Add Clifford.from_matrix #9475

itoko · 2023-01-27T12:53:52Z

Add Clifford.from_matrix method that create a Clifford object from Clifford unitary matrix. More importantly, using this method internally, Clifford.__init__ is updated so that it can take any Gate object up to 3 qubits as long it supports to_matrix method, including parameterized gates such as Rz(pi/2), which were not convertible before. As a result, it fixes an issue in qiskit-experiments.

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coveralls · 2023-01-27T13:31:01Z

Pull Request Test Coverage Report for Build 4676599158

123 of 147 (83.67%) changed or added relevant lines in 2 files are covered.
3 unchanged lines in 2 files lost coverage.
Overall coverage decreased (-0.004%) to 85.432%

Changes Missing Coverage	Covered Lines	Changed/Added Lines	%
qiskit/quantum_info/operators/symplectic/clifford.py	72	82	87.8%
qiskit/quantum_info/operators/symplectic/clifford_circuits.py	51	65	78.46%

Files with Coverage Reduction	New Missed Lines	%
qiskit/transpiler/passes/synthesis/unitary_synthesis.py	1	95.14%
qiskit/extensions/quantum_initializer/squ.py	2	80.0%

Totals
Change from base Build 4672911381:	-0.004%
Covered Lines:	67947
Relevant Lines:	79533

💛 - Coveralls

ShellyGarion · 2023-01-30T12:17:18Z

Why do you need to add a general method to the Clifford class? and not add specific additional Clifford gates (like: Rz(pi), ECRGate, iSwapGate) to the equivalence library, where you can add a decomposition of these gates into other Clifford gates?

alexanderivrii · 2023-01-30T15:09:05Z

qiskit/quantum_info/operators/symplectic/clifford_circuits.py

-    # are a single qubit Clifford gate rather than raise an exception.
+    # If the gate is not in predefined basis gates but with up to 3 qubits,
+    # we try to construct a Clifford to be appended from its matrix representation.
+    if isinstance(gate, Gate) and len(qargs) <= 3:


Hi, a quick question. With the current order of if-statements, would the new code be executed even for gates that already have a definition? I have not done any experiments, but it feels that constructing a Clifford from a matrix could be slower than constructing a Clifford from the defining quantum circuit.

Good question. I know construction from definition is faster if possible but it does not always work because the definition may contain non-Clifford gates. For example, the definition of ECRGate contains RZX(pi/4), which is not a Clifford. The definition of a gate is up to the gate designer, so we cannot fully rely on it. And I just prioritize capability to performance in this commit.

Another suggestion would be to manually define all the relevant gates here:
https://github.com/Qiskit/qiskit-terra/blob/main/qiskit/quantum_info/operators/symplectic/clifford_circuits.py
(you can check both gate name and parameters, and see if they fit one of the known patterns)

If I understand correctly from the tests, there about 10-15 gates, where theta is an integer product of pi/2 or pi, right?

Thanks! I was merely suggesting to change the order of checks:

if gate.definition is not None: return _append_circuit(clifford, gate.definition, qargs) try: # new code here raise QiskitError(f"Cannot apply {gate}")

If we change the order of check, we may need to copy clifford and when we have any exception, i.e. we fails to all-Clifford decomposition (based on definition), we need to restore the clifford that was before trying unroll. So the actual code would require more lines, but it's possible, so I'll try that in another branch for comparison.

@alexanderivrii I've tried the implementation that changes the order of check in this branch. I've confirmed that it gets faster by increasing the complexity of the implementation. Do you want to include the change in this PR?

It's generally good to add more gate (like Rz(pi/2) and u for angles that are multiples of pi/2) to clifford_circuits.py.
My PR #9623 may also be useful. Would you like to add other gates (also with parameters) directly to clifford_circuits.py?

@ShellyGarion I'm not thinking adding more _append_* to clifford_circuits.py is the best approach but it should a option to be considered for improving the performance of Clifford.from_circuit (see my comment in #9582 for other options). Let's continue to discuss it in #9582.

Regarding the order of check, I've added at b64d969 with the conversion of U gate c4bc00a

alexanderivrii · 2023-01-30T15:11:41Z

qiskit/quantum_info/operators/symplectic/clifford.py

+                    break
+            else:
+                raise QiskitError("Non-Clifford matrix is not convertible")
+


One more quick question. I have not done the math, but I am wondering if it's possible to check whether a given matrix (here U * Xi * Udg) is close to some Pauli matrix without explicitly going over all of the Pauli matrices?

These lines are using a bit strange grammar of Python: This else clause is coupled with for not if. So they do go over all of the Pauli matrices.

Sorry, I did not highlight the right lines. I believe (but I have not done the math) that the (tensor products of) Pauli matrices are very special unitary matrices, and it should be possible to check whether a given matrix (either U * Xi * Udg or U * Zi * Udg) is close to a Pauli matrix without explicitly checking np.close() against the 2*4^n Pauli matrices.

Yeah, I'm a bit concerned that there may be a more efficient algorithm then current one. If anyone knows such an algorithm, please let me know.

I believe that if you look at the 2^N x 2^N unitary matrix corresponding to a Pauli matrix, then this unitary matrix must have only one nonzero entry in every row and every column, moreover each nonzero element can only be 1, -1, i or -i. Intuitively, I think this should be enough to work out the exact Pauli.

Great suggestion, thanks! The new algorithm should be

Check if the U * Xi * Udg (or U * Zi * Udg) has exactly 2^N non-zero (i.e. 1, -1, i or -i) elements (if not, U is non-Clifford)

Reconstruct the Pauli string (a row of the resulting tableau) from the positions and values of the 2^N non-zero elements (if impossible, U is non-Clifford)

Hence, we don't need to create the table with 2^N x 2^N matrices corresponding 4^N Paulis in advance. I'll try the above algorithm.

Thank you! Here are my five cents (and @ikkoham and @ShellyGarion are welcome to correct this):

If a gate is going to be used a lot, it might be best to provide methods that directly operate on the Clifford tableau (like what is done in _append_cx or _append_w )

However, having a generic fallback mechanism is a great idea, so I think this development is very useful

If the gate has a definition, then it might be more efficient to consider the definition first, before constructing the unitary matrix and converting it to Clifford. On the other hand, it is possible that the default definition of a Clifford gate might contain non-Clifford gates, so the construction based on the definition alone might not be possible

Regarding the more efficient O(4^n) (instead of O(16^n)) algorithm, implemented at bad10de

itoko · 2023-01-31T01:17:50Z

Excuse me for my short explanation @ShellyGarion .
It's for catching all cases without increasing the maintenance cost.
I just prioritize capability to performance in this commit.

With this, we no longer need to update Clifford class or an equivalence library when we introduce a new gate in future (at least up to 3 qubits). I'm not sure the equivalence library approach works well for parameterized gates (e.g. what should we do for RZGate(5*pi/2)?).

Another good use case for this new function is construction from a custom gate (suggested by @nkanazawa1989). The previous logic rely on the gate name, so for example when we define a custom cx gate subclassing the standard CXGate, class CustomCX(CXGate), and instantiate with a different name, custom_cx = CustomCX(name="custom_cx"), we were not able to do Clifford(custom_cx). With this commit, we can do that since the CustomCX inherits the matrix definition of the standard CXGate.

itoko · 2023-02-10T14:24:01Z

I've tried a new algorithm suggested by @alexanderivrii in another branch and confirmed it works well, i.e it's much faster than the naive algorithm currently implemented as expected (see the benchmark results in the link).
So I'll update this pull-request to use the new algorithm.

kdk

Thanks @itoko , this will be a nice improvement. I think @ShellyGarion 's comment is hinting that another thing that would be nice to have is something like Clifford.from_operation or similar, that could rely on methods that might be quicker than generating and checking the unitary matrix representation.

For example, checking if the name is in the list of hard coded names in _BASIS_1Q/_BASIS_2Q to know if an Instruction is Clifford, or utilizing the equivalence library to see if a Gate has an all Clifford decomposition, or for cases like the parameterized rotations where there may be a simple arithmetic check on the params to know if it is Clifford.

It doesn't look like this is necessary for this PR though, so I will open a new issue for it.

ShellyGarion · 2023-02-15T09:32:29Z

According to tests we have 3 types of gates to handle:

The gate ECRGate() - this gate can be added to the file clifford_circuits.py as described in Add ECR/iSwap to list of gates handled by Clifford.from_circuit #9582
Gates that are not in the clifford_circuits.py but their definition contains only Clifford gates, so they are automatically converted into Cliffords (but we can easily add them to the file if needed):

            CYGate(),
            iSwapGate(),
            SXGate
            SXdgGate

Gates that are Cliffords only for certain parameters (e.g. an integer multiplication of pi or pi/2).
Perhaps they can also be added to the file clifford_circuits.py, defining new lists of gates:
_BASIS_1Q_with_params and _BASIS_2Q_with_params, and check both the gate name and the gate params here.

            RXGate(theta=np.pi / 2),
            RYGate(theta=np.pi / 2),
            RZGate(phi=np.pi / 2),
            CPhaseGate(theta=np.pi),
            CRXGate(theta=np.pi),
            CRYGate(theta=np.pi),
            CRZGate(theta=np.pi),
            RXXGate(theta=np.pi / 2),
            RYYGate(theta=np.pi / 2),
            RZZGate(theta=np.pi / 2),
            RZXGate(theta=np.pi / 2),
            XXMinusYYGate(theta=np.pi),
            XXPlusYYGate(theta=-np.pi),

Only if a gate does not fit anyone of these conventions, one will use the suggested Clifford.from_matrix() method.

itoko · 2023-02-15T14:59:33Z

@ShellyGarion I think the above comment is a good starting point of the discussion on #9576 , while I think it is beyond the scope of this PR. Let me focus on the addition of Clifford.from_matrix function and its minimal use (fallback function for _append_operation) in this PR.

ikkoham

Thank you. Great work. The direction looks good to me. Could you implement from_operator method as well for consistency in quantum_info.

qiskit/quantum_info/operators/symplectic/clifford_circuits.py

ikkoham · 2023-02-21T11:59:44Z

qiskit/quantum_info/operators/symplectic/clifford_circuits.py

+
+
+def _n_half_pis(param) -> int:
+    try:


How about if not isinstance(param, ParameterExpression)?

We need to try cast here because that checks if a ParameterExpression is bounded or not (not checking the type of param).

itoko · 2023-02-22T05:23:44Z

@ikkoham I've updated based on the review comment. Could you take a final look?

…atrix

test/python/quantum_info/operators/symplectic/test_clifford.py

ikkoham

LGTM! Perhaps performance could be improved, but I can't think of any idea right now and will leave it open for future work.

ikkoham · 2023-04-12T09:01:05Z

test/python/quantum_info/operators/symplectic/test_clifford.py

@@ -989,13 +1037,58 @@ def test_instruction_name(self, num_qubits):
        clifford = random_clifford(num_qubits, seed=777)
        self.assertEqual(clifford.to_instruction().name, str(clifford))

-    def visualize_does_not_throw_error(self):
+    def test_visualize_does_not_throw_error(self):


Nice catch!

* Add Clifford.from_matrix * Add tests * Add reno * Faster Clifford.from_matrix O(16^n)->O(4^n) * Add infinite recursion test case * Change to try append with definition first * Add u gate handling for speed * Improve implematation following review comments * Add Clifford.from_operator * Update reno * Lint * more accurate reno --------- Co-authored-by: Ikko Hamamura <[email protected]>

Add Clifford.from_matrix

37bce39

itoko mentioned this pull request Jan 30, 2023

RB experiment fails to interleave specific Clifford gates qiskit-community/qiskit-experiments#1028

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itoko added 2 commits January 30, 2023 17:41

Add tests

6019306

Add reno

dba2eff

itoko marked this pull request as ready for review January 30, 2023 09:42

itoko requested review from a team and ikkoham as code owners January 30, 2023 09:42

ikkoham added Changelog: New Feature Include in the "Added" section of the changelog mod: quantum info Related to the Quantum Info module (States & Operators) labels Jan 30, 2023

ikkoham added this to the 0.24.0 milestone Jan 30, 2023

alexanderivrii reviewed Jan 30, 2023

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This was referenced Feb 13, 2023

Add Clifford.from_operation to shortcut checking matrix representation #9576

Open

Add ECR/iSwap to list of gates handled by Clifford.from_circuit #9582

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itoko added 2 commits February 15, 2023 20:17

Faster Clifford.from_matrix O(16^n)->O(4^n)

bad10de

Add infinite recursion test case

7a0c373

ShellyGarion mentioned this pull request Feb 19, 2023

Add the gates ECR, iSwap, CY, SX, SXdg, DCX to the Clifford class #9623

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itoko added 2 commits February 21, 2023 20:41

Change to try append with definition first

b64d969

Add u gate handling for speed

c4bc00a

ikkoham reviewed Feb 21, 2023

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Improve implematation following review comments

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Add Clifford.from_operator

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itoko added 3 commits February 24, 2023 00:11

Merge remote-tracking branch 'upstream/main' into add-clifford-from-m…

577f306

…atrix

Update reno

96af80b

Lint

c34d9ca

ShellyGarion reviewed Feb 24, 2023

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test/python/quantum_info/operators/symplectic/test_clifford.py Show resolved Hide resolved

more accurate reno

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coruscating mentioned this pull request Mar 22, 2023

Clifford Mirror RB experiment qiskit-community/qiskit-experiments#1090

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ikkoham approved these changes Apr 12, 2023

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Merge branch 'main' into add-clifford-from-matrix

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ikkoham enabled auto-merge April 12, 2023 09:18

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Merged via the queue into Qiskit:main with commit 6392665 Apr 12, 2023

alexanderivrii mentioned this pull request May 1, 2023

Linear function usability improvements #10053

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jakelishman mentioned this pull request Jul 11, 2023

Cyclic-definition checking in Clifford segfaults Python on Windows #10415

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ShellyGarion mentioned this pull request Mar 27, 2024

Pauli.evolve() should recognize common rotations by (n*pi/2) as Clifford gates #12085

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