Basis ordering (#237)

* first working version

* puts all the tests in the same class

* making bots happy

* updates autosummary

* One extra test

* updates changelog

* Fixes error message

* Update thewalrus/symplectic.py

Co-authored-by: Josh Izaac <[email protected]>

* Update thewalrus/symplectic.py

Co-authored-by: Josh Izaac <[email protected]>

* Update thewalrus/symplectic.py

Co-authored-by: Josh Izaac <[email protected]>

.github/CHANGELOG.md

@@ -11,6 +11,8 @@
 
 * Adds new functions `total_photon_number_distribution` and `characteristic_function` to study properties of the total photon number distribution of a `k` identical lossy squeezers. [#230](https://github.com/XanaduAI/thewalrus/pull/230/)
 
+* Adds new functions `xxpp_to_xpxp` and `xpxp_to_xxpp` in the `symplectic` module to swap the ordering of the quadrature operators in vectors and matrices. [#237](https://github.com/XanaduAI/thewalrus/pull/237/)
+
 
 ### Improvements
 

thewalrus/symplectic.py

@@ -30,6 +30,8 @@
     reduced_state
     is_symplectic
     sympmat
+    xxpp_to_xpxp
+    xpxp_to_xxpp
 
 Gaussian states
 ---------------
@@ -361,3 +363,53 @@ def autonne(A, rtol=1e-05, atol=1e-08, svd_order=True):
     if svd_order:
         return (vals[n : 2 * n])[::-1], U[:, ::-1]
     return vals[n : 2 * n], U
+
+def xxpp_to_xpxp(S):
+    """Permutes the entries of the input from xxpp ordering to xpxp ordering.
+
+    Args:
+        S (array): input even dimensional square matrix or array
+
+    Returns:
+        (array): permuted matrix or array
+    """
+    shape = S.shape
+    n = shape[0]
+
+    if n % 2 != 0:
+        raise ValueError("The input array is not even-dimensional")
+
+    n = n // 2
+    ind = np.arange(2 * n).reshape(2, -1).T.flatten()
+
+    if len(shape) == 2:
+        if shape[0] != shape[1]:
+            raise ValueError("The input matrix is not square")
+        return S[:, ind][ind]
+
+    return S[ind]
+
+def xpxp_to_xxpp(S):
+    """Permutes the entries of the input from xpxp ordering to xxpp ordering.
+
+    Args:
+        S (array): input even dimensional square matrix or vector
+
+    Returns:
+        (array): permuted matrix or vector
+    """
+    shape = S.shape
+    n = shape[0]
+
+    if n % 2 != 0:
+        raise ValueError("The input array is not even-dimensional")
+
+    n = n // 2
+    ind = np.arange(2 * n).reshape(-1, 2).T.flatten()
+
+    if len(shape) == 2:
+        if shape[0] != shape[1]:
+            raise ValueError("The input matrix is not square")
+        return S[:, ind][ind]
+
+    return S[ind]

thewalrus/tests/test_symplectic.py

@@ -658,3 +658,57 @@ def test_autonne_error():
     A = np.random.rand(n, m)
     with pytest.raises(ValueError, match="The input matrix is not symmetric"):
         symplectic.autonne(A)
+
+
+class TestPhaseSpaceFunctions:
+    """Tests for the shared phase space operations"""
+
+    def test_means_changebasis(self):
+        """Test the change of basis function applied to vectors. This function
+        converts from xp to symmetric ordering, and vice versa."""
+        means_xp = np.array([1, 2, 3, 4, 5, 6])
+        means_symmetric = np.array([1, 4, 2, 5, 3, 6])
+
+        assert np.all(symplectic.xxpp_to_xpxp(means_xp) == means_symmetric)
+        assert np.all(symplectic.xpxp_to_xxpp(means_symmetric) == means_xp)
+
+    def test_cov_changebasis(self):
+        """Test the change of basis function applied to matrices. This function
+        converts from xp to symmetric ordering, and vice versa."""
+        cov_xp = np.array(
+            [[0, 1, 2, 3], [4, 5, 6, 7], [8, 9, 10, 11], [12, 13, 14, 15]]
+        )
+
+        cov_symmetric = np.array(
+            [[0, 2, 1, 3], [8, 10, 9, 11], [4, 6, 5, 7], [12, 14, 13, 15]]
+        )
+
+        assert np.all(symplectic.xxpp_to_xpxp(cov_xp) == cov_symmetric)
+        assert np.all(symplectic.xpxp_to_xxpp(cov_symmetric) == cov_xp)
+
+    @pytest.mark.parametrize("fun", [symplectic.xxpp_to_xpxp, symplectic.xpxp_to_xxpp])
+    def test_change_basis_raises_not_square(self, fun):
+        """Test correct error is raised when a non-square matrix is passed"""
+        A = np.random.rand(4,6)
+        with pytest.raises(ValueError, match="The input matrix is not square"):
+            fun(A)
+
+    @pytest.mark.parametrize("fun", [symplectic.xxpp_to_xpxp, symplectic.xpxp_to_xxpp])
+    @pytest.mark.parametrize("dim", [1, 2])
+    def test_change_basis_raises_not_even(self, fun, dim):
+        """Test correct error is raised when a non-even-dimensional array is passed"""
+        size = (5,) * dim
+        A = np.random.rand(*size)
+        with pytest.raises(ValueError, match="The input array is not even-dimensional"):
+            fun(A)
+
+    @pytest.mark.parametrize("dim", [2, 4, 6, 8])
+    def test_functional_inverse(self, dim):
+        """Check that xxpp_to_xpxp is the inverse of xpxp_to_xxpp and viceversa"""
+        M = np.random.rand(dim, dim)
+        assert np.all(M == symplectic.xxpp_to_xpxp(symplectic.xpxp_to_xxpp(M)))
+        assert np.all(M == symplectic.xpxp_to_xxpp(symplectic.xxpp_to_xpxp(M)))
+
+        v = np.random.rand(dim)
+        assert np.all(v == symplectic.xxpp_to_xpxp(symplectic.xpxp_to_xxpp(v)))
+        assert np.all(v == symplectic.xpxp_to_xxpp(symplectic.xxpp_to_xpxp(v)))