Add support for the Matsumoto-Amano normal form. by codrut3 · Pull Request #1801 · quantumlib/Qualtran

codrut3 · 2026-02-04T20:51:02Z

codrut3 · 2026-02-05T18:55:07Z

@NoureldinYosri please have a look when you have time!

NoureldinYosri

overall looks good, but $T == T_z$, so you can update the representation of T to just be the same as Tz, thanks for the contribution @codrut3

codrut3 · 2026-02-06T20:23:52Z

Thank you a lot for your review, Noureldine! Do you mean set TSqrt2 = Tz in _su2_ct.py?

For me it wasn't obvious that T can be scaled to be a member of SU2CliffordT, and it took me a bit to work out the constant $c$ so that c / (2(2+\sqrt{2})) T is in SU2CliffordT :) That's why I defined TSqrt2 in addition to Tz. But I can set TSqrt2 = Tz and put the other definition in a comment above, would this work?

NoureldinYosri · 2026-02-07T04:54:07Z

yes, there is no need to define a TSqrt2, the normal T becomes Tz in SU2. Given any 1Q unitary gate $U$ you can get its SU2 version by dividing by $\sqrt{det|U|}$ since the determinant is a on the unit circle and dividing by its square root cancels the global phase.

Tx and Ty are the X and Y axis version of the T gate ($\frac{\pi}{4}$ rotations around their axes)

codrut3 · 2026-02-07T10:31:13Z

Actually now I realize that if I set TSqrt2 = Tz then the gates property in SU2CliffordT is Tz, and so everywhere instead of T it would print Tz. For example, the Matsumoto-Amano sequence would be Tz H Tz S H Tz .... Isn't this confusing for the user?

NoureldinYosri · 2026-02-10T22:34:07Z

good point, @mpharrigan what do you think? should we create a separate T from Tz ?

mpharrigan · 2026-02-10T23:11:10Z

I don't have the full context, but if the issue is just how the same logical object gets formatted as a string, I'd recommend putting that logic with the string formatting

codrut3 · 2026-02-11T23:06:03Z

Thank you for the comments! I removed the TSqrt2 matrix and I used Tz everywhere instead. The sequence element is printed as T.

to_cirq which converts the sequence to a Cirq representation still needs to handle the T character, and same for to_quirk.

NoureldinYosri

thanks @codrut3 this looks really nice, just a few nits

NoureldinYosri · 2026-02-10T22:29:09Z

    Allowable format strings are
     - 'xyz' uses Tx, Ty, Tz gates.
     - 'xz' uses $Tx, Tz, Tx^\dagger, Tz^\dagger$
+     - 't' uses T gates, and returns the Matsumoto-Amano normal form.


Suggested change

- 't' uses T gates, and returns the Matsumoto-Amano normal form.

- 't' uses only Tz gates, and returns the Matsumoto-Amano normal form.

NoureldinYosri · 2026-02-12T19:34:53Z

+            break
+    gates: tuple[str, ...] = ()
+    new: Union[_su2_ct.SU2CliffordT, None]
+    if np.array_equal(parity, np.array([[1, 1, 0], [1, 1, 0], [0, 0, 0]])):


can you move this if/else block into a separate method and turn _matsumoto_amano_sequence into an iterative procedure rather than recursive?

NoureldinYosri · 2026-02-12T19:35:39Z

    Args:
        matrix: The matrix to represent.
-        fmt: A string from the set {'xz', 'xyz'} representing the allowed T gates described above.
+        fmt: A string from the set {'xz', 'xyz', t'} representing the allowed T gates described above.


typo:

Suggested change

fmt: A string from the set {'xz', 'xyz', t'} representing the allowed T gates described above.

fmt: A string from the set {'xz', 'xyz', 't'} representing the allowed T gates described above.

NoureldinYosri · 2026-02-13T22:14:38Z

 @pytest.mark.parametrize("g", _make_random_su(50, 5, random_cliffords=True, seed=0))
-def test_to_cirq(g):
-    circuit = cirq.Circuit(ctr.to_cirq(g, 'xyz'))
+@pytest.mark.parametrize("fmt", ('xyz', 't'))


lets add xz as well

Suggested change

@pytest.mark.parametrize("fmt", ('xyz', 't'))

@pytest.mark.parametrize("fmt", ('xyz', 'xz', 't'))

NoureldinYosri

thanks @codrut3

… issue-1762

codrut3 · 2026-02-18T20:16:42Z

I saw there was a pylint error and I fixed it.

codrut3 · 2026-02-25T22:08:35Z

@NoureldinYosri is there anything else I need to do here?

Add support for the Matsumoto-Amano normal form.

4285f8f

NoureldinYosri reviewed Feb 5, 2026

View reviewed changes

Fix format, mypy and pylint errors.

66f759c

Remove TSqrt2 and use Tz instead.

8a45698

Fix error.

d7a0b0d

NoureldinYosri reviewed Feb 13, 2026

View reviewed changes

codrut3 and others added 2 commits February 15, 2026 23:07

Address review comments.

e6921ad

Merge branch 'main' into issue-1762

337a5c4

NoureldinYosri enabled auto-merge (squash) February 17, 2026 16:02

NoureldinYosri approved these changes Feb 17, 2026

View reviewed changes

codrut3 added 2 commits February 18, 2026 21:03

Fix pylint error.

4e153e4

Merge branch 'issue-1762' of https://github.com/codrut3/Qualtran into…

b285caa

… issue-1762

auto-merge was automatically disabled February 18, 2026 20:13
Head branch was pushed to by a user without write access

NoureldinYosri enabled auto-merge (squash) February 19, 2026 00:00

Merge branch 'main' into issue-1762

2f57634

NoureldinYosri merged commit e6dcafb into quantumlib:main Feb 25, 2026
9 checks passed

	- 't' uses T gates, and returns the Matsumoto-Amano normal form.
	- 't' uses only Tz gates, and returns the Matsumoto-Amano normal form.

	fmt: A string from the set {'xz', 'xyz', t'} representing the allowed T gates described above.
	fmt: A string from the set {'xz', 'xyz', 't'} representing the allowed T gates described above.

	@pytest.mark.parametrize("fmt", ('xyz', 't'))
	@pytest.mark.parametrize("fmt", ('xyz', 'xz', 't'))

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codrut3 commented Feb 4, 2026

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codrut3 commented Feb 6, 2026

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NoureldinYosri commented Feb 7, 2026

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NoureldinYosri commented Feb 10, 2026

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mpharrigan commented Feb 10, 2026

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codrut3 commented Feb 18, 2026

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codrut3 commented Feb 25, 2026

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