Repository: tomekzaw/ewl (language: python)

Issue:
Rewrite code to use sympy



Discussion / hints:

Fix patch:
diff --git a/README.md b/README.md
index 911054b..7da868b 100644
--- a/README.md
+++ b/README.md
@@ -2,7 +2,7 @@
 
 A simple Python library to simulate and execute EWL quantum circuits on IBM Q.
 
-![](docs/ewl.png)
+![](https://raw.githubusercontent.com/tomekzaw/ewl/master/docs/ewl.png)
 
 ## Installation
 
@@ -15,12 +15,16 @@ pip install ewl
 ```python
 from ewl import *
 
-psi = (ket('00') + i * ket('11')) / sqrt(2)  # initial state
+psi = (Qubit('00') + i * Qubit('11')) / sqrt2  # initial state
 
-alice = U(theta=pi/2, alpha=pi/2, beta=0)  # quantum strategy
+alice = U(theta=pi / 2, alpha=pi / 2, beta=0)  # quantum strategy
 bob = U(theta=0, alpha=0, beta=0)  # classical strategy (C)
 
-ewl = ExtendedEWL(psi, [alice, bob])
+ewl = EWL(psi, [alice, bob])
+
+ewl.J
+
+ewl.J_H
 
 ewl.draw()
 
diff --git a/examples/example.ipynb b/examples/example.ipynb
index 145f889..d29e9e1 100644
--- a/examples/example.ipynb
+++ b/examples/example.ipynb
@@ -2,28 +2,17 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": null,
    "id": "elder-breach",
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Collecting ewl\n",
-      "  Downloading ewl-0.1.0-py3-none-any.whl (3.8 kB)\n",
-      "Installing collected packages: ewl\n",
-      "Successfully installed ewl-0.1.0\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "!pip install ewl"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 1,
    "id": "parliamentary-story",
    "metadata": {},
    "outputs": [],
@@ -31,35 +20,177 @@
     "from ewl import *"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "50bb208f",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle \\frac{\\sqrt{2} \\left({\\left|00\\right\\rangle } + i {\\left|11\\right\\rangle }\\right)}{2}$"
+      ],
+      "text/plain": [
+       "sqrt(2)*(|00> + I*|11>)/2"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "psi = (Qubit('00') + i * Qubit('11')) / sqrt2  # initial state\n",
+    "psi"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 3,
-   "id": "sweet-earthquake",
+   "id": "c7ab5d79",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle \\left[\\begin{matrix}\\frac{\\sqrt{2} i}{2} & \\frac{\\sqrt{2} i}{2}\\\\\\frac{\\sqrt{2} i}{2} & - \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right]$"
+      ],
+      "text/plain": [
+       "Matrix([\n",
+       "[sqrt(2)*I/2,  sqrt(2)*I/2],\n",
+       "[sqrt(2)*I/2, -sqrt(2)*I/2]])"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
-    "psi = (ket('00') + i * ket('11')) / sqrt(2)  # initial state\n",
-    "\n",
-    "alice = U(theta=pi/2, alpha=pi/2, beta=0)  # quantum strategy\n",
-    "bob = U(theta=0, alpha=0, beta=0)  # classical strategy (C)\n",
-    "\n",
-    "ewl = ExtendedEWL(psi, [alice, bob])"
+    "alice = U(theta=pi / 2, alpha=pi / 2, beta=0)  # quantum strategy\n",
+    "alice"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 4,
+   "id": "bda163ee",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle \\left[\\begin{matrix}1 & 0\\\\0 & 1\\end{matrix}\\right]$"
+      ],
+      "text/plain": [
+       "Matrix([\n",
+       "[1, 0],\n",
+       "[0, 1]])"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "bob = U(theta=0, alpha=0, beta=0)  # classical strategy (C)\n",
+    "bob"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "sweet-earthquake",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<ewl.EWL at 0x1cb3d495af0>"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "ewl = EWL(psi, [alice, bob])\n",
+    "ewl"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "2455b29b",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & 0 & 0 & - \\frac{\\sqrt{2} i}{2}\\\\0 & \\frac{\\sqrt{2} i}{2} & - \\frac{\\sqrt{2}}{2} & 0\\\\0 & - \\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2} i}{2} & 0\\\\\\frac{\\sqrt{2} i}{2} & 0 & 0 & - \\frac{\\sqrt{2}}{2}\\end{matrix}\\right]$"
+      ],
+      "text/plain": [
+       "Matrix([\n",
+       "[  sqrt(2)/2,           0,           0, -sqrt(2)*I/2],\n",
+       "[          0, sqrt(2)*I/2,  -sqrt(2)/2,            0],\n",
+       "[          0,  -sqrt(2)/2, sqrt(2)*I/2,            0],\n",
+       "[sqrt(2)*I/2,           0,           0,   -sqrt(2)/2]])"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "ewl.J"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "78f38da4",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & 0 & 0 & - \\frac{\\sqrt{2} i}{2}\\\\0 & - \\frac{\\sqrt{2} i}{2} & - \\frac{\\sqrt{2}}{2} & 0\\\\0 & - \\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2} i}{2} & 0\\\\\\frac{\\sqrt{2} i}{2} & 0 & 0 & - \\frac{\\sqrt{2}}{2}\\end{matrix}\\right]$"
+      ],
+      "text/plain": [
+       "Matrix([\n",
+       "[  sqrt(2)/2,            0,            0, -sqrt(2)*I/2],\n",
+       "[          0, -sqrt(2)*I/2,   -sqrt(2)/2,            0],\n",
+       "[          0,   -sqrt(2)/2, -sqrt(2)*I/2,            0],\n",
+       "[sqrt(2)*I/2,            0,            0,   -sqrt(2)/2]])"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "ewl.J_H"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
    "id": "serious-organization",
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "<Figure size 779.079x204.68 with 1 Axes>"
       ]
      },
-     "execution_count": 4,
+     "execution_count": 8,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -70,18 +201,18 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 9,
    "id": "upset-forum",
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
       "text/plain": [
-       "<Figure size 1503.73x385.28 with 1 Axes>"
+       "<Figure size 1443.53x385.28 with 1 Axes>"
       ]
      },
-     "execution_count": 5,
+     "execution_count": 9,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -92,7 +223,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 10,
    "id": "surprising-shuttle",
    "metadata": {},
    "outputs": [
@@ -100,17 +231,17 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "{'11': 500, '01': 524}\n"
+      "{'01': 501, '11': 523}\n"
      ]
     },
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "<Figure size 504x360 with 1 Axes>"
       ]
      },
-     "execution_count": 6,
+     "execution_count": 10,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -123,7 +254,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 11,
    "id": "insured-opera",
    "metadata": {
     "scrolled": false
@@ -134,17 +265,17 @@
      "output_type": "stream",
      "text": [
       "Job Status: job has successfully run\n",
-      "{'00': 42, '01': 589, '10': 19, '11': 374}\n"
+      "{'00': 46, '01': 466, '10': 56, '11': 456}\n"
      ]
     },
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "<Figure size 504x360 with 1 Axes>"
       ]
      },
-     "execution_count": 7,
+     "execution_count": 11,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -157,18 +288,18 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 12,
    "id": "occasional-vancouver",
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "<Figure size 504x360 with 1 Axes>"
       ]
      },
-     "execution_count": 8,
+     "execution_count": 12,
      "metadata": {},
      "output_type": "execute_result"
     }
diff --git a/setup.py b/setup.py
index 8d12a01..9f0c21a 100644
--- a/setup.py
+++ b/setup.py
@@ -5,7 +5,7 @@
 
 setuptools.setup(
     name='ewl',
-    version='0.2.0',
+    version='0.3.0',
     author='Piotr Kotara, Tomasz Zawadzki',
     author_email='piotrekkotara@gmail.com, tomekzawadzki98@gmail.com',
     description='A simple Python library to simulate and execute EWL quantum circuits on IBM Q.',
diff --git a/src/ewl/__init__.py b/src/ewl/__init__.py
index 6aded9c..33a12a9 100644
--- a/src/ewl/__init__.py
+++ b/src/ewl/__init__.py
@@ -1,10 +1,11 @@
-from cmath import sqrt, pi, sin, cos, exp
-from functools import cached_property, reduce
+import cmath
+from functools import cached_property
 from itertools import product
 from math import log2
 from typing import Optional, Sequence
 
 import numpy as np
+import sympy as sp
 from qiskit import QuantumCircuit, execute, Aer, IBMQ
 from qiskit.compiler import transpile
 from qiskit.providers.ibmq import least_busy
@@ -13,51 +14,43 @@
 from qiskit.quantum_info.operators import Operator
 from qiskit.tools import job_monitor
 from qiskit.visualization import plot_histogram  # noqa: F401
+from sympy import Matrix
+from sympy.physics.quantum import TensorProduct, Dagger
+from sympy.physics.quantum.qubit import Qubit, qubit_to_matrix  # noqa: F401
 
 try:
     IBMQ.load_account()
 except IBMQAccountCredentialsNotFound:
     pass
 
-i = 1j
-sqrt2 = sqrt(2)
+i = sp.I
+pi = sp.pi
+sqrt2 = sp.sqrt(2)
 
 
-def ket(base_state: str, /) -> np.array:
-    qbits = len(base_state)
-    assert qbits > 0, 'Number of qbits must be at least 1'
-    assert set(base_state) <= {'0', '1'}, 'Base state must consist of only 0s and 1s'
+def number_of_qubits(psi) -> int:
+    return int(log2(len(qubit_to_matrix(psi))))
 
-    vector = np.zeros(2 ** qbits)
-    vector[int(base_state, 2)] = 1
-    return vector
 
+def sympy_to_numpy_matrix(matrix: Matrix) -> np.array:
+    return np.array(matrix).astype(complex)
 
-def is_unit_vector(vec: np.array) -> bool:
-    return np.isclose(np.linalg.norm(vec), 1)
 
-
-def number_of_qbits(psi: np.array) -> int:
-    n = psi.shape[0]
-    assert (n & (n - 1) == 0) and n != 0, 'Vector size must be a power of two'
-    return int(log2(n))
-
-
-def U_theta_alpha_beta(*, theta: complex, alpha: complex, beta: complex = 3 * pi / 2) -> np.array:
-    return np.array([
-        [exp(i * alpha) * cos(theta / 2), i * exp(i * beta) * sin(theta / 2)],
-        [i * exp(-i * beta) * sin(theta / 2), exp(-i * alpha) * cos(theta / 2)]
+def U_theta_alpha_beta(*, theta: complex, alpha: complex, beta: complex = 3 * cmath.pi / 2) -> Matrix:
+    return Matrix([
+        [sp.exp(i * alpha) * sp.cos(theta / 2), i * sp.exp(i * beta) * sp.sin(theta / 2)],
+        [i * sp.exp(-i * beta) * sp.sin(theta / 2), sp.exp(-i * alpha) * sp.cos(theta / 2)]
     ])
 
 
-def U_theta_phi_lambda(*, theta: complex, phi: complex, lambda_: complex) -> np.array:
-    return np.array([
-        [exp(-i * (phi + lambda_) / 2) * cos(theta / 2), -exp(-i * (phi - lambda_) / 2) * sin(theta / 2)],
-        [exp(i * (phi - lambda_) / 2) * sin(theta / 2), exp(i * (phi + lambda_) / 2) * cos(theta / 2)]
+def U_theta_phi_lambda(*, theta: complex, phi: complex, lambda_: complex) -> Matrix:
+    return Matrix([
+        [sp.exp(-i * (phi + lambda_) / 2) * sp.cos(theta / 2), -sp.exp(-i * (phi - lambda_) / 2) * sp.sin(theta / 2)],
+        [sp.exp(i * (phi - lambda_) / 2) * sp.sin(theta / 2), sp.exp(i * (phi + lambda_) / 2) * sp.cos(theta / 2)]
     ])
 
 
-def U(*args, **kwargs: complex) -> np.array:
+def U(*args, **kwargs: complex) -> Matrix:
     if args:
         raise Exception('Please use keyword arguments')
     if set(kwargs) in [{'theta', 'alpha'}, {'theta', 'alpha', 'beta'}]:
@@ -67,17 +60,16 @@ def U(*args, **kwargs: complex) -> np.array:
     raise Exception('Invalid parametrization')
 
 
-def J(psi: np.array, C: np.array, D: np.array) -> np.array:
-    return np.column_stack([
-        np.dot(reduce(np.kron, base), psi)
-        for base in product((C, D), repeat=number_of_qbits(psi))
+def J(psi, C: Matrix, D: Matrix) -> Matrix:
+    return Matrix.hstack(*[
+        TensorProduct(*base) @ qubit_to_matrix(psi)
+        for base in product((C, D), repeat=number_of_qubits(psi))
     ])
 
 
-class ExtendedEWL:
-    def __init__(self, psi: np.array, strategies: Sequence[np.array], provider: Optional[AccountProvider] = None):
-        assert is_unit_vector(psi), 'Initial state must be a unit vector'
-        assert len(strategies) == number_of_qbits(psi), 'Number of strategies must be equal to number of qbits'
+class EWL:
+    def __init__(self, psi, strategies: Sequence[Matrix], provider: Optional[AccountProvider] = None):
+        assert number_of_qubits(psi) == len(strategies)
 
         self.psi = psi
         self.strategies = strategies
@@ -95,15 +87,20 @@ def number_of_players(self) -> int:
         return len(self.strategies)
 
     @cached_property
-    def j(self) -> np.array:
+    def J(self) -> Matrix:
         C = U(theta=0, alpha=0, beta=0)
         D = U(theta=pi, alpha=0, beta=0)
         return J(self.psi, C, D)
 
+    @cached_property
+    def J_H(self) -> Matrix:
+        return Dagger(self.J)
+
     @cached_property
     def qc(self) -> QuantumCircuit:
-        j = Operator(self.j)
-        j_h = Operator(np.conjugate(self.j).T)
+        j = Operator(sympy_to_numpy_matrix(self.J))
+        j_h = Operator(sympy_to_numpy_matrix(self.J_H))
+
         all_qbits = list(range(self.number_of_players))
 
         qc = QuantumCircuit(self.number_of_players)
@@ -111,8 +108,7 @@ def qc(self) -> QuantumCircuit:
         qc.barrier()
 
         for qbit, strategy in enumerate(self.strategies):
-            u_a = Operator(strategy)
-            qc.append(u_a, [qbit])
+            qc.append(Operator(sympy_to_numpy_matrix(strategy)), [qbit])
 
         qc.barrier()
         qc.append(j_h, all_qbits)


Test patch:
diff --git a/tests/test_ewl.py b/tests/test_ewl.py
index 0616014..a62ac39 100644
--- a/tests/test_ewl.py
+++ b/tests/test_ewl.py
@@ -1,81 +1,136 @@
-from math import sqrt
 from typing import Dict
 
 import numpy as np
 import pytest
+import sympy as sp
+from qiskit import QuantumCircuit
+from qiskit.quantum_info.operators import Operator
+from sympy import Matrix
+from sympy.physics.quantum.qubit import Qubit
 
-from ewl import i, pi, sqrt2, ket, is_unit_vector, number_of_qbits, U_theta_alpha_beta, U_theta_phi_lambda, U, J
+from ewl import U, EWL
+from ewl import i, pi, sqrt2, number_of_qubits, sympy_to_numpy_matrix, U_theta_alpha_beta, U_theta_phi_lambda, J
 
 
-@pytest.mark.parametrize('base_state, expected', [
-    ('0', [1, 0]),
-    ('1', [0, 1]),
-    ('00', [1, 0, 0, 0]),
-    ('01', [0, 1, 0, 0]),
-    ('10', [0, 0, 1, 0]),
-    ('11', [0, 0, 0, 1]),
-    ('000', [1] + [0] * 7),
-    ('011', [0] * 3 + [1] + [0] * 4),
-    ('111', [0] * 7 + [1]),
-    ('01010', [0] * 10 + [1] + [0] * 21),
+@pytest.mark.parametrize('psi, expected', [
+    ((Qubit('0') + i * Qubit('1')) / sqrt2, 1),
+    ((Qubit('00') + i * Qubit('11')) / sqrt2, 2),
+    ((Qubit('000') + i * Qubit('111')) / sqrt2, 3),
 ])
-def test_ket(base_state: str, expected: np.array):
-    assert np.array_equal(ket(base_state), np.array(expected))
+def test_number_of_qubits(psi, expected: int):
+    assert number_of_qubits(psi) == expected
 
 
-@pytest.mark.parametrize('invalid_state', ['', '0a'])
-def test_ket_error(invalid_state: str):
-    with pytest.raises(AssertionError):
-        ket(invalid_state)
+def test_sympy_to_numpy_matrix():
+    values = [[1, 2], [3, 4]]
+    assert np.allclose(sympy_to_numpy_matrix(Matrix(values)), np.array(values))
 
 
-@pytest.mark.parametrize('vec, expected', [
-    (ket('10'), True),
-    (ket('10') * 2, False),
-    ((ket('00') + i * ket('11')) / sqrt2, True),
-    ((ket('00') + i * ket('11')) / sqrt(3), False),
-    ((ket('000') + i * ket('111')) / sqrt2, True),
+@pytest.mark.parametrize('kwargs, expected', [
+    (dict(theta=0, alpha=0, beta=pi / 2), Matrix([[1, 0], [0, 1]])),
+    (dict(theta=pi / 2, alpha=pi / 2, beta=0), Matrix([[i / sqrt2, i / sqrt2], [i / sqrt2, -i / sqrt2]])),
+    (dict(theta=0, alpha=pi / 2), Matrix([[i, 0], [0, -i]])),
+    (dict(theta=0, alpha=0, beta=0), Matrix([[1, 0], [0, 1]])),  # C
+    (dict(theta=pi, alpha=0, beta=0), Matrix([[0, i], [i, 0]])),  # D
 ])
-def test_is_unit_vector(vec: np.array, expected: bool):
-    assert is_unit_vector(vec) == expected
+def test_U_theta_alpha(kwargs: Dict[str, complex], expected: Matrix):
+    assert U_theta_alpha_beta(**kwargs) == expected
 
 
-@pytest.mark.parametrize('psi, expected', [
-    (ket('1'), 1),
-    (ket('10'), 2),
-    (ket('101'), 3),
-    (ket('1011'), 4),
-    (ket('10110'), 5),
+@pytest.mark.parametrize('kwargs, expected', [
+    (dict(theta=pi, phi=0, lambda_=0), Matrix([[0, -1], [1, 0]])),
 ])
-def test_number_of_qbits(psi: np.array, expected: int):
-    assert number_of_qbits(psi) == expected
+def test_U_theta_phi_lambda(kwargs: Dict[str, complex], expected: Matrix):
+    assert U_theta_phi_lambda(**kwargs) == expected
 
 
-@pytest.mark.parametrize('kwargs, expected', [
-    (dict(theta=0, alpha=0, beta=pi / 2), np.array([[1, 0], [0, 1]])),
-    (dict(theta=0, alpha=pi / 2), np.array([[i, 0], [0, -i]])),
-    (dict(theta=0, alpha=0, beta=0), np.array([[1, 0], [0, 1]])),  # C
-    (dict(theta=pi, alpha=0, beta=0), np.array([[0, i], [i, 0]])),  # D
-])
-def test_U_theta_alpha(kwargs: Dict[str, complex], expected: np.array):
-    assert np.allclose(U_theta_alpha_beta(**kwargs), expected)
+def test_J():
+    psi = (Qubit('00') + i * Qubit('11')) / sqrt2
+    C = U(theta=0, alpha=0, beta=0)
+    D = U(theta=pi, alpha=0, beta=0)
 
+    expected = Matrix([
+        [1 / sqrt2, 0, 0, -i / sqrt2],
+        [0, i / sqrt2, -1 / sqrt2, 0],
+        [0, -1 / sqrt2, i / sqrt2, 0],
+        [i / sqrt2, 0, 0, -1 / sqrt2],
+    ])
 
-@pytest.mark.parametrize('kwargs, expected', [
-    (dict(theta=pi, phi=0, lambda_=0), np.array([[0, -1], [1, 0]])),
-])
-def test_U_theta_phi_lambda(kwargs: Dict[str, complex], expected: np.array):
-    assert np.allclose(U_theta_phi_lambda(**kwargs), expected)
+    assert J(psi, C, D) == expected
 
 
-def test_J():
-    assert np.allclose(J(
-        psi=np.array([1, 0, 0, i]) / sqrt2,
-        C=U(theta=0, alpha=0, beta=0),
-        D=U(theta=pi, alpha=0, beta=0)
-    ), np.array([
+@pytest.fixture
+def ewl() -> EWL:
+    i = sp.I
+    pi = sp.pi
+    sqrt2 = sp.sqrt(2)
+
+    psi = (Qubit('00') + i * Qubit('11')) / sqrt2
+    alice = U(theta=pi / 2, alpha=pi / 2, beta=0)
+    bob = U(theta=0, alpha=0, beta=0)
+
+    return EWL(psi, [alice, bob])
+
+
+def test_ewl_J(ewl: EWL):
+    i = sp.I
+    sqrt2 = sp.sqrt(2)
+
+    assert ewl.J == Matrix([
+        [1 / sqrt2, 0, 0, -i / sqrt2],
+        [0, i / sqrt2, -1 / sqrt2, 0],
+        [0, -1 / sqrt2, i / sqrt2, 0],
+        [i / sqrt2, 0, 0, -1 / sqrt2],
+    ])
+
+
+def test_ewl_J_H(ewl: EWL):
+    i = sp.I
+    sqrt2 = sp.sqrt(2)
+
+    assert ewl.J_H == Matrix([
+        [1 / sqrt2, 0, 0, -i / sqrt2],
+        [0, -i / sqrt2, -1 / sqrt2, 0],
+        [0, -1 / sqrt2, -i / sqrt2, 0],
+        [i / sqrt2, 0, 0, -1 / sqrt2],
+    ])
+
+
+def test_ewl_qc(ewl: EWL):
+    i = 1j
+    sqrt2 = np.sqrt(2)
+
+    j = Operator(np.array([
         [1 / sqrt2, 0, 0, -i / sqrt2],
         [0, i / sqrt2, -1 / sqrt2, 0],
         [0, -1 / sqrt2, i / sqrt2, 0],
         [i / sqrt2, 0, 0, -1 / sqrt2],
     ]))
+
+    j_h = Operator(np.array([
+        [1 / sqrt2, 0, 0, -i / sqrt2],
+        [0, -i / sqrt2, -1 / sqrt2, 0],
+        [0, -1 / sqrt2, -i / sqrt2, 0],
+        [i / sqrt2, 0, 0, -1 / sqrt2],
+    ]))
+
+    u_a = Operator(np.array([
+        [i / sqrt2, i / sqrt2],
+        [i / sqrt2, -i / sqrt2]
+    ]))
+
+    u_b = Operator(np.array([
+        [1, 0],
+        [0, 1],
+    ]))
+
+    qc = QuantumCircuit(2)
+    qc.append(j, [0, 1])
+    qc.barrier()
+    qc.append(u_a, [0])
+    qc.append(u_b, [1])
+    qc.barrier()
+    qc.append(j_h, [0, 1])
+    qc.measure_all()
+
+    assert ewl.qc == qc