def main():
qc_a = QuantumComputer(2)
qc_a.X(0)
qc_a.CNOT(0, 1)
print("2 (A): ", qc_a.ket_notation())
qc_b = QuantumComputer(2)
qc_b.H(0)
qc_b.CNOT(0, 1)
print("2 (B): ", qc_b.ket_notation())
def question4():
state = 1 / np.sqrt(2) * (np.kron(ZERO, ZERO) - np.kron(ONE, ONE))
ix = QuantumComputer(state).I(0).X(1).ket_notation()
iy = QuantumComputer(state).I(0).Y(1).ket_notation()
xy = QuantumComputer(state).X(0).Y(1).ket_notation()
print()
print("Question 4: ")
print(f"IX({to_ket_notation(state)}) = {ix} = |O-⟩")
print(f"IY({to_ket_notation(state)}) = {iy} = i|O+⟩")
print(f"XY({to_ket_notation(state)}) = {xy} = i|E+⟩")
def question3():
qc = QuantumComputer(2)
qc.H(0)
qc.H(1)
probabilities, new_states = zz_parity_measurement(qc.state)
print()
print("Question 3: ")
print("After H gate on each qubit.")
print(
f"{to_ket_notation(new_states[0])} with prob = {probabilities[0]:.2f}")
print(
f"{to_ket_notation(new_states[1])} with prob = {probabilities[1]:.2f}")
def question4():
qc = QuantumComputer(2)
qc.H(0)
qc.H(1)
qc.CNOT(0, 1)
qc.H(0)
qc.H(1)
qc_dash = QuantumComputer(2)
qc_dash.CNOT(1, 0)
print("Question 4:", np.isclose(qc.unitary, qc_dash.unitary).all()) # True
def question5():
T_GATE = np.array([
[1, 0],
[0, np.power(np.e, complex(0, np.pi / 4))]
])
TOFFOLI_GATE = np.array([
[1, 0, 0, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0, 0, 0],
[0, 0, 0, 1, 0, 0, 0, 0],
[0, 0, 0, 0, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 1],
[0, 0, 0, 0, 0, 0, 1, 0]
])
qc = QuantumComputer(3)
qc.H(2)
qc.CNOT(1, 2)
qc.gates(T_GATE.conjugate().transpose(), 2)
qc.CNOT(0, 2)
qc.gates(T_GATE, 2)
qc.CNOT(1, 2)
qc.gates(T_GATE.conjugate().transpose(), 2)
qc.CNOT(0, 2)
qc.gates(T_GATE, 1)
qc.gates(T_GATE, 2)
qc.CNOT(0, 1)
qc.H(2)
qc.gates(T_GATE, 0)
qc.gates(T_GATE.conjugate().transpose(), 1)
qc.CNOT(0, 1)
print("Question 5:", np.isclose(qc.unitary, TOFFOLI_GATE).all()) # True
def question3():
qc = QuantumComputer(2)
qc.H(1)
qc.controlled_gate(Z_GATE, 1, 0)
qc.H(1)
print("Question 3:", np.isclose(qc.unitary, CNOT_GATE).all()) # True
def question1():
qc = QuantumComputer(1)
qc.H(0)
qc.Y(0)
qc.H(0)
print("Question 1 (XYX = -Y):", np.isclose(qc.unitary, -Y_GATE).all()) # True