Remove cvxopt and use cvxpy instead (qiskit-community#1035)

* Remove cvxopt and use cvxpy instead

This commit removes the usage of cvxopt from aqua. It was supposed to be
removed as part of the 0.7 release since some users have issue
installing it, and other users aren't allowed to have GPL code installed
in their environment. However, cvxopt is still used for the quadratic
program solver utility. cvxopt is not needed to solve a quadratic
program and other elements are already doing this with cvxpy which
doesn't have the same issues [1][2]. This commit migrates the cvxopt
usage to cvxpy to be consistent with the rest of qiskit.

[1] Qiskit/qiskit-aer@e41d868
[2] qiskit-community/qiskit-ignis@42cbbf8

* fix lint, unit tests

* remove cvxopt from travis

Co-authored-by: Manoel Marques <manoel@us.ibm.com>
(cherry picked from commit b79f835)

Conflicts:
    .travis.yml
    test/aqua/test_qsvm.py

.travis.yml

@@ -148,7 +148,6 @@ jobs:
             - aqua137.dep
       before_script:
         - pip install cplex
-        - pip install cvxopt
         - export PYTHON="coverage3 run --source qiskit/aqua,qiskit/chemistry,qiskit/finance,qiskit/ml,qiskit/optimization --omit */gauopen/* --parallel-mode"
       script:
         - stestr --test-path test/aqua run --blacklist-file selection.txt 2> >(tee /dev/stderr out.txt > /dev/null)
@@ -163,8 +162,6 @@ jobs:
           name: aqua138
           paths: aqua138.dep
       python: 3.8
-      before_script:
-        - pip install cvxopt
       script:
         - stestr --test-path test/aqua run --blacklist-file selection.txt 2> >(tee /dev/stderr out.txt > /dev/null)
         - python tools/extract_deprecation.py -file out.txt -output aqua138.dep
@@ -179,7 +176,6 @@ jobs:
             - aqua237.dep
       before_script:
         - pip install cplex
-        - pip install cvxopt
         - export PYTHON="coverage3 run --source qiskit/aqua,qiskit/chemistry,qiskit/finance,qiskit/ml,qiskit/optimization --omit */gauopen/* --parallel-mode"
       script:
         - stestr --test-path test/aqua run --whitelist-file selection.txt 2> >(tee /dev/stderr out.txt > /dev/null)
@@ -194,8 +190,6 @@ jobs:
           name: aqua238
           paths: aqua238.dep
       python: 3.8
-      before_script:
-        - pip install cvxopt
       script:
         - stestr --test-path test/aqua run --whitelist-file selection.txt 2> >(tee /dev/stderr out.txt > /dev/null)
         - python tools/extract_deprecation.py -file out.txt -output aqua238.dep

qiskit/aqua/utils/qp_solver.py

@@ -16,17 +16,12 @@
 
 from typing import Optional, Tuple
 import logging
+
 import numpy as np
+import cvxpy
 
 logger = logging.getLogger(__name__)
 
-_HAS_CVXOPT = False
-try:
-    from cvxopt import matrix, solvers
-    _HAS_CVXOPT = True
-except ImportError:
-    logger.info('CVXOPT is not installed. See http://cvxopt.org/install/index.html')
-
 
 def optimize_svm(kernel_matrix: np.ndarray,
                  y: np.ndarray,
@@ -36,9 +31,6 @@ def optimize_svm(kernel_matrix: np.ndarray,
     """
     Solving quadratic programming problem for SVM; thus, some constraints are fixed.
 
-    The notation is follows the equation here:
-    http://cvxopt.org/userguide/coneprog.html#quadratic-programming
-
     Args:
         kernel_matrix: NxN array
         y: Nx1 array
@@ -51,13 +43,8 @@ def optimize_svm(kernel_matrix: np.ndarray,
         np.ndarray: Sx1 array, where S is the number of supports
         np.ndarray: Sx1 array, where S is the number of supports
         np.ndarray: Sx1 array, where S is the number of supports
-
-    Raises:
-        NameError: CVXOPT not installed.
     """
-    # pylint: disable=invalid-name
-    if not _HAS_CVXOPT:
-        raise NameError('CVXOPT is not installed. See http://cvxopt.org/install/index.html')
+    # pylint: disable=invalid-name, unused-argument
     if y.ndim == 1:
         y = y[:, np.newaxis]
     H = np.outer(y, y) * kernel_matrix
@@ -69,17 +56,20 @@ def optimize_svm(kernel_matrix: np.ndarray,
     tolerance = 1e-2
     n = kernel_matrix.shape[1]
 
-    P = matrix(H)
-    q = matrix(f)
-    G = matrix(-np.eye(n))
-    h = matrix(np.zeros(n))
-    A = matrix(y, y.T.shape)
-    b = matrix(np.zeros(1), (1, 1))
-    solvers.options['maxiters'] = max_iters
-    solvers.options['show_progress'] = show_progress
-
-    ret = solvers.qp(P, q, G, h, A, b, kktsolver='ldl')
-    alpha = np.asarray(ret['x']) * scaling
+    P = np.array(H)
+    q = np.array(f)
+    G = -np.eye(n)
+    h = np.zeros(n)
+    A = y.reshape(y.T.shape)
+    b = np.zeros((1, 1))
+    x = cvxpy.Variable(n)
+    prob = cvxpy.Problem(
+        cvxpy.Minimize((1 / 2) * cvxpy.quad_form(x, P) + q.T@x),
+        [G@x <= h,
+         A@x == b])
+    prob.solve(verbose=show_progress)
+    result = np.asarray(x.value).reshape((n, 1))
+    alpha = result * scaling
     avg_y = np.sum(y)
     avg_mat = (alpha * y).T.dot(kernel_matrix.dot(np.ones(y.shape)))
     b = (avg_y - avg_mat) / n

setup.py

@@ -41,6 +41,7 @@
     "h5py",
     "networkx>=2.2",
     "pyscf; sys_platform != 'win32'",
+    'cvxpy>1.0.0,<1.1.0',
 ]
 
 if not hasattr(setuptools, 'find_namespace_packages') or not inspect.ismethod(setuptools.find_namespace_packages):

test/aqua/test_qsvm.py

@@ -77,9 +77,9 @@ def test_qsvm_binary(self, data_preparation_type):
                                        [0.33608333, 0.3765, 0.02316667, 0.15858333]])
 
         # ref_alpha = np.array([0.36064489, 1.49204209, 0.0264953, 1.82619169])
-        ref_alpha = np.array([0.34903335, 1.48325498, 0.03074852, 1.80153981])
+        ref_alpha = np.array([0.34902907, 1.48325913, 0.03073616, 1.80155205])
         # ref_bias = np.array([-0.03380763])
-        ref_bias = np.array([-0.03059226])
+        ref_bias = np.array([-0.03059395])
 
         ref_support_vectors = np.array([[2.95309709, 2.51327412], [3.14159265, 4.08407045],
                                         [4.08407045, 2.26194671], [4.46106157, 2.38761042]])