def test_random_decompose(self):
"""
Test that random elements are CNOTDihedral
and to_circuit, to_instruction, _from_circuit, _is_valid methods
"""
rng = np.random.default_rng(1234)
samples = 10
for num_qubits in range(1, 9):
for _ in range(samples):
# Test of random_cnotdihedral method
elem = random_cnotdihedral(num_qubits, seed=rng)
self.assertIsInstance(
elem, CNOTDihedral,
"Error: random element is not CNOTDihedral")
self.assertTrue(elem._is_valid(),
"Error: random element is not CNOTDihedral")
# Test of to_circuit and _from_circuit methods
test_circ = elem.to_circuit()
self.assertTrue(
test_circ,
"Error: cannot decompose a random "
"CNOTDihedral element to a circuit",
)
test_elem = CNOTDihedral(test_circ)
self.assertEqual(
elem,
test_elem,
"Error: decomposed circuit is not equal "
"to the original circuit",
)
# Test that _is_valid fails if linear part is wrong
test_elem.linear = np.zeros((num_qubits, num_qubits))
value = test_elem._is_valid()
self.assertFalse(
value, "Error: CNOTDihedral _is_valid is not correct.")
# Test of to_instruction and _from_circuit methods
test_gates = elem.to_instruction()
self.assertIsInstance(
test_gates,
Gate,
"Error: cannot decompose a random "
"CNOTDihedral element to a Gate",
)
self.assertEqual(
test_gates.num_qubits,
test_circ.num_qubits,
"Error: wrong num_qubits in decomposed gates",
)
test_elem1 = CNOTDihedral(test_gates)
self.assertEqual(
elem,
test_elem1,
"Error: decomposed gates are not equal "
"to the original gates",
)
def test_conjugate(self):
"""Test transpose method"""
samples = 10
rng = np.random.default_rng(777)
for num_qubits in range(1, 5):
for _ in range(samples):
circ = random_cnotdihedral_circuit(num_qubits, 5 * num_qubits, seed=rng)
elem = CNOTDihedral(circ)
value = elem.conjugate().to_operator()
target = Operator(circ).conjugate()
self.assertTrue(target.equiv(value), "Error: conjugate circuit is not the same")
def test_dot_method(self):
"""Test dot method"""
samples = 10
rng = np.random.default_rng(222)
for num_qubits in range(1, 6):
for _ in range(samples):
circ1 = random_cnotdihedral_circuit(num_qubits, 5 * num_qubits, seed=rng)
circ2 = random_cnotdihedral_circuit(num_qubits, 5 * num_qubits, seed=rng)
elem1 = CNOTDihedral(circ1)
elem2 = CNOTDihedral(circ2)
value = elem1.dot(elem2)
target = CNOTDihedral(circ2.compose(circ1))
self.assertEqual(target, value, "Error: composed circuit is not the same")
def test_init_circuit_decompose(self):
"""
Test initialization from circuit and to_circuit, to_instruction methods
"""
rng = np.random.default_rng(1234)
samples = 10
for num_qubits in range(1, 9):
for _ in range(samples):
# Test of to_circuit and _from_circuit methods
circ = random_cnotdihedral_circuit(num_qubits,
5 * num_qubits,
seed=rng)
elem = CNOTDihedral(circ)
test_circ = elem.to_circuit()
test_elem = CNOTDihedral(test_circ)
self.assertEqual(
elem,
test_elem,
"Error: decomposed gates are not equal to the original gates",
)
# Test of to_instruction and _from_circuit methods
circ = random_cnotdihedral_circuit(num_qubits,
5 * num_qubits,
seed=rng)
elem = CNOTDihedral(circ)
test_circ = elem.to_instruction()
test_elem = CNOTDihedral(test_circ)
self.assertEqual(
elem,
test_elem,
"Error: decomposed gates are not equal to the original gates",
)
def test_barrier_delay_sim(self):
"""Test barrier and delay instructions can be simulated"""
target_circ = QuantumCircuit(2)
target_circ.x(0)
target_circ.cx(0, 1)
target = CNOTDihedral(target_circ)
circ = QuantumCircuit(2)
circ.x(0)
circ.delay(100, 0)
circ.barrier([0, 1])
circ.cx(0, 1)
value = CNOTDihedral(circ)
self.assertEqual(value, target)
def test_to_matrix(self):
"""Test to_matrix method"""
samples = 10
rng = np.random.default_rng(888)
for num_qubits in range(1, 5):
for _ in range(samples):
circ = random_cnotdihedral_circuit(num_qubits, 5 * num_qubits, seed=rng)
elem = CNOTDihedral(circ)
mat = elem.to_matrix()
self.assertIsInstance(mat, np.ndarray)
self.assertEqual(mat.shape, 2 * (2**num_qubits,))
value = Operator(mat)
target = Operator(circ)
self.assertTrue(value.equiv(target), "Error: matrix of the circuit is not the same")
def test_expand_method(self):
"""Test expand method"""
samples = 10
rng = np.random.default_rng(333)
for num_qubits_1 in range(1, 5):
for num_qubits_2 in range(1, 5):
for _ in range(samples):
elem1 = random_cnotdihedral(num_qubits_1, seed=rng)
elem2 = random_cnotdihedral(num_qubits_2, seed=rng)
circ1 = elem1.to_instruction()
circ2 = elem2.to_instruction()
value = elem2.expand(elem1)
circ = QuantumCircuit(num_qubits_1 + num_qubits_2)
qargs = list(range(num_qubits_1))
for instr, qregs, _ in circ1.definition:
new_qubits = [
qargs[circ1.definition.qubits.index(tup)]
for tup in qregs
]
circ.append(instr, new_qubits)
qargs = list(
range(num_qubits_1, num_qubits_1 + num_qubits_2))
for instr, qregs, _ in circ2.definition:
new_qubits = [
qargs[circ2.definition.qubits.index(tup)]
for tup in qregs
]
circ.append(instr, new_qubits)
target = CNOTDihedral(circ)
self.assertEqual(target, value,
"Error: expand circuit is not the same")
def test_init_from_pauli(self):
"""Test initialization from Pauli"""
samples = 10
rng = np.random.default_rng(999)
for num_qubits in range(1, 5):
for _ in range(samples):
pauli = random.random_pauli(num_qubits, seed=rng)
elem = CNOTDihedral(pauli)
value = Operator(pauli)
target = Operator(elem)
self.assertTrue(value.equiv(target), "Error: Pauli operator is not the same.")
def test_1_qubit_identities(self):
"""Tests identities for 1-qubit gates"""
# T*X*T = X
circ1 = QuantumCircuit(1)
circ1.t(0)
circ1.x(0)
circ1.t(0)
elem1 = CNOTDihedral(circ1)
elem = CNOTDihedral(XGate())
self.assertEqual(elem1, elem, "Error: 1-qubit identity does not hold")
# X*T*X = Tdg
circ1 = QuantumCircuit(1)
circ1.x(0)
circ1.t(0)
circ1.x(0)
elem1 = CNOTDihedral(circ1)
elem = CNOTDihedral(TdgGate())
self.assertEqual(elem1, elem, "Error: 1-qubit identity does not hold")
# X*Tdg*X = T
circ1 = QuantumCircuit(1)
circ1.x(0)
circ1.tdg(0)
circ1.x(0)
elem1 = CNOTDihedral(circ1)
elem = CNOTDihedral(TGate())
self.assertEqual(elem1, elem, "Error: 1-qubit identity does not hold")
# X*S*X = Sdg
circ1 = QuantumCircuit(1)
circ1.x(0)
circ1.s(0)
circ1.x(0)
elem1 = CNOTDihedral(circ1)
elem = CNOTDihedral(SdgGate())
self.assertEqual(elem1, elem, "Error: 1-qubit identity does not hold")
# X*Sdg*X = S
circ1 = QuantumCircuit(1)
circ1.x(0)
circ1.sdg(0)
circ1.x(0)
elem1 = CNOTDihedral(circ1)
elem = CNOTDihedral(SGate())
self.assertEqual(elem1, elem, "Error: 1-qubit identity does not hold")
# T*X*Tdg = S*X
circ1 = QuantumCircuit(1)
circ1.t(0)
circ1.x(0)
circ1.tdg(0)
circ2 = QuantumCircuit(1)
circ2.s(0)
circ2.x(0)
elem1 = CNOTDihedral(circ1)
elem2 = CNOTDihedral(circ2)
self.assertEqual(elem1, elem2, "Error: 1-qubit identity does not hold")
def test_2_qubit_identities(self):
"""Tests identities for 2-qubit gates"""
# SI * CX * SdgI = CX
elem = CNOTDihedral(CXGate())
circ1 = QuantumCircuit(2)
circ1.s(0)
circ1.cx(0, 1)
circ1.sdg(0)
elem1 = CNOTDihedral(circ1)
self.assertEqual(elem, elem1,
"Error: 2-qubit CX identity does not hold")
# SI * CZ * SdgI = CZ
elem = CNOTDihedral(CZGate())
circ1 = QuantumCircuit(2)
circ1.s(0)
circ1.cz(1, 0)
circ1.sdg(0)
elem1 = CNOTDihedral(circ1)
self.assertEqual(elem, elem1,
"Error: 2-qubit CZ identity does not hold")
# SWAP = CX01 * CX10 * CX01 = CX10 * CX01 * CX10
elem = CNOTDihedral(SwapGate())
circ1 = QuantumCircuit(2)
circ1.cx(0, 1)
circ1.cx(1, 0)
circ1.cx(0, 1)
circ2 = QuantumCircuit(2)
circ2.cx(1, 0)
circ2.cx(0, 1)
circ2.cx(1, 0)
elem1 = CNOTDihedral(circ1)
elem2 = CNOTDihedral(circ2)
self.assertEqual(elem, elem1,
"Error: 2-qubit SWAP identity does not hold")
self.assertEqual(elem1, elem2,
"Error: 2-qubit SWAP identity does not hold")
# CS01 = CS10 (symmetric)
#
# ┌───┐
# q_0: ┤ T ├──■───────────■──
# ├───┤┌─┴─┐┌─────┐┌─┴─┐
# q_1: ┤ T ├┤ X ├┤ Tdg ├┤ X ├
# └───┘└───┘└─────┘└───┘
circ1 = QuantumCircuit(2)
circ1.t(0)
circ1.t(1)
circ1.cx(0, 1)
circ1.tdg(1)
circ1.cx(0, 1)
# ┌───┐┌───┐┌─────┐┌───┐
# q_0: ┤ T ├┤ X ├┤ Tdg ├┤ X ├
# ├───┤└─┬─┘└─────┘└─┬─┘
# q_1: ┤ T ├──■───────────■──
# └───┘
circ2 = QuantumCircuit(2)
circ2.t(1)
circ2.t(0)
circ2.cx(1, 0)
circ2.tdg(0)
circ2.cx(1, 0)
elem1 = CNOTDihedral(circ1)
elem2 = CNOTDihedral(circ2)
self.assertEqual(elem1, elem2,
"Error: 2-qubit CS identity does not hold")
# TI*CS*TdgI = CS
#
# ┌───┐┌───┐ ┌─────┐
# q_0: ┤ T ├┤ T ├──■───────────■──┤ Tdg ├
# ├───┤└───┘┌─┴─┐┌─────┐┌─┴─┐└─────┘
# q_1: ┤ T ├─────┤ X ├┤ Tdg ├┤ X ├───────
# └───┘ └───┘└─────┘└───┘
circ3 = QuantumCircuit(2)
circ3.t(0)
circ3.t(0)
circ3.t(1)
circ3.cx(0, 1)
circ3.tdg(1)
circ3.cx(0, 1)
circ3.tdg(0)
elem3 = CNOTDihedral(circ3)
self.assertEqual(elem1, elem3,
"Error: 2-qubit CS identity does not hold")
# IT*CS*ITdg = CS
#
# ┌───┐
# q_0: ┤ T ├───────■───────────■─────────
# ├───┤┌───┐┌─┴─┐┌─────┐┌─┴─┐┌─────┐
# q_1: ┤ T ├┤ T ├┤ X ├┤ Tdg ├┤ X ├┤ Tdg ├
# └───┘└───┘└───┘└─────┘└───┘└─────┘
circ4 = QuantumCircuit(2)
circ4.t(1)
circ4.t(0)
circ4.t(1)
circ4.cx(0, 1)
circ4.tdg(1)
circ4.cx(0, 1)
circ4.tdg(1)
elem4 = CNOTDihedral(circ4)
self.assertEqual(elem1, elem4,
"Error: 2-qubit CS identity does not hold")
# XX*CS*XX*SS = CS
#
# ┌───┐┌───┐ ┌───┐┌───┐
# q_0: ┤ X ├┤ T ├──■───────────■──┤ X ├┤ S ├
# ├───┤├───┤┌─┴─┐┌─────┐┌─┴─┐├───┤├───┤
# q_1: ┤ X ├┤ T ├┤ X ├┤ Tdg ├┤ X ├┤ X ├┤ S ├
# └───┘└───┘└───┘└─────┘└───┘└───┘└───┘
circ5 = QuantumCircuit(2)
circ5.x(0)
circ5.x(1)
circ5.t(0)
circ5.t(1)
circ5.cx(0, 1)
circ5.tdg(1)
circ5.cx(0, 1)
circ5.x(0)
circ5.x(1)
circ5.s(0)
circ5.s(1)
elem5 = CNOTDihedral(circ5)
self.assertEqual(elem1, elem5,
"Error: 2-qubit CS identity does not hold")
# CSdg01 = CSdg10 (symmetric)
#
# ┌─────┐
# q_0: ┤ Tdg ├──■─────────■──
# ├─────┤┌─┴─┐┌───┐┌─┴─┐
# q_1: ┤ Tdg ├┤ X ├┤ T ├┤ X ├
# └─────┘└───┘└───┘└───┘
circ1 = QuantumCircuit(2)
circ1.tdg(0)
circ1.tdg(1)
circ1.cx(0, 1)
circ1.t(1)
circ1.cx(0, 1)
# ┌─────┐┌───┐┌───┐┌───┐
# q_0: ┤ Tdg ├┤ X ├┤ T ├┤ X ├
# ├─────┤└─┬─┘└───┘└─┬─┘
# q_1: ┤ Tdg ├──■─────────■──
# └─────┘
circ2 = QuantumCircuit(2)
circ2.tdg(1)
circ2.tdg(0)
circ2.cx(1, 0)
circ2.t(0)
circ2.cx(1, 0)
elem1 = CNOTDihedral(circ1)
elem2 = CNOTDihedral(circ2)
self.assertEqual(elem1, elem2,
"Error: 2-qubit CSdg identity does not hold")
# XI*CS*XI*ISdg = CSdg
#
# ┌───┐┌───┐ ┌───┐
# q_0: ┤ X ├┤ T ├──■───────────■───┤ X ├─
# ├───┤└───┘┌─┴─┐┌─────┐┌─┴─┐┌┴───┴┐
# q_1: ┤ T ├─────┤ X ├┤ Tdg ├┤ X ├┤ Sdg ├
# └───┘ └───┘└─────┘└───┘└─────┘
circ3 = QuantumCircuit(2)
circ3.x(0)
circ3.t(0)
circ3.t(1)
circ3.cx(0, 1)
circ3.tdg(1)
circ3.cx(0, 1)
circ3.x(0)
circ3.sdg(1)
elem3 = CNOTDihedral(circ3)
self.assertEqual(elem1, elem3,
"Error: 2-qubit CSdg identity does not hold")
# IX*CS*IX*SdgI = CSdg
#
# ┌───┐ ┌─────┐
# q_0: ┤ T ├───────■───────────■──┤ Sdg ├
# ├───┤┌───┐┌─┴─┐┌─────┐┌─┴─┐└┬───┬┘
# q_1: ┤ X ├┤ T ├┤ X ├┤ Tdg ├┤ X ├─┤ X ├─
# └───┘└───┘└───┘└─────┘└───┘ └───┘
circ4 = QuantumCircuit(2)
circ4.x(1)
circ4.t(0)
circ4.t(1)
circ4.cx(0, 1)
circ4.tdg(1)
circ4.cx(0, 1)
circ4.x(1)
circ4.sdg(0)
elem4 = CNOTDihedral(circ4)
self.assertEqual(elem1, elem4,
"Error: 2-qubit CSdg identity does not hold")
# relations for CZ
# CZ(0,1) = CZ(1,0)
elem = CNOTDihedral(CZGate())
circ1 = QuantumCircuit(2)
circ1.cz(0, 1)
circ2 = QuantumCircuit(2)
circ2.cz(1, 0)
elem1 = CNOTDihedral(circ1)
elem2 = CNOTDihedral(circ2)
self.assertEqual(elem, elem1,
"Error: 2-qubit CZ identity does not hold")
self.assertEqual(elem1, elem2,
"Error: 2-qubit CZ identity does not hold")
# CZ = CS * CS
#
# ┌───┐ ┌───┐
# q_0: ┤ T ├──■───────────■──┤ T ├──■───────────■──
# ├───┤┌─┴─┐┌─────┐┌─┴─┐├───┤┌─┴─┐┌─────┐┌─┴─┐
# q_1: ┤ T ├┤ X ├┤ Tdg ├┤ X ├┤ T ├┤ X ├┤ Tdg ├┤ X ├
# └───┘└───┘└─────┘└───┘└───┘└───┘└─────┘└───┘
circ3 = QuantumCircuit(2)
circ3.t(0)
circ3.t(1)
circ3.cx(0, 1)
circ3.tdg(1)
circ3.cx(0, 1)
circ3.t(0)
circ3.t(1)
circ3.cx(0, 1)
circ3.tdg(1)
circ3.cx(0, 1)
elem3 = CNOTDihedral(circ3)
self.assertEqual(elem1, elem3,
"Error: 2-qubit CZ identity does not hold")
# CZ = CSdg * CSdg
#
# ┌─────┐ ┌─────┐
# q_0: ┤ Tdg ├──■─────────■──┤ Tdg ├──■─────────■──
# ├─────┤┌─┴─┐┌───┐┌─┴─┐├─────┤┌─┴─┐┌───┐┌─┴─┐
# q_1: ┤ Tdg ├┤ X ├┤ T ├┤ X ├┤ Tdg ├┤ X ├┤ T ├┤ X ├
# └─────┘└───┘└───┘└───┘└─────┘└───┘└───┘└───┘
circ4 = QuantumCircuit(2)
circ4.tdg(0)
circ4.tdg(1)
circ4.cx(0, 1)
circ4.t(1)
circ4.cx(0, 1)
circ4.tdg(0)
circ4.tdg(1)
circ4.cx(0, 1)
circ4.t(1)
circ4.cx(0, 1)
elem4 = CNOTDihedral(circ4)
self.assertEqual(elem1, elem4,
"Error: 2-qubit CZ identity does not hold")
# CZ = TdgTdg * CX * T^2I * CX * TdgTdg
#
# ┌─────┐┌───┐┌───┐┌───┐┌───┐┌─────┐
# q_0: ┤ Tdg ├┤ X ├┤ T ├┤ T ├┤ X ├┤ Tdg ├
# ├─────┤└─┬─┘└───┘└───┘└─┬─┘├─────┤
# q_1: ┤ Tdg ├──■──────────────■──┤ Tdg ├
# └─────┘ └─────┘
circ5 = QuantumCircuit(2)
circ5.tdg(0)
circ5.tdg(1)
circ5.cx(1, 0)
circ5.t(0)
circ5.t(0)
circ5.cx(1, 0)
circ5.tdg(0)
circ5.tdg(1)
elem5 = CNOTDihedral(circ5)
self.assertEqual(elem1, elem5,
"Error: 2-qubit CZ identity does not hold")
# relations for CX
circ1 = QuantumCircuit(2)
circ1.cx(0, 1)
elem1 = CNOTDihedral(circ1)
# TI*CX*TdgI = CX
#
# ┌───┐ ┌─────┐
# q_0: ┤ T ├──■──┤ Tdg ├
# └───┘┌─┴─┐└─────┘
# q_1: ─────┤ X ├───────
# └───┘
circ2 = QuantumCircuit(2)
circ2.t(0)
circ2.cx(0, 1)
circ2.tdg(0)
elem2 = CNOTDihedral(circ2)
self.assertEqual(elem1, elem2,
"Error: 2-qubit CX identity does not hold")
# IZ*CX*ZZ = CX
#
# ┌───┐
# q_0: ───────■──┤ Z ├
# ┌───┐┌─┴─┐├───┤
# q_1: ┤ Z ├┤ X ├┤ Z ├
# └───┘└───┘└───┘
circ3 = QuantumCircuit(2)
circ3.z(1)
circ3.cx(0, 1)
circ3.z(0)
circ3.z(1)
elem3 = CNOTDihedral(circ3)
self.assertEqual(elem1, elem3,
"Error: 2-qubit CX identity does not hold")
# IX*CX*IX = CX
#
# q_0: ───────■───────
# ┌───┐┌─┴─┐┌───┐
# q_1: ┤ X ├┤ X ├┤ X ├
# └───┘└───┘└───┘
circ4 = QuantumCircuit(2)
circ4.x(1)
circ4.cx(0, 1)
circ4.x(1)
elem4 = CNOTDihedral(circ4)
self.assertEqual(elem1, elem4,
"Error: 2-qubit CX identity does not hold")
# XI*CX*XX = CX
#
# ┌───┐ ┌───┐
# q_0: ┤ X ├──■──┤ X ├
# └───┘┌─┴─┐├───┤
# q_1: ─────┤ X ├┤ X ├
# └───┘└───┘
circ5 = QuantumCircuit(2)
circ5.x(0)
circ5.cx(0, 1)
circ5.x(0)
circ5.x(1)
elem5 = CNOTDihedral(circ5)
self.assertEqual(elem1, elem5,
"Error: 2-qubit CX identity does not hold")
# IT*CX01*CX10*TdgI = CX01*CX10
#
# ┌───┐
# q_0: ──■──┤ X ├
# ┌─┴─┐└─┬─┘
# q_1: ┤ X ├──■──
# └───┘
circ1 = QuantumCircuit(2)
circ1.cx(0, 1)
circ1.cx(1, 0)
# ┌───┐┌─────┐
# q_0: ───────■──┤ X ├┤ Tdg ├
# ┌───┐┌─┴─┐└─┬─┘└─────┘
# q_1: ┤ T ├┤ X ├──■─────────
# └───┘└───┘
circ2 = QuantumCircuit(2)
circ2.t(1)
circ2.cx(0, 1)
circ2.cx(1, 0)
circ2.tdg(0)
elem1 = CNOTDihedral(circ1)
elem2 = CNOTDihedral(circ2)
self.assertEqual(elem1, elem2,
"Error: 2-qubit CX01*CX10 identity does not hold")
def test_2_qubit_identities(self):
"""Tests identities for 2-qubit gates"""
# SI * CX * SdgI = CX
elem = CNOTDihedral(CXGate())
circ1 = QuantumCircuit(2)
circ1.s(0)
circ1.cx(0, 1)
circ1.sdg(0)
elem1 = CNOTDihedral(circ1)
self.assertEqual(elem, elem1,
"Error: 2-qubit CX identity does not hold")
# SI * CZ * SdgI = CZ
elem = CNOTDihedral(CZGate())
circ1 = QuantumCircuit(2)
circ1.s(0)
circ1.cz(1, 0)
circ1.sdg(0)
elem1 = CNOTDihedral(circ1)
self.assertEqual(elem, elem1,
"Error: 2-qubit CZ identity does not hold")
# SWAP = CX01 * CX10 * CX01 = CX10 * CX01 * CX10
elem = CNOTDihedral(SwapGate())
circ1 = QuantumCircuit(2)
circ1.cx(0, 1)
circ1.cx(1, 0)
circ1.cx(0, 1)
circ2 = QuantumCircuit(2)
circ2.cx(1, 0)
circ2.cx(0, 1)
circ2.cx(1, 0)
elem1 = CNOTDihedral(circ1)
elem2 = CNOTDihedral(circ2)
self.assertEqual(elem, elem1,
"Error: 2-qubit SWAP identity does not hold")
self.assertEqual(elem1, elem2,
"Error: 2-qubit SWAP identity does not hold")
# CS01 = CS10 (symmetric)
circ1 = QuantumCircuit(2)
circ1.t(0)
circ1.t(1)
circ1.cx(0, 1)
circ1.tdg(1)
circ1.cx(0, 1)
circ2 = QuantumCircuit(2)
circ2.t(1)
circ2.t(0)
circ2.cx(1, 0)
circ2.tdg(0)
circ2.cx(1, 0)
elem1 = CNOTDihedral(circ1)
elem2 = CNOTDihedral(circ2)
self.assertEqual(elem1, elem2,
"Error: 2-qubit CS identity does not hold")
# TI*CS*TdgI = CS
circ3 = QuantumCircuit(2)
circ3.t(0)
circ3.t(0)
circ3.t(1)
circ3.cx(0, 1)
circ3.tdg(1)
circ3.cx(0, 1)
circ3.tdg(0)
elem3 = CNOTDihedral(circ3)
self.assertEqual(elem1, elem3,
"Error: 2-qubit CS identity does not hold")
# IT*CS*ITdg = CS
circ4 = QuantumCircuit(2)
circ4.t(1)
circ4.t(0)
circ4.t(1)
circ4.cx(0, 1)
circ4.tdg(1)
circ4.cx(0, 1)
circ4.tdg(1)
elem4 = CNOTDihedral(circ4)
self.assertEqual(elem1, elem4,
"Error: 2-qubit CS identity does not hold")
# XX*CS*XX*SS = CS
circ5 = QuantumCircuit(2)
circ5.x(0)
circ5.x(1)
circ5.t(0)
circ5.t(1)
circ5.cx(0, 1)
circ5.tdg(1)
circ5.cx(0, 1)
circ5.x(0)
circ5.x(1)
circ5.s(0)
circ5.s(1)
elem5 = CNOTDihedral(circ5)
self.assertEqual(elem1, elem5,
"Error: 2-qubit CS identity does not hold")
# CSdg01 = CSdg10 (symmetric)
circ1 = QuantumCircuit(2)
circ1.tdg(0)
circ1.tdg(1)
circ1.cx(0, 1)
circ1.t(1)
circ1.cx(0, 1)
circ2 = QuantumCircuit(2)
circ2.tdg(1)
circ2.tdg(0)
circ2.cx(1, 0)
circ2.t(0)
circ2.cx(1, 0)
elem1 = CNOTDihedral(circ1)
elem2 = CNOTDihedral(circ2)
self.assertEqual(elem1, elem2,
"Error: 2-qubit CSdg identity does not hold")
# XI*CS*XI*ISdg = CSdg
circ3 = QuantumCircuit(2)
circ3.x(0)
circ3.t(0)
circ3.t(1)
circ3.cx(0, 1)
circ3.tdg(1)
circ3.cx(0, 1)
circ3.x(0)
circ3.sdg(1)
elem3 = CNOTDihedral(circ3)
self.assertEqual(elem1, elem3,
"Error: 2-qubit CSdg identity does not hold")
# IX*CS*IX*SdgI = CSdg
circ4 = QuantumCircuit(2)
circ4.x(1)
circ4.t(0)
circ4.t(1)
circ4.cx(0, 1)
circ4.tdg(1)
circ4.cx(0, 1)
circ4.x(1)
circ4.sdg(0)
elem4 = CNOTDihedral(circ4)
self.assertEqual(elem1, elem4,
"Error: 2-qubit CSdg identity does not hold")
# relations for CZ
# CZ(0,1) = CZ(1,0)
elem = CNOTDihedral(CZGate())
circ1 = QuantumCircuit(2)
circ1.cz(0, 1)
circ2 = QuantumCircuit(2)
circ2.cz(1, 0)
elem1 = CNOTDihedral(circ1)
elem2 = CNOTDihedral(circ2)
self.assertEqual(elem, elem1,
"Error: 2-qubit CZ identity does not hold")
self.assertEqual(elem1, elem2,
"Error: 2-qubit CZ identity does not hold")
# CZ = CS * CS
circ3 = QuantumCircuit(2)
circ3.t(0)
circ3.t(1)
circ3.cx(0, 1)
circ3.tdg(1)
circ3.cx(0, 1)
circ3.t(0)
circ3.t(1)
circ3.cx(0, 1)
circ3.tdg(1)
circ3.cx(0, 1)
elem3 = CNOTDihedral(circ3)
self.assertEqual(elem1, elem3,
"Error: 2-qubit CZ identity does not hold")
# CZ = CSdg * CSdg
circ4 = QuantumCircuit(2)
circ4.tdg(0)
circ4.tdg(1)
circ4.cx(0, 1)
circ4.t(1)
circ4.cx(0, 1)
circ4.tdg(0)
circ4.tdg(1)
circ4.cx(0, 1)
circ4.t(1)
circ4.cx(0, 1)
elem4 = CNOTDihedral(circ4)
self.assertEqual(elem1, elem4,
"Error: 2-qubit CZ identity does not hold")
# CZ = TdgTdg * CX * T^2I * CX * TdgTdg
circ5 = QuantumCircuit(2)
circ5.tdg(0)
circ5.tdg(1)
circ5.cx(1, 0)
circ5.t(0)
circ5.t(0)
circ5.cx(1, 0)
circ5.tdg(0)
circ5.tdg(1)
elem5 = CNOTDihedral(circ5)
self.assertEqual(elem1, elem5,
"Error: 2-qubit CZ identity does not hold")
# relations for CX
circ1 = QuantumCircuit(2)
circ1.cx(0, 1)
elem1 = CNOTDihedral(circ1)
# TI*CX*TdgI = CX
circ2 = QuantumCircuit(2)
circ2.t(0)
circ2.cx(0, 1)
circ2.tdg(0)
elem2 = CNOTDihedral(circ2)
self.assertEqual(elem1, elem2,
"Error: 2-qubit CX identity does not hold")
# IZ*CX*ZZ = CX
circ3 = QuantumCircuit(2)
circ3.z(1)
circ3.cx(0, 1)
circ3.z(0)
circ3.z(1)
elem3 = CNOTDihedral(circ3)
self.assertEqual(elem1, elem3,
"Error: 2-qubit CX identity does not hold")
# IX*CX*IX = CX
circ4 = QuantumCircuit(2)
circ4.x(1)
circ4.cx(0, 1)
circ4.x(1)
elem4 = CNOTDihedral(circ4)
self.assertEqual(elem1, elem4,
"Error: 2-qubit CX identity does not hold")
# XI*CX*XX = CX
circ5 = QuantumCircuit(2)
circ5.x(0)
circ5.cx(0, 1)
circ5.x(0)
circ5.x(1)
elem5 = CNOTDihedral(circ5)
self.assertEqual(elem1, elem5,
"Error: 2-qubit CX identity does not hold")
# IT*CX01*CX10*TdgI = CX01*CX10
circ1 = QuantumCircuit(2)
circ1.cx(0, 1)
circ1.cx(1, 0)
circ2 = QuantumCircuit(2)
circ2.t(1)
circ2.cx(0, 1)
circ2.cx(1, 0)
circ2.tdg(0)
elem1 = CNOTDihedral(circ1)
elem2 = CNOTDihedral(circ2)
self.assertEqual(elem1, elem2,
"Error: 2-qubit CX01*CX10 identity does not hold")