two-qubit decomposition into sqrt(iSWAP) + approximation #9375

ajavadia · 2023-01-13T19:57:24Z

Summary

Adds the sqrt(iSWAP) (SiSwapGate) as well as a method to decompose into it that uses 2 applications for ~79% of Haar-random unitaries and 3 applications for the rest.

Based on https://arxiv.org/pdf/2105.06074v3.pdf. This does not exactly follow the paper but is inspired by that result. The algorithm given in the paper seems to have some bugs so this is a different implementation.

In addition this PR implements an approximate synthesis, which results in further reductions: for ~95% of Haar-random unitaries 2-applications of SiSwap suffice when the gate has 99% fidelity.

Optimal approximation is found by distance in the Weyl chamber, which is a proxy for trace distance. The algorithm approximates more when the gate has less fidelity.

I added extensive tests because there are lots and lots of corner cases.

Co-authored by @thomasverrill. Closes #9333

Cryoris · 2023-01-24T20:05:13Z

With our gate naming scheme, should this be called SiSwapGate? Since we started to use the single letter S to indicate square roots in the SXGate 🙂

ajavadia · 2023-01-24T23:11:25Z

With our gate naming scheme, should this be called SiSwapGate? Since we started to use the single letter S to indicate square roots in the SXGate 🙂

I started the branch with that naming scheme but quickly got annoyed at all the up and down of the camel case :)
Still I don't particularly mind either way. I'd note that SZ is just called S at the moment because that's more common

ajavadia · 2023-01-24T23:13:12Z

Also @Cryoris would you like to review this? :)

coveralls · 2023-01-24T23:57:10Z

Pull Request Test Coverage Report for Build 4340575136

200 of 204 (98.04%) changed or added relevant lines in 9 files are covered.
1 unchanged line in 1 file lost coverage.
Overall coverage increased (+0.03%) to 85.389%

Changes Missing Coverage	Covered Lines	Changed/Added Lines	%
qiskit/synthesis/su4/siswap_decompose.py	144	146	98.63%
qiskit/synthesis/su4/utils.py	25	27	92.59%

Files with Coverage Reduction	New Missed Lines	%
qiskit/transpiler/passes/synthesis/unitary_synthesis.py	1	95.04%

Totals
Change from base Build 4336854592:	0.03%
Covered Lines:	68233
Relevant Lines:	79908

💛 - Coveralls

Cryoris

The decomposition looks mostly good! I only encountered one case where the final decomposition doesn't actually include the SQiSWGate but just an Gate with the same name, I think due to taking the inverse of the decomposition. We could e.g. fix that by adding a SQiSWdgGate but maybe there's also another solution. Here's a reproducing example:

import numpy as np
from qiskit.circuit import QuantumCircuit
from qiskit.circuit.library import SQiSWGate
from qiskit.synthesis.two_qubit import SQiSWDecomposer
from qiskit.quantum_info import Operator

circuit = QuantumCircuit(2)
circuit.rxx(0.2, 0, 1)
circuit.ryy(0.2, 0, 1)
circuit.rzz(0.2, 0, 1)

op = Operator(circuit).data

decomp = SQiSWDecomposer(euler_basis=["u"])
out = decomp(op)

print(out.draw())

for inst in out.data:
    if len(inst.qubits) == 2:
        print(type(inst.operation))

which prints

global phase: 2.6038
     ┌─────────────────────┐┌────────┐ ┌─────────────────────────┐  ┌────────┐┌────────────────────────────┐┌────────┐┌────────────────────────────┐
q_0: ┤ U(0,2.2455,-2.2455) ├┤0       ├─┤ U(2.9419,1.2433,2.4222) ├──┤0       ├┤ U(0.34939,2.4962,-0.64543) ├┤0       ├┤ U(2.9419,-0.71935,-1.8983) ├
     └──┬────────────────┬─┘│  sqisw │┌┴─────────────────────────┴─┐│  sqisw │└──┬─────────────────────┬───┘│  sqisw │├────────────────────────────┤
q_1: ───┤ U(-π,π/2,-π/2) ├──┤1       ├┤ U(-2.2067,-2.4822,0.54952) ├┤1       ├───┤ U(-1.0943,-π/2,π/2) ├────┤1       ├┤ U(-0.93488,2.5921,-2.4822) ├
        └────────────────┘  └────────┘└────────────────────────────┘└────────┘   └─────────────────────┘    └────────┘└────────────────────────────┘
<class 'qiskit.circuit.gate.Gate'>  # <-- should be type SQiSWGate!
<class 'qiskit.circuit.gate.Gate'>
<class 'qiskit.circuit.gate.Gate'>

Concerning the gate itself: I think it would be more consistent to go back to the name SiSwapGate to be consistent with our naming scheme. We've also moved away from other aliases like "Fredkin" or "Toffoli" in favor of consistency. I'd be open to add an alias SQiSW = SiSwapGate but I think it would be better if the base class would follow our convention 🙂

qiskit/circuit/library/standard_gates/sqisw.py

qiskit/synthesis/__init__.py

Cryoris · 2023-02-02T15:22:49Z

qiskit/synthesis/two_qubit/sqisw_decompose.py

+                for instruction in inverse_decomposition:
+                    if isinstance(instruction.operation, SQiSWGate):
+                        inverse_decomposition_with_sqisw_dg.z(0)
+                        inverse_decomposition_with_sqisw_dg.append(SQiSWGate().inverse(), [0, 1])


If I understand this correctly, the final decomposition should contain a SQiSWGate right? Won't inverting this twice end up with an Instruction which though called "sqisw" is not actually an instance of SQiSWGate?

I started trying to fix this as you suggest but thinking about it I think the overhead of adding a new gate (and all that goes along with it like definitions and adding to equivalence library) is not worth it. This problem has to be fixed in Qiskit such that taking the inverse of a gate twice gives the same gate. I opened an issue on this 18 months ago #6879. This has become a higher priority recently and I think once it gets fixed this automatically gets fixed too. Right now it's not really a problem because if the device supports siswap gate then the generated qasm is correct.

Cryoris · 2023-02-02T17:03:58Z

test/python/synthesis/test_sqisw_synthesis.py

+
+
+@ddt
+class TestSQiSWSynth(QiskitTestCase):


It would be nice to add a test for each of the different regions (green, blue, brown and red) in the paper so we're sure each of the cases is triggered 🙂

i added a bunch of tests

qiskit/circuit/library/standard_gates/sqisw.py

ShellyGarion · 2023-02-05T07:22:31Z

qiskit/synthesis/__init__.py

+.. autosummary::
+   :toctree: ../stubs/
+
+   SQiSWDecomposer


Should it be called SQiSWDecomposer or SQiSWDecomposition like SolovayKitaevDecomposition?

Right now it's named like TwoQubitBasisDecomposer and XXDecomposer which are more related to this class as they all take SU(4) and decompose it over some basis.
I agree we need consistency and my intent is to do this as I move stuff over to qiskit.synthesis (over a few different PRs)

qiskit/synthesis/two_qubit/sqisw_decompose.py

test/python/synthesis/test_sqisw_synthesis.py

ShellyGarion · 2023-02-05T08:55:23Z

qiskit/synthesis/two_qubit/sqisw_decompose.py

+
+class SQiSWDecomposer:
+    """
+    A class for decomposing 2-qubit unitaries into at most 3 uses of the sqrt(iSWAP) gate.


Perhaps it's worth to explain somewhere the difference from the usual two-qubit decomposition, and when to use each of the algorithms.

I would still like to check the docs, after they will be generated when the conflict is solved.

ajavadia · 2023-02-17T18:30:43Z

I addressed the review comments. Also I added approximation which is a good boost to the performance of the method (details in the PR description). I also added more corner case tests.

…imation

qiskit/synthesis/__init__.py

Cryoris

Thanks for the updates and the additional tests! I left some more comments below. 🙂

qiskit/circuit/library/standard_gates/siswap.py

qiskit/synthesis/su4/siswap_decompose.py

Cryoris · 2023-02-24T13:34:54Z

qiskit/synthesis/su4/siswap_decompose.py

+        Returns:
+            QuantumCircuit: Synthesized circuit.
+        """
+        if not approximate:


That's a more general question: isn't basis_fidelity and approximate redundant?

hmm good question. I was copying the structure of the XXDecomposer code. I can think about removing approximate but I have to see if there is some underlying reason. I'm making some changes to the whole qiskit.synthesis folder so I can have this on the list.

approximate is used by XXDecomposer only when computing infidelities. The method used doesn't depend on the values of the fidelities in basis_fidelity, in particular does not depend on whether they are less than one. I don't know "less than one" means, maybe it's advice on what to choose if you know you are passing 1.0. The same holds if basis_fidelity is not a dict, but a float, as it is here. In this case infidelities are computed for several values of strength (which corresponds to a rotation angle I think) that are hardcoded in XXDecomposer. The infidelities are computed from the strengths by a linear model. If approximate is True the parameters of the linear model are determined from basis_fidelity. If approximate is False then basis_fidelity is ignored completely and infidelities are computed without any reference to parameters passed when calling the object nor those passed when constructing it. That's sort of the reverse of what I would expect, but that's what the code does.

Cryoris · 2023-02-24T13:36:11Z

qiskit/synthesis/su4/siswap_decompose.py

+            circuit = circuit.compose(red_decomp, [0, 1])
+            if eigenphase_crossing:
+                # y, z -> -z, -y
+                circuit = circuit.compose(XGate().power(1 / 2), [0], front=True)


Is there a reason to not use the SX(dg)Gate for this? 🙂

hmm no its the same

Cryoris · 2023-02-24T13:41:52Z

qiskit/synthesis/su4/siswap_decompose.py

+    if abs(C) < _EPS:
+        C = 0.0
+
+    α = np.arccos(np.cos(2 * x) - np.cos(2 * y) + np.cos(2 * z) + 2 * np.sqrt(C))


I don't know what the best practice for non-ASCII characters is -- my feeling would say to rather use alpha etc to make life easier for future developers 😉 but I'm not fixed on this if you want to keep it as is 🙂

it's just nicer i think to read :)

I really like reading $\alpha$ in code. But I really don't enjoy searching for it with my editor.

Cryoris · 2023-02-24T13:43:06Z

qiskit/synthesis/su4/siswap_decompose.py

+    larger volume when approximation is enabled.
+
+    Args:
+        euler_basis (list(str)): single-qubit gates basis in the decomposition.


What do you think about adding an example on how to use this class here? 🙂 Would be nice to advertise this feature to users.

Cryoris · 2023-02-24T13:43:21Z

releasenotes/notes/sqisw-decomposition-2478b9f0b7c54044.yaml

+
+    An associated decomposition method that synthesizes arbitrary two-qubit
+    unitaries into two or three applications of SiSwap has been added in
+    :class:`.SiSwapDecomposer`.


It would be cool to show an example in the release notes, too 😄

Cryoris · 2023-02-24T13:44:30Z

test/python/synthesis/test_siswap_synthesis.py

+# copyright notice, and modified files need to carry a notice indicating
+# that they have been altered from the originals.
+
+# pylint: disable=invalid-name


is this only because of the variable u? If yes maybe we could just rename that one and avoid a global disable 🙂

yes. these variable naming rules are pretty annoying I think. I think we need to relax this at the qiskit level. Like why should naming my unitary u be a problem? @mtreinish what do you think?

I'm in favour of relaxing the lint-enforced naming rules in general, although I've got to say the code in this PR isn't exactly the greatest advert for it. There's a lot of mix-and-match of variable styles with no clear relation to the mathematical paper they're drawn from (the non-iSWAP-specific code), and "why should naming my unitary u be a problem?" is indicative - u is mostly a bad name, because the majority of things we deal with in Qiskit are unitary. In tests you can use some name that identifies it as the base of the test, and in synthesis code, I'm guessing there's a lot of different unitaries kicking around at different points, so they ought to have proper names as well.

But often the main point of a function is to do something with a single unitary. In this case naming it unitary seems reasonable. XXDecomposer does this and it looks pretty good there. I don't like u, but if I used a editor that had good support for Python semantics, I might not mind it. I have to distinguish occurrences of u visually. If it's really just as easy with a modern editor to deal with, I'd say go ahead and use it.

Cryoris · 2023-02-24T13:46:20Z

qiskit/synthesis/su4/siswap_decompose.py

+
+class SiSwapDecomposer:
+    """
+    A class for decomposing 2-qubit unitaries into at most 3 uses of the sqrt(iSWAP) gate.


In the PR text you're mentioning this code differs from the paper, would it make sense to summarize the differences either here or as comments in the code to know what's going on when we come back to this code in the future?

Co-authored-by: Julien Gacon <gaconju@gmail.com>

jakelishman · 2023-03-06T12:59:40Z

qiskit/circuit/library/standard_gates/__init__.py

-Standard gates
+=============================================================
+Standard gates (:mod:`qiskit.circuit.library.standard_gates`)
+=============================================================


I think there's been a bad merge here - this file had its docstring reduced to a single by Shelly just recently to avoid mistakes in the documentation, and it should stay a single line. This file isn't built into the documentation at all (the only changes needed are to qiskit/circuit/library/__init__.py), but we've had a few cases where this file was erroneously updated instead only, leading to missing documentation.

It's better to put this back to just being one line, but the import should stay.

Indeed, see the details in PR #9668. Please add this gate to the docs in the init file of circuit/library.

jakelishman · 2023-03-06T13:03:54Z

qiskit/quantum_info/synthesis/xx_decompose/decomposer.py

+from qiskit.synthesis.su4.utils import average_infidelity

 from .circuits import apply_reflection, apply_shift, canonical_xx_circuit
 from .utilities import EPSILON
 from .polytopes import XXPolytope


-def _average_infidelity(p, q):
-    """
-    Computes the infidelity distance between two points p, q expressed in positive canonical
-    coordinates.
-    """
-
-    a0, b0, c0 = p
-    a1, b1, c1 = q
-
-    return 1 - 1 / 20 * (
-        4
-        + 16
-        * (
-            math.cos(a0 - a1) ** 2 * math.cos(b0 - b1) ** 2 * math.cos(c0 - c1) ** 2
-            + math.sin(a0 - a1) ** 2 * math.sin(b0 - b1) ** 2 * math.sin(c0 - c1) ** 2
-        )
-    )
-
-


qiskit.quantum_info shouldn't be able to access qiskit.synthesis, because the latter is way higher up in the hierarchy. Of course, the actual solution is that all the code currently in qiskit.quantum_info.synthesis, and at least the bits that are concerned with circuit objects not just matrices, ought to move into qiskit.synthesis, but that's a problem for a different PR.

For right now, it might be a shade better just to eat this code duplication right now to avoid creating even larger circular import cycles - I saw you already hit one caused by this in a file above, because you had to make an import more specific.

jakelishman · 2023-03-06T13:04:33Z

qiskit/circuit/library/standard_gates/siswap.py

+        self.definition = qc
+
+    def __array__(self, dtype=None):
+        """Return a numpy.array for the DCX gate."""


Suggested change

"""Return a numpy.array for the DCX gate."""

"""Return a numpy.array for the :math:`\\sqrt{iSWAP}` gate."""

perhaps?

jakelishman · 2023-03-06T13:07:45Z

qiskit/circuit/library/standard_gates/siswap.py

+        q = QuantumRegister(2, "q")
+        qc = QuantumCircuit(q, name=self.name)
+        rules = [(RXXGate(-np.pi / 4), [q[0], q[1]], []), (RYYGate(-np.pi / 4), [q[0], q[1]], [])]
+        for instr, qargs, cargs in rules:
+            qc._append(instr, qargs, cargs)


If we're going to use the _append form, we ought to construct a validated CircuitInstruction to add - the form of allowing qargs and cargs to _append will be deprecated, as part of drawing a clearer distinction between the responsibilities of the caller of append and the caller of _append.

If you don't want to worry about it, it shouldn't really matter for performance to just use append.

jakelishman · 2023-03-06T13:15:43Z

qiskit/synthesis/su4/siswap_decompose.py

+    def __init__(self, euler_basis: Optional[List[str]]):
+        # decomposer for the local single-qubit gates
+        from qiskit.transpiler.passes.optimization.optimize_1q_decomposition import (
+            Optimize1qGatesDecomposition,  # pylint: disable=cyclic-import
+        )
+
+        euler_basis = euler_basis or ["u"]
+        self._decomposer1q = Optimize1qGatesDecomposition(euler_basis)


I don't know how much you mind about the type hints, but List is only very rarely what's meant when it's in an input position. Most likely, you just want anything that can be converted to a list, which is typing.Iterable[str]. If so, you'd need to change your assignment code to euler_basis = ["u"] if euler_basis is None else list(euler_basis) to be properly correct.

It also probably doesn't matter, but your current code will convert euler_basis=[] to ["u"]. I don't know if that's intended, or if it's something you'd want Optimize1qGatesDecomposition to throw an error on. I would also mention that the more ideal case would be making a dummy Target than passing the basis directly, because Matthew wants to start getting all transpiler passes transitioned to remove the old-style interfaces for easier maintainability moving forwards.

jakelishman · 2023-03-06T13:34:09Z

qiskit/synthesis/su4/utils.py

+    Function from
+    https://scipy-cookbook.readthedocs.io/items/Finding_Convex_Hull_Minimum_Point.html


It's not clear to me what the licence of this code is. The best I can find is in the repo of the docs website, which has a stipulation that source-code reproductions must include their licence header and binary distributions must include it in their documentation. The licence comes from the times when Scipy was part of Enthought.

I think we need to be more careful about just copy-pasting code like this - it's not clear to me if we're actually safe to use this.

jakelishman · 2023-03-06T13:35:41Z

qiskit/synthesis/su4/utils.py

+    return 1 - 1 / 20 * (
+        4
+        + 16
+        * (
+            np.cos(a0 - a1) ** 2 * np.cos(b0 - b1) ** 2 * np.cos(c0 - c1) ** 2
+            + np.sin(a0 - a1) ** 2 * np.sin(b0 - b1) ** 2 * np.sin(c0 - c1) ** 2
+        )
+    )


Similar comment about preferring math functions if appropriate here.

jakelishman · 2023-03-06T13:40:44Z

test/python/synthesis/test_siswap_synthesis.py

+# copyright notice, and modified files need to carry a notice indicating
+# that they have been altered from the originals.
+
+# pylint: disable=invalid-name


I'm in favour of relaxing the lint-enforced naming rules in general, although I've got to say the code in this PR isn't exactly the greatest advert for it. There's a lot of mix-and-match of variable styles with no clear relation to the mathematical paper they're drawn from (the non-iSWAP-specific code), and "why should naming my unitary u be a problem?" is indicative - u is mostly a bad name, because the majority of things we deal with in Qiskit are unitary. In tests you can use some name that identifies it as the base of the test, and in synthesis code, I'm guessing there's a lot of different unitaries kicking around at different points, so they ought to have proper names as well.

jakelishman · 2023-03-06T13:42:32Z

test/python/synthesis/test_siswap_synthesis.py

+        u = random_unitary(4, seed=seed)
+        decomposer = SiSwapDecomposer(euler_basis=["rz", "ry"])
+        circuit = decomposer(u)
+        self.assertLessEqual(circuit.count_ops().get("siswap", 0), 3)
+        self.assertEqual(Operator(circuit), Operator(u))


In all these in this file, should we also be testing that the only gates in the output are those in the Euler basis as well?

jakelishman · 2023-03-06T13:43:28Z

test/python/synthesis/test_siswap_synthesis.py

+    @combine(
+        p=[
+            [np.pi / 4, np.pi / 6, -np.pi / 12],  # red and blue intersection (bottom face)
+            [np.pi / 4, np.pi / 6, np.pi / 12],  # inverse of above (and locally equivalent)
+            [np.pi / 4, np.pi / 8, np.pi / 8],  # half-way between CX and SWAP (peak red polytope)
+            [np.pi / 4, np.pi / 8, -np.pi / 8],  # inverse of above (and locally equivalent)
+            [np.pi / 4, np.pi / 16, np.pi / 16],  # quarter-way between CX and SWAP
+            [np.pi / 4, np.pi / 16, np.pi / 16],  # inverse of above (and locally equivalent)
+            [np.pi / 6, np.pi / 8, np.pi / 24],  # red and blue and green intersection
+            [np.pi / 6, np.pi / 8, -np.pi / 24],  # inverse of above (not locally equivalent)
+            [np.pi / 16, np.pi / 24, np.pi / 48],  # red and blue and purple intersection
+            [np.pi / 16, np.pi / 24, -np.pi / 48],  # inverse of above (not locally equivalent)
+            [np.pi / 6, np.pi / 12, -np.pi / 16],  # inside red polytope
+        ]
+    )
+    def test_siswap_special_points(self, p):


It's really good to see this test - also great to have very explicit testing of a load of points we know to be special.

ShellyGarion · 2023-03-06T14:34:03Z

qiskit/circuit/library/__init__.py

@@ -113,6 +113,7 @@
   SdgGate
   SwapGate
   iSwapGate
+   SiSwapGate


The SiSwap Gate should also be added to the documentation in this init file, and removed from the docs in circuit/library/standard_gates.
See the following PR: #9668

mtreinish · 2023-10-04T16:07:19Z

Is there any update on this? Is this something we want to target for 0.45.0?

evmckinney9 · 2024-03-28T04:12:18Z

Is there any update on this? Is this something we want to target for 0.45.0?

Hello, hoping this feature gets merged eventually.
Is there anything I might be able to do to help finalize this PR?
For reference, here is a notebook I use for compiling into the sqrtiswap basis with the changes from this PR that I have moved into a separate fork since I find this functionality very necessary.

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add siswap gate to standard gates

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Co-authored-by: Julien Gacon <gaconju@gmail.com>

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Structure of the synthesis library #9667

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ShellyGarion reviewed Mar 6, 2023

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Cryoris mentioned this pull request Aug 16, 2024

Support for PhasedXZ and sqrt(iSWAP) basis gates in GenericBackendV2 #12764

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ShellyGarion added synthesis mod: circuit Related to the core of the `QuantumCircuit` class or the circuit library labels Jan 1, 2025

	"""Return a numpy.array for the DCX gate."""
	"""Return a numpy.array for the :math:`\\sqrt{iSWAP}` gate."""

		Function from
		https://scipy-cookbook.readthedocs.io/items/Finding_Convex_Hull_Minimum_Point.html

two-qubit decomposition into sqrt(iSWAP) + approximation #9375

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two-qubit decomposition into sqrt(iSWAP) + approximation #9375

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ajavadia commented Jan 13, 2023 • edited Loading

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Pull Request Test Coverage Report for Build 4340575136

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ajavadia commented Feb 17, 2023

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mtreinish commented Oct 4, 2023

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