Add partial transpose function in quantum_info #9566

PayalSolanki2906 · 2023-02-10T12:25:29Z

Summary

The partial transpose of a density matrix is a mathematical operation that transforms the matrix by interchanging only certain indices of the matrix elements. This operation is significant in the study of quantum entanglement as it provides information about the entanglement structure of a quantum system, with positive partial transpose indicating separable states and negative partial transpose indicating entangled states.

Details and comments

I and @pranay1990 have contributed to this code. We have added a new function named partial_transpose in quantum_info (under utility functions).

qiskit-bot · 2023-02-10T12:25:33Z

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CLAassistant · 2023-02-10T12:25:34Z

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coveralls · 2023-02-13T07:34:51Z

Pull Request Test Coverage Report for Build 4706198971

10 of 10 (100.0%) changed or added relevant lines in 1 file are covered.
29 unchanged lines in 3 files lost coverage.
Overall coverage increased (+0.009%) to 85.793%

Files with Coverage Reduction	New Missed Lines	%
crates/accelerate/src/sabre_swap/layer.rs	4	97.32%
crates/qasm2/src/lex.rs	7	90.13%
crates/qasm2/src/parse.rs	18	96.65%

Totals
Change from base Build 4704167625:	0.009%
Covered Lines:	70498
Relevant Lines:	82172

💛 - Coveralls

Cryoris

Thanks for your contribution! I left some general comments below 🙂

Cryoris · 2023-02-14T07:34:36Z

qiskit/quantum_info/states/utils.py

+        raise QiskitError("Indices of subsystems to be transposed are invalid")
+    ptden = np.empty((2**n, 2**n), complex)
+    ptden[:] = np.nan
+    if isinstance(state, Statevector):


I don't quite understand what a partial transpose of a vector is, do you have a definition for this? 🙂 Maybe this operation should only be supported for actual DensityMatrix objects, as you also mentioned in the typehint?

Hey @Cryoris, it seems what you're saying is true. We had considered allowing input as a Statevector and converting it to a pure state density matrix, similar to partial trace code. However, if you're suggesting that it's not necessary, we can remove that option. Please let us know.

If a user would like to do that they could always construct the DensityMatrix explicitly and then use your function:

dm = DensityMatrix(state) partial_transpose(dm, ...)

so I think you don't have to cover this case here 🙂

Cryoris · 2023-02-14T07:44:18Z

qiskit/quantum_info/states/utils.py

+        for i in range(2**n):
+            for j in range(2**n):
+                if math.isnan(ptden[i, j]):


Could this loop be made more efficient by only visiting entries that we know need to be populated, or maybe transposing sub-blocks of the matrix all at once? As it is now, this scales as 2 ^ (2n) which is going to be very expensive.

We will try to optimize it.

For most operators, I would imagine you can do this in vectorised Numpy by casting state.data (a Numpy array) to a multi-dimensional tensor (e.g. using np.reshape(state.data, state._op_shape.tensor_shape) or something like that), calling np.transpose as appropriate, then restoring it to be a 2D array. If that's correct, then that should be much faster than looping in Python space.

quantum_info.Operator also isn't guaranteed to be square. I don't think the partial trace is reasonably defined for tensor-product spaces where the number of input and output spaces are unequal, but it could in theory work for things like a mapping of a (2, 3) Hilbert space to a (1, 4) one. Probably best not to worry about that, though, and just error out if the dims_r of the OpShape aren't equal to the dims_l.

@jakelishman This helps. Thank you.

Cryoris · 2023-02-14T07:46:56Z

qiskit/quantum_info/states/utils.py

+    """
+    state = _format_state(state, validate=False)
+    n = len(state.dims())
+    lst = np.zeros(2**n, int)


The DensityMatrix also allows qudit subsystems (see the dims argument 🙂), but in this implementation you assume qubits. We'd either have to add a check that the input density matrix is defined on qubits or generalize this code to work on arbitrary dimensions.

Thank you for bringing this to our attention. We will take steps to rectify the issue.

PayalSolanki2906 · 2023-03-01T08:27:46Z

@ikkoham requested changes have been incorporated, and we kindly request your assistance for further process.

pranay1990 · 2023-03-21T05:58:58Z

@ikkoham, @Cryoris, and @jakelishman, could any one of you please tell us what is the progress regarding the pull request?

ikkoham

Thank you. Sorry for late. This direction looks good to me.
inplace option can be optional and feature request in the future.

I left some comments.

ikkoham · 2023-03-23T12:40:46Z

qiskit/quantum_info/states/densitymatrix.py

+        """
+        from qiskit.quantum_info.states import utils
+
+        state = utils._format_state(self, validate=False)


Why do you need _format_state and reshape? self is DensityMatrix by definition.

ikkoham · 2023-03-23T12:44:18Z

test/python/quantum_info/states/test_densitymatrix.py

+        rho1[4, 5] = 0.5
+        rho1[5, 4] = 0.5
+        rho1[5, 5] = 0.5
+        self.assertEqual(DensityMatrix.partial_transpose(rho, [0, 1]), DensityMatrix(rho1))


DensityMatrix.partial_transpose is not classmethod, so DensityMatrix(rho).partial_transpose([0, 1]) is correct.

ikkoham · 2023-04-12T14:18:17Z

@PayalSolanki2906 @pranay1990 Thank you for your great contributions. I would like to merge this PR for 0.24. Please check my PR to your repo. PayalSolanki2906#1

Finalize the PR

pranay1990 · 2023-04-13T07:37:46Z

Thank you for allowing us to make our first contribution. We sincerely appreciate the support and guidance provided during the process, which made it very smooth for us. We are eager to continue contributing in the future and look forward to working with you again.

pranay1990 · 2023-04-13T07:51:34Z

Hi @ikkoham, after this pull request is merged, we would be interested in contributing towards the implementation of logarithmic negativity as an entanglement measure. We would appreciate your input on whether this is a feasible addition and would be grateful for any guidance or feedback you may have. Thank you for your time and consideration.

ikkoham

Thank you! LGTM.

For the log negativity, I think a function would be nice (not method), but let's discuss. I would be glad if you could make an issue,

* partial_transpose included * included partial_transpose * included partial_transpose * included partial_transpose * included partial_transpose * included partial_transpose * included partial_transpose * included partial_transpose * included partial_transpose * included partial_transpose * included partial_transpose * included partial_transpose * included test for partial transpose * included test for partial transpose * included test for partial transpose * added docstring * included DensityMatrix(rho1) * changed rho1 * addition of release note * fix * fix * fir partial_transpose * Update utils.py * refactor and add tests --------- Co-authored-by: Ikko Hamamura <ikkoham@users.noreply.github.com>

diemilio · 2023-05-24T15:55:26Z

Hello @ikkoham, @PayalSolanki2906, @pranay1990. I just bump into this new partial_transpose feature while searching thru the qiskit repo because it shares some similarities with the PR I am working on. While looking at the code, I noticed a small issue. If the density matrix is not for a qubit system (i.e., the dimensions are not for 2-level systems), the output density matrix will have different dimensions wrt the input density matrix.

This can be easily fixed by just having the function return

return DensityMatrix(rho, dims=self.dims())

Not sure if a separate PR needs to be issued since this one has already been merged, but happy to help if needed.

jakelishman · 2023-05-24T17:00:47Z

Diego: if there's a bug, we'll need a PR to fix it. Could you open an issue with an example showing the bug, then you (or us, if you don't have time) can make a PR fixing it.

PayalSolanki2906 added 19 commits February 9, 2023 20:33

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PayalSolanki2906 requested review from a team and ikkoham as code owners February 10, 2023 12:25

qiskit-bot added the Community PR PRs from contributors that are not 'members' of the Qiskit repo label Feb 10, 2023

woodsp-ibm added Changelog: New Feature Include in the "Added" section of the changelog mod: quantum info Related to the Quantum Info module (States & Operators) labels Feb 10, 2023

Merge branch 'main' into pp-parttr

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Merge branch 'main' into pp-parttr

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Cryoris reviewed Feb 14, 2023

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PayalSolanki2906 requested review from ikkoham and jakelishman and removed request for Cryoris, ikkoham and jakelishman February 20, 2023 12:20

ikkoham reviewed Mar 23, 2023

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ikkoham added this to the 0.24.0 milestone Mar 23, 2023

ikkoham self-assigned this Apr 12, 2023

ikkoham added 2 commits April 12, 2023 18:24

Merge branch 'main' into pp-parttr

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refactor and add tests

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ikkoham mentioned this pull request Apr 12, 2023

Finalize the PR PayalSolanki2906/qiskit-terra#1

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PayalSolanki2906 added 2 commits April 13, 2023 12:15

Merge pull request #1 from ikkoham/pp-parttr

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Finalize the PR

Merge branch 'main' into pp-parttr

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Merge branch 'main' into pp-parttr

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Merged via the queue into Qiskit:main with commit 580590f Apr 17, 2023

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Add partial transpose function in quantum_info #9566

Add partial transpose function in quantum_info #9566

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Add partial transpose function in quantum_info #9566

Add partial transpose function in quantum_info #9566

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PayalSolanki2906 commented Feb 10, 2023

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