Feature/bures distance [unitaryHACK] by victor-onofre · Pull Request #60 · vprusso/toqito

victor-onofre · 2021-05-15T02:28:26Z

Description

This function takes as input two density matrices and performs the following calculation:

from toqito.state_metrics import fidelity

np.sqrt(2.0 * (1.0 - fidelity(rho_1, rho_2)))

where rho_1 and rho_2 are density operators and where the fidelity function comes from toqito.state_metrics.fidelity.

Todos

Compute the bures distance
When rho_1 = rho_2, fidelity(rho_1, rho_2) = 1.0000000000000002. This will create an error in the sqrt. I added the round function to the 10 decimal to avoid it.
I added the tests for the function in tests/test_state_metrics/test_bures_distance.py
I added from toqito.state_metrics.bures_distance import bures_distance to toqito/state_metrics/__init__.py

Questions

Perhaps add something in the fidelity function for the case rho_1 = rho_2 and avoid the numeric error 1.0000000000000002. That 2 may cause problems somewhere else.

Status

Ready to go

codecov · 2021-05-15T02:34:47Z

Codecov Report

Merging #60 (937018e) into master (57bd2ef) will increase coverage by 0.3%.
The diff coverage is 100.0%.

@@           Coverage Diff            @@
##           master     #60     +/-   ##
========================================
+ Coverage    98.3%   98.7%   +0.3%     
========================================
  Files         116     117      +1     
  Lines        2142    2159     +17     
  Branches      494     499      +5     
========================================
+ Hits         2107    2131     +24     
+ Misses         18      12      -6     
+ Partials       17      16      -1

Impacted Files	Coverage Δ
toqito/state_metrics/bures_distance.py	`100.0% <100.0%> (ø)`
toqito/state_ops/schmidt_decomposition.py	`92.5% <0.0%> (+7.7%)`	⬆️
toqito/state_props/is_product_vector.py	`96.9% <0.0%> (+9.0%)`	⬆️
toqito/state_props/schmidt_rank.py	`96.6% <0.0%> (+12.0%)`	⬆️

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vprusso · 2021-05-15T15:11:05Z

+    if round_fidelity > 1 :
+        raise ValueError("Numeric Error: fidelity(rho_1, rho_2) greater than 1")
+
+    distance =  np.sqrt(2.0 * (1.0 - round_fidelity))


Can simplify these lines by just returning the calculation--that is:

return np.sqrt(2.0 * (1.0 - round_fidelity))

vprusso · 2021-05-15T15:11:31Z

+        raise ValueError("InvalidDim: `rho_1` and `rho_2` must be matrices of the same size.")
+
+    # Round fidelity to only 10 decimals to avoid error when rho_1 = rho_2
+    round_fidelity =  round(fidelity(rho_1, rho_2),10)


Space between , and 10.

vprusso · 2021-05-15T15:13:27Z

+    Calculate the bures distance between the two density matrices : rho_1 and rho_2, defined
+    by:
+
+     D = sqrt(2 * (1 - fidelity(rho_1, rho_2) ) )


Ideally, this should be formatted using LaTeX such as:

.. math:: \sqrt{2 (1 - F(\rho_1, \rho_2)}

where :math:F(\cdot) is the fidelity function and where :math:\rho_1 and :math:\rho_2 are density operators.

vprusso · 2021-05-15T15:13:51Z

+
+def bures_distance(rho_1: np.ndarray, rho_2: np.ndarray ) -> float:
+    r"""
+    Calculate the bures distance between the two density matrices : rho_1 and rho_2, defined


This is one of the lines the liner is complaining about being too long I think.

vprusso · 2021-05-15T15:15:00Z

@@ -0,0 +1,61 @@
+"""Tests for bures distance."""


bures distance -> bures_distance.

vprusso · 2021-05-16T00:02:24Z

+
+from toqito.state_metrics import fidelity
+
+def bures_distance(rho_1: np.ndarray, rho_2: np.ndarray ) -> float:


Extra space between np.ndarray and ).

vprusso · 2021-05-16T00:02:34Z

+
+def bures_distance(rho_1: np.ndarray, rho_2: np.ndarray ) -> float:
+    r"""
+    Compute the bures distance of two density matrices [WikFid]_.


bures -> Bures.

vprusso · 2021-05-16T00:03:09Z

+
+def bures_distance(rho_1: np.ndarray, rho_2: np.ndarray ) -> float:
+    r"""
+    Compute the bures distance of two density matrices [WikFid]_.


[WikFid]_ should probably have something different like [WikBures]_.

I'm so sorry. I used the fidelity function as a template. I didn't notice the error. Next time I will write the docs from scratch to avoid this type of mistake.

vprusso · 2021-05-16T00:03:19Z

+    r"""
+    Compute the bures distance of two density matrices [WikFid]_.
+
+    Calculate the bures distance between the two density matrices:


bures -> Bures.

vprusso · 2021-05-16T00:04:40Z

+    Compute the bures distance of two density matrices [WikFid]_.
+
+    Calculate the bures distance between the two density matrices:
+    `rho_1` and `rho_2`, defined by:


Should be ":code:`rho_1`" and ":code:`rho_2`".

vprusso · 2021-05-16T00:11:36Z

+
+    :param rho_1: Density operator.
+    :param rho_2: Density operator.
+    :return: The Bures distance between :code:`rho_1` and :code:`sigma_2`.


The Bures distance between :code:`rho_1` and :code:`rho_2`, right?

vprusso · 2021-05-16T00:12:11Z

+    :return: The Bures distance between :code:`rho_1` and :code:`sigma_2`.
+    """
+    # Perform some error checking.
+    if not np.all(rho_1.shape == (rho_2.shape)):


Redundant parens around (rho_2.shape)?

vprusso · 2021-05-16T00:13:24Z

+    if not np.all(rho_1.shape == (rho_2.shape)):
+        raise ValueError("InvalidDim: `rho_1` and `rho_2` must be matrices of the same size.")
+    # Round fidelity to only 10 decimals to avoid error when rho_1 = rho_2
+    return np.sqrt(2.0 * (1.0 - round(fidelity(rho_1, rho_2), 10) ))


Consider using np.around() as opposed to round(). Also, should use an optional parameter for decimal precision instead of something hardcoded. Refer to functions like is_hermitian for reference on how to do that.

vprusso · 2021-05-16T00:15:13Z

@@ -0,0 +1,61 @@
+"""Tests for bures_distance."""


I'm curious if there are any specific examples in the literature, academic course notes, etc. where the Bures distance is calculated between two different specific density matrices with a known result. That might be nice to add as a test case for a sanity check. One could also look at the unit tests for say the qutip package that also has a function for the bures_distance.

I checked the test in qutip but they don't have any specific test for the bures_dist. They only check an inequality, here is the test: https://github.com/qutip/qutip/blob/master/qutip/tests/test_metrics.py.

I have added an example for pure states shown in this book: Elements of Quantum Computation and Quantum Communication, the example is the 3.42 in the book. I couldn't find more examples but I will keep searching.

vprusso · 2021-05-16T00:16:05Z

+    e_0, e_1 = basis(2, 0), basis(2, 1)
+    rho = 3 / 4 * e_0 * e_0.conj().T + 1 / 4 * e_1 * e_1.conj().T
+    sigma = 1 / 8 * e_0 * e_0.conj().T + 7 / 8 * e_1 * e_1.conj().T
+    np.testing.assert_equal(np.isclose(bures_distance(rho, sigma), 0.6724, rtol=1e-03), True)


Nice to have cases like this, but I suppose aside from this value being arbitrarily the value that you see when you run is, is there any other way to verify that this value is indeed correct?

In this case, I used the qutip function bures_dist to compare the result.

vprusso · 2021-05-16T14:50:24Z

You'll also want to make sure that the bures_distance function gets picked up in the documentation generation. So in docs/states.rst make sure you add a line toqito.state_metrics.bures_distance under Distance Metrics for Quantum States.

vprusso · 2021-05-16T21:45:52Z

+    np.testing.assert_equal(np.isclose(res, 0), True)
+
+
+def test_bures_distance_cvx():


Running this test yields a failure. I don't believe you need to account for the case when the inputs are CVX-type objects, so I think you can safely remove this test so long as doing so does not decrease your overall testing coverage.

vprusso · 2021-05-16T21:46:33Z

+import numpy as np
+
+from toqito.state_metrics import fidelity
+


There should be an extra blank line between from toqito.state_metrics import fidelity and def bures_distance(rho_1: np.ndarray, rho_2: np.ndarray, decimals: int = 10) -> float: (PEP-8 requirement).

vprusso · 2021-05-16T21:47:21Z

+    if not np.all(rho_1.shape == rho_2.shape):
+        raise ValueError("InvalidDim: `rho_1` and `rho_2` must be matrices of the same size.")
+    # Round fidelity to only 10 decimals to avoid error when rho_1 = rho_2
+    return np.sqrt(2.0 * (1.0 - np.round(fidelity(rho_1, rho_2), decimals) ))


Extra space between the ) and )) closing parens.

vprusso · 2021-05-16T21:51:13Z

+    r"""
+    Compute the Bures distance of two density matrices [WikBures]_.
+
+    Calculate the Bures distance between the two density matrices:


Running the doc generation seems to yield an unexpected indentation warning. This paragraph should be formatted as:

Calculate the Bures distance between the two density matrices: :code:`rho_1` and :code:`rho_2`, defined by:

vprusso · 2021-05-16T21:52:55Z

+        \sqrt{2 (1 - F(\rho_1, \rho_2)},
+
+    where :math:`F(\cdot)` denotes the fidelity between :math:`\rho_1` and :math:`\rho_2`.
+    The return is a value between :math:`0` and :math:`\sqrt(2)`,with


You should alter the instances of \sqrt(2) to \sqrt{2} (note the ( and ) vs. the { and }.

vprusso · 2021-05-16T21:53:29Z

+                       \end{pmatrix} \in \text{D}(\mathcal{X}).
+
+    In the event where we calculate the Bures distance between states that are identical, we
+    should obtain the value of :math:`0`.This can be observed in :code:`toqito` as follows.


There is a missing space between the "." and the word "This"

vprusso · 2021-05-16T22:20:01Z

+    Calculate the Bures distance between the two density matrices:
+    ":code:`rho_1` and ":code:`rho_2`, defined by:
+    .. math::
+        \sqrt{2 (1 - F(\rho_1, \rho_2)},


Looks like there's a missing closing parens here.

victor-onofre added 3 commits May 14, 2021 18:55

function bures_distance

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test for bures_distance

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update __init__ for bures_distance

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vprusso reviewed May 15, 2021

View reviewed changes

victor-onofre added 10 commits May 15, 2021 13:21

updated function bures_distance

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updated test for bures_distance

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vprusso reviewed May 16, 2021

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victor-onofre added 4 commits May 16, 2021 12:19

updated docs for bures_distance

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update test for bures_distance

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updated function bures_distance

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updated function bures_distance

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vprusso reviewed May 16, 2021

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victor-onofre added 3 commits May 16, 2021 18:25

update test for bures_distance

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updated function bures_distance

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update test for bures_distance

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vprusso merged commit 17b272e into vprusso:master May 17, 2021


		from toqito.state_metrics import fidelity

		def bures_distance(rho_1: np.ndarray, rho_2: np.ndarray ) -> float:

		np.testing.assert_equal(np.isclose(res, 0), True)


		def test_bures_distance_cvx():

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victor-onofre commented May 15, 2021

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vprusso commented May 16, 2021

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codecov bot commented May 15, 2021 •

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