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Build Your Own Quantum
Computer for Fun and Profit!
Stephen Granade
Bits are 1s and 0s (i.e. base 2)
16 8 4
1 0 0 11
16 +
2
1
2 + 1 = 19
Save Us, Gordon Moore!
I2 w/9MB cache
1E+09
100000000
10000000
Pentium
80486
1000000
Transistors
80286
100000
10000
Pentium 4
Itanium 2
Pentium III
Itanium
Pentium II
80386
8086
4004
8080
8008
1000
100
10
1
1970
1975
1980
1985
1990
Year
1995
2000
2005
Parallel Computation
Takes More Space
Photo credit: pure_martin
Light Polarization States

Vertical light:

Horizontal light:
A mix:
1
1
 

2
2
Amplitudes
Square for probabilities:
1
,
2
1

2
What’s Going On With The 3 Polarizers
Vertical polarizer:

Horizontal polarizer:
nada
What’s Going On With The 3 Polarizers
Vertical polarizer:
45 degree polarizer:
Horizontal polarizer:

1
1
 

2
2

Bits Hold 1 Number
Qubits Can Hold All Numbers!
3-Bit Number
101
3-Qubit Number
 000

 010
1 
8  100

 110
 001  

 011  

 101  

 111 
Superposition makes
this possible
Tangent: Entanglement Happens
When One Qubit’s State Depends on
Another’s
1
Entangled
Not Entangled

00
2
1
 11 
If you measure the first
qubit and it’s 0, you know
the second qubit is 0 too.
They’re entangled!

00
2
 01 
If you measure the first
qubit and it’s 0, you don’t
know the second qubit.
They’re independent!
You Can Add All Numbers At Once!
Classical Computer
0111  100
Quantum Computer
1
1

00
4

00
4
 01  10  11  
 01  10  11  
 00  2 01  3 10  4 11  
1



44  3 100  2 101  110

It’s Just an Algorithm
Choose p, q ( very large prime)
n  pq
d  e  1 mod  p  1q  1
encrypt  msg  mod n
e
msg  encrypt  mod n
d
Public
Private
Turning Factoring into Period Finding
2
x mod n, x mod n,
3
4
x mod n, x mod n,
Leonhard Euler
If n has the factors p and q,
then, if you pick a random x,
the above sequence has a
period that evenly divides
into (p-1)(q-1)
Shor’s Algorithm is Fast
Classical factoring

O2
logn1 / 3

Shor’s Algorithm

O log n 
3

Grover’s Algorithm Finds Stuff Quickly
Searches unsorted data
Number of items
Approx. Speedup
100
10
1,000
32
Photo credit: seanabrady
10,000
100
100,000
316
1,000,000
1000
10,000,000
3162
100,000,000
10000
1,000,000,000
31623
Decoherence Smears Out States
1
1
alive 
dead
2
2
dead
There are Lots of Ways to Make a
Quantum Computer
Photons
Trapped Ions
Liquid NMR
Spintronics
Optical Lattice
7-Qubit Computer from IBM
2001. Chuang et. al.
Factored 15
3
5
First Qubyte from Innsbruck
Quantum Computer Onna Chip
Sadly I have no good
pictures of the group
or its research besides
this graphic from the
cover of Science
D-Wave…maybe