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April 27, 2011 23:34
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limitedmage revised this gist
May 2, 2011 . 1 changed file with 215 additions and 9 deletions.There are no files selected for viewing
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Learn more about bidirectional Unicode charactersOriginal file line number Diff line number Diff line change @@ -1,11 +1,9 @@ import math import random class Qubit: def __init__(self, a = 1, b = 0): '''Initialize a single qubit''' self.zero = complex(a) self.one = complex(b) @@ -14,13 +12,17 @@ def xgate(self): self.zero, self.one = self.one, self.zero return self def zgate(self): '''Apply a Z gate''' self.one = -self.one def hgate(self): '''Apply a Hadamard gate''' a = self.zero b = self.one self.zero = a + b self.one = a - b self.normalize() return self def measure(self): @@ -37,9 +39,213 @@ def measure(self): self.one = complex(1) return 1 def normalize(self): norm = (abs(self.zero) ** 2 + abs(self.one) ** 2) ** 0.5 self.zero /= norm self.one /= norm return self def __repr__(self): return str(self.zero) + " |0> + " + str(self.one) + " |1>\n" class TwoQubit: def __init__(self, a = 1, b = 0, c = 0, d = 0): '''Initialize a two-qubit entanglement''' self.zerozero = complex(a) self.zeroone = complex(b) self.onezero = complex(c) self.oneone = complex(d) def cnot(self): '''Controlled NOT operation''' self.onezero, self.oneone = self.oneone, self.onezero return self def hgate(self): '''Perform Hadamard operation on first qubit''' a = self.zerozero b = self.zeroone c = self.onezero d = self.oneone self.zerozero = a + c self.zeroone = b + d self.onezero = a - c self.oneone = b - d self.normalize() return self def xgate(self): '''Apply an X (NOT) gate to the first qubit''' a = self.zerozero b = self.zeroone c = self.onezero d = self.oneone self.zerozero = c self.zeroone = d self.onezero = a self.oneone = b return self def zgate(self): '''Apply a Z gate on the first qubit''' self.onezero *= -1 self.oneone *= -1 return self def normalize(self): norm = (abs(self.zerozero) ** 2 + abs(self.zeroone) ** 2 + abs(self.onezero) ** 2 + abs(self.oneone) ** 2) ** 0.5 self.zerozero /= norm self.zeroone /= norm self.onezero /= norm self.oneone /= norm return self def measure(self): '''Measure the two-qubit in the computational basis''' zerozeroprob = abs(self.zerozero) ** 2 zerooneprob = abs(self.zeroone) ** 2 onezeroprob = abs(self.onezero) ** 2 randomchoice = random.random() if randomchoice < zerozeroprob: self.zerozero = complex(1) self.zeroone = complex(0) self.onezero = complex(0) self.oneone = complex(0) return (0, 0) elif randomchoice < zerooneprob: self.zerozero = complex(0) self.zeroone = complex(1) self.onezero = complex(0) self.oneone = complex(0) return (0, 1) elif randomchoice < onezeroprob: self.zerozero = complex(0) self.zeroone = complex(0) self.onezero = complex(1) self.oneone = complex(0) return (1, 0) else: self.zerozero = complex(0) self.zeroone = complex(0) self.onezero = complex(0) self.oneone = complex(1) return (1, 1) def __repr__(self): comp = [self.zerozero, self.zeroone, self.onezero, self.oneone] comp = [i.real if i.real == i else i for i in comp] comp = [str(i) for i in comp] comp = ["" if i == "1.0" else i for i in comp] ls = [] if abs(self.zerozero) > 0: ls += [comp[0] + " |00>"] if abs(self.zeroone) > 0: ls += [comp[1] + " |01>"] if abs(self.onezero) > 0: ls += [comp[2] + " |10>"] if abs(self.oneone) > 0: ls += [comp[3] + " |11>"] comp = " + ".join(ls) return comp def superdense_coding(): '''The superdense coding protocol This protocol will show how two classical bits can be stored in a single qubit''' print "==============================================" print "==========Superdense coding protocol==========" print "==============================================" print a = TwoQubit() print "Eve starts with two qubits in state", a print print "Eve prepares Bell state, first with Hadamard gate on first qubit:" a.hgate() print a print "and then with controlled Not gate on the two qubits:" a.cnot() print a print print "Eve sends one qubit to Alice and another to Bob." print print "Alice wants to encode two classical bits to send to Bob" print "with only her one qubit" print x = raw_input("First bit: ") while x not in ["0", "1"]: print "Wrong input (0 or 1 only)" x = raw_input("First bit: ") y = raw_input("Second bit: ") while y not in ["0", "1"]: print "Wrong input (0 or 1 only)" y = raw_input("Second bit: ") x = int(x) y = int(y) print if x == 0 and y == 0: print "For encoding 00, nothing is done (I gate is applied)" elif x == 0 and y == 1: print "For encoding 01, the X (NOT) gate is applied" a.xgate() elif x == 1 and y == 0: print "For encoding 10, the Z gate is applied" a.zgate() else: print "For encoding 11, the X and Z gates are applied" a.xgate().zgate() print a print print "Because Alice and Bob's qubits were entangled by Eve," print "Alice's operations affect both, despite being far apart." print print "Alice sends her qubit to Bob. Now Bob has both original qubits." print print "Bob applies a reverse operation of Eve's original operation" print "First a controlled Not:" a.cnot() print a print "Then a Hadamard on the first Qubit:" a.hgate() print a print print "Finally, Bob measures the qubits in the computational basis." res = a.measure() print "The result of Bob's measurement is", res, ", Alice's two bits." if __name__ == '__main__': superdense_coding() -
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This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters. Learn more about bidirectional Unicode charactersOriginal file line number Diff line number Diff line change @@ -0,0 +1,45 @@ from numpy import matrix from numpy import linalg import numpy import math import random class Qubit: def __init__(self, a, b): self.zero = complex(a) self.one = complex(b) def xgate(self): '''Apply a NOT (X) gate''' self.zero, self.one = self.one, self.zero return self def hgate(self): '''Apply a Hadamard gate''' h = matrix([[1, 1], [1, -1]]) * (1.0 / math.sqrt(2)) curr = matrix([[self.zero],[self.one]]) new = numpy.asarray(h * curr) self.zero = new[0][0] self.one = new[1][0] return self def measure(self): '''Measure the qubit in the computational basis''' zeroprob = abs(self.zero) ** 2 randomchoice = random.random() if randomchoice < zeroprob: self.zero = complex(1) self.one = complex(0) return 0 else: self.zero = complex(0) self.one = complex(1) return 1 def __repr__(self): return str(self.zero) + " |0> + " + str(self.one) + " |1>\n"