1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
|
#!/usr/bin/env python
"""Demonstration of quantum dense coding."""
from sympy import pprint
from sympy.physics.quantum import qapply
from sympy.physics.quantum.gate import H, X, Z, CNOT
from sympy.physics.quantum.grover import superposition_basis
def main():
psi = superposition_basis(2)
psi
# Dense coding demo:
# Assume Alice has the left QBit in psi
print("An even superposition of 2 qubits. Assume Alice has the left QBit.")
pprint(psi)
# The corresponding gates applied to Alice's QBit are:
# Identity Gate (1), Not Gate (X), Z Gate (Z), Z Gate and Not Gate (ZX)
# Then there's the controlled not gate (with Alice's as control):CNOT(1, 0)
# And the Hadamard gate applied to Alice's Qbit: H(1)
# To Send Bob the message |0>|0>
print("To Send Bob the message |00>.")
circuit = H(1)*CNOT(1, 0)
result = qapply(circuit*psi)
result
pprint(result)
# To send Bob the message |0>|1>
print("To Send Bob the message |01>.")
circuit = H(1)*CNOT(1, 0)*X(1)
result = qapply(circuit*psi)
result
pprint(result)
# To send Bob the message |1>|0>
print("To Send Bob the message |10>.")
circuit = H(1)*CNOT(1, 0)*Z(1)
result = qapply(circuit*psi)
result
pprint(result)
# To send Bob the message |1>|1>
print("To Send Bob the message |11>.")
circuit = H(1)*CNOT(1, 0)*Z(1)*X(1)
result = qapply(circuit*psi)
result
pprint(result)
if __name__ == "__main__":
main()
|
