2. System State is
captured by a
Probability
Our Two Worlds
Distribution
Σ vi = 1 , 0<=vi<=1
T is stochastic (non-neg, col sums 1)
Classical
Measurement
Quantum
|v|2 = v†v = Σ |vi|2 = 1
System State is T is Unitary T†T = I
captured by an
Amplitude
Distribution
4. Simple Search
• Given n items, A[1..n]
• Exactly one satisfies f()=1
– all others have f()=0
• Find the unique object for which f()=1
• How many f() calls are needed?
5. Classical Algorithm
x Random item in 1..n
Repeat
–
– If f(x)=1
• Stay at x
– Else
• Choose another (never previously picked) value for x,
each possible value equi-probably
K times
7. Grover’s Quantum Algorithm
x Random item in 1..n
Repeat
– If f(x)=1
• then stay at x with amplitude -1
• else stay at x with amplitude 1
– Choose
– this x with amplitude a
– another value for x, each possible value with equal
amplitude, say b
K times