def test_2_qubit_identities(self):
"""Tests identities for 2-qubit gates"""
# CX01 * CX10 * CX01 = CX10 * CX01 * CX10
elem1 = CNOTDihedral(2)
elem1.cnot(0, 1)
elem1.cnot(1, 0)
elem1.cnot(0, 1)
elem2 = CNOTDihedral(2)
elem2.cnot(1, 0)
elem2.cnot(0, 1)
elem2.cnot(1, 0)
self.assertEqual(elem1, elem2,
'Error: 2-qubit SWAP identity does not hold')
# CS01 = CS10 (symmetric)
elem1 = CNOTDihedral(2)
elem1.phase(1, 0)
elem1.phase(1, 1)
elem1.cnot(0, 1)
elem1.phase(7, 1)
elem1.cnot(0, 1)
elem2 = CNOTDihedral(2)
elem2.phase(1, 1)
elem2.phase(1, 0)
elem2.cnot(1, 0)
elem2.phase(7, 0)
elem2.cnot(1, 0)
self.assertEqual(elem1, elem2,
'Error: 2-qubit CS identity does not hold')
# TI*CS*TdgI = CS"
elem3 = CNOTDihedral(2)
elem3.phase(1, 0)
elem3.phase(1, 0)
elem3.phase(1, 1)
elem3.cnot(0, 1)
elem3.phase(7, 1)
elem3.cnot(0, 1)
elem3.phase(7, 0)
self.assertEqual(elem1, elem3,
'Error: 2-qubit CS identity does not hold')
# IT*CS*ITdg = CS
elem4 = CNOTDihedral(2)
elem4.phase(1, 1)
elem4.phase(1, 0)
elem4.phase(1, 1)
elem4.cnot(0, 1)
elem4.phase(7, 1)
elem4.cnot(0, 1)
elem4.phase(7, 1)
self.assertEqual(elem1, elem4,
'Error: 2-qubit CS identity does not hold')
# XX*CS*XX*SS = CS
elem5 = CNOTDihedral(2)
elem5.flip(0)
elem5.flip(1)
elem5.phase(1, 0)
elem5.phase(1, 1)
elem5.cnot(0, 1)
elem5.phase(7, 1)
elem5.cnot(0, 1)
elem5.flip(0)
elem5.flip(1)
elem5.phase(2, 0)
elem5.phase(2, 1)
self.assertEqual(elem1, elem5,
'Error: 2-qubit CS identity does not hold')
# CSdg01 = CSdg10 (symmetric)
elem1 = CNOTDihedral(2)
elem1.phase(7, 0)
elem1.phase(7, 1)
elem1.cnot(0, 1)
elem1.phase(1, 1)
elem1.cnot(0, 1)
elem2 = CNOTDihedral(2)
elem2.phase(7, 1)
elem2.phase(7, 0)
elem2.cnot(1, 0)
elem2.phase(1, 0)
elem2.cnot(1, 0)
self.assertEqual(elem1, elem2,
'Error: 2-qubit CSdg identity does not hold')
# XI*CS*XI*ISdg = CSdg
elem3 = CNOTDihedral(2)
elem3.flip(0)
elem3.phase(1, 0)
elem3.phase(1, 1)
elem3.cnot(0, 1)
elem3.phase(7, 1)
elem3.cnot(0, 1)
elem3.flip(0)
elem3.phase(6, 1)
self.assertEqual(elem1, elem3,
'Error: 2-qubit CSdg identity does not hold')
# IX*CS*IX*SdgI = CSdg
elem4 = CNOTDihedral(2)
elem4.flip(1)
elem4.phase(1, 0)
elem4.phase(1, 1)
elem4.cnot(0, 1)
elem4.phase(7, 1)
elem4.cnot(0, 1)
elem4.flip(1)
elem4.phase(6, 0)
self.assertEqual(elem1, elem4,
'Error: 2-qubit CSdg identity does not hold')
# relations for CZ
elem1 = CNOTDihedral(2)
elem1.phase(1, 0)
elem1.phase(1, 1)
elem1.cnot(0, 1)
elem1.phase(7, 1)
elem1.cnot(0, 1)
elem1.phase(1, 0)
elem1.phase(1, 1)
elem1.cnot(0, 1)
elem1.phase(7, 1)
elem1.cnot(0, 1)
elem2 = CNOTDihedral(2)
elem2.phase(7, 0)
elem2.phase(7, 1)
elem2.cnot(0, 1)
elem2.phase(1, 1)
elem2.cnot(0, 1)
elem2.phase(7, 0)
elem2.phase(7, 1)
elem2.cnot(0, 1)
elem2.phase(1, 1)
elem2.cnot(0, 1)
elem3 = CNOTDihedral(2)
elem3.phase(1, 1)
elem3.phase(1, 0)
elem3.cnot(1, 0)
elem3.phase(7, 0)
elem3.cnot(1, 0)
elem3.phase(1, 1)
elem3.phase(1, 0)
elem3.cnot(1, 0)
elem3.phase(7, 0)
elem3.cnot(1, 0)
elem4 = CNOTDihedral(2)
elem4.phase(7, 1)
elem4.phase(7, 0)
elem4.cnot(1, 0)
elem4.phase(1, 0)
elem4.cnot(1, 0)
elem4.phase(7, 1)
elem4.phase(7, 0)
elem4.cnot(1, 0)
elem4.phase(1, 0)
elem4.cnot(1, 0)
# CZ = TdgTdg * CX * T^2I * CX * TdgTdg
elem5 = CNOTDihedral(2)
elem5.phase(7, 1)
elem5.phase(7, 0)
elem5.cnot(1, 0)
elem5.phase(2, 0)
elem5.cnot(1, 0)
elem5.phase(7, 1)
elem5.phase(7, 0)
self.assertEqual(elem1, elem2,
'Error: 2-qubit CZ identity does not hold')
self.assertEqual(elem1, elem3,
'Error: 2-qubit CZ identity does not hold')
self.assertEqual(elem1, elem4,
'Error: 2-qubit CZ identity does not hold')
self.assertEqual(elem1, elem5,
'Error: 2-qubit CZ identity does not hold')
# relations for CX
elem1 = CNOTDihedral(2)
elem1.cnot(0, 1)
# TI*CX*TdgI = CX
elem2 = CNOTDihedral(2)
elem2.phase(1, 0)
elem2.cnot(0, 1)
elem2.phase(7, 0)
# IZ*CX*ZZ = CX
elem3 = CNOTDihedral(2)
elem3.phase(4, 1)
elem3.cnot(0, 1)
elem3.phase(4, 0)
elem3.phase(4, 1)
# IX*CX*IX = CX
elem4 = CNOTDihedral(2)
elem4.flip(1)
elem4.cnot(0, 1)
elem4.flip(1)
# XI*CX*XX = CX
elem5 = CNOTDihedral(2)
elem5.flip(0)
elem5.cnot(0, 1)
elem5.flip(0)
elem5.flip(1)
self.assertEqual(elem1, elem2,
'Error: 2-qubit CX identity does not hold')
self.assertEqual(elem1, elem3,
'Error: 2-qubit CX identity does not hold')
self.assertEqual(elem1, elem4,
'Error: 2-qubit CX identity does not hold')
self.assertEqual(elem1, elem5,
'Error: 2-qubit CX identity does not hold')
# IT*CX01*CX10*TdgI = CX01*CX10
elem1 = CNOTDihedral(2)
elem1.cnot(0, 1)
elem1.cnot(1, 0)
elem2 = CNOTDihedral(2)
elem2.phase(1, 1)
elem2.cnot(0, 1)
elem2.cnot(1, 0)
elem2.phase(7, 0)
self.assertEqual(elem1, elem2,
'Error: 2-qubit CX01*CX10 identity does not hold')
def test_1_qubit_identities(self):
"""Tests identities for 1-qubit gates"""
# T*X*T = X
elem1 = CNOTDihedral(1)
elem1.phase(1, 0)
elem1.flip(0)
elem1.phase(1, 0)
elem2 = CNOTDihedral(1)
elem2.flip(0)
self.assertEqual(elem1, elem2,
'Error: 1-qubit identity does not hold')
# X*T*X = Tdg
elem1 = CNOTDihedral(1)
elem1.flip(0)
elem1.phase(1, 0)
elem1.flip(0)
elem2 = CNOTDihedral(1)
elem2.phase(7, 0)
self.assertEqual(elem1, elem2,
'Error: 1-qubit identity does not hold')
# T*X*Tdg = S*X
elem1 = CNOTDihedral(1)
elem1.phase(1, 0)
elem1.flip(0)
elem1.phase(7, 0)
elem2 = CNOTDihedral(1)
elem2.phase(2, 0)
elem2.flip(0)
self.assertEqual(elem1, elem2,
'Error: 1-qubit identity does not hold')