

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[eliottrosenberg]

I suspect that the bug is in the logic of how to pull Pauli gates through Clifford gates (e.g. cirq.CZ)

[babacry]

• [x] For single-qubit-gate moments insertion only: the bug was fixed in this commit. And it was tested via

cirq.testing.assert_circuits_have_same_unitary_given_final_permutation(
        input_circuit, transformed_circuit, {q: q for q in input_circuit.all_qubits()}
    )

and

sampler = cirq.Simulator(dtype=np.complex128)
psi0 = sampler.simulate(input_circuit).final_state_vector
psi1 = sampler.simulate(transformed_circuit).final_state_vector
assert np.isclose(np.abs(np.vdot(psi0, psi1)) ** 2, 1.0)

both passed for all test cases.

• [ ] For non-single-qubit-gate moments insertion, there are 2 issues
  • [x] op wasn't inserted from first active moment, it's fixed in the latest commit.
  • [ ] Now, we fill in operations in consecutive idle pieces only, while I am not sure what is the expected transformed circuit for the following cases.
• Input circuit:

  a: ───H───@───────?───────────────H───
        │
  b: ───────X───@───@───@───@───@───H───
            │   │   │   │   │
  c: ───────────X───X───X───X───X───H───

  where ? can be any single-qubit-gate, e.g., X / H.

• Transformed circuit with schema="XX_PAIR"
  • Current code would transform the circuit into as for a, the idle pieces lengths are 1, 3

    a: ───H───@───────?───X───X───────H───
      │
    b: ───────X───@───@───@───@───@───H───
          │   │   │   │   │
    c: ───────────X───X───X───X───X───H───

    Is this expected? I suspect we can't commute through the moment ? at due to non commutativity, right? or should we take care of ? case by case? for example, if ?=X, then, we can add 2 more X gates for qubit a in the transformed circuit above. while, '?=H', we can't insert more, right?

[babacry]

Now, we rely on cirq.has_stabilizer_effect to determine if an operation is Clifford. While, cirq.has_stabilizer_effect(cirq.M) returns True, resulting in a polluted clifford piece. Add a criteria for function _is_clifford_moment and the test case in the comment above.

[babacry]

Also changed default schema in the new commit.