1. Quantum Circuit Visualization
Bradley S. Rubin, Ph.D.
Associate Professor
Graduate Programs in Software
University of St. Thomas
St. Paul, MN

2. In The Beginning... 0s and 1s (bits) It was all a simple matter of
(conventional computing)

3. Then In 1981... Qubits Richard Feynman thought about a computer built
with quantum particles
Qubits
(quantum computing)

4. ( ) The Qubit α β α | 0 〉+ β | 1〉 = Physicist Computer Scientist
α, β ∈ Complex
| α |2 + | β |2 = 1

5. Occupy multiple states simultaneously
Qubit Power
Superposition
Occupy multiple states simultaneously
Entanglement
Correlation amongst
states

6. Can represent ONE of 23=8 states
Example: 3 Bits
Can represent ONE of 23=8 states
000
001
010
011
100
101
110
111

7. Can represent ALL 23=8 states SIMULTANEOUSLY
Example: 3 Qubits
Can represent ALL 23=8 states SIMULTANEOUSLY
000
001
010
011
100
101
110
111
and 100 qubits → 1030 states

8. The Catch Even though n qubits can represent
a superposition of 2n states...
When we measure them, we only
read one state, and all the others disappear...
The probability of reading a state is given
by the norm of the qubit’s complex
coefficient, squared

9. The Big Deal (Theory) Shor’s Quantum Factoring Algorithm (1994)
Exponential Speedup in Integer Factoring
Breaks the RSA cryptosystem (and most others)
Grover’s Quantum Search Algorithm (1996)
Quadratic Speedup in Unordered Search
And many others... but only a narrow subset of
algorithms benefit from quantum computation
+ Feynman’s dream of quantum quantum simulation

10. The Little Deal (Practice)
Currently, quantum information theory
FAR outpaces physical implementation
The best Shor hardware implementation (2009):
15=3x5
Quantum states are fragile (decoherence) →
Quantum Error Correction

11. Learning Quantum Computing
Physicists must learn some computer science
Computer scientists must learn some quantum mechanics
Both must learn a new paradigm:
states, operators/gates,
circuit diagrams, algorithms

12. How can we gain some intuition
Circuits
Familiar
How can we gain some intuition
about how this works?

13. Leverage Mathematica Color States Dash Entangled States
Draw Circuit Diagrams
Show Intermediate States
Compute Output from Input
MANIPULATE INPUT
Some Examples...

14. 1-Qubit Gates

15. Bell States and Swapping

16. Deutsch’s Algorithm Experiment using colored balls
to represent qubit state

17. Quantum Teleportation

18. Grover Search

19. Shor Factoring

20. Why Explore Quantum Computing?
Rethink algorithms/computational complexity
Probe the foundations of quantum mechanics
Dream about quantum quantum simulators
RETHINK WHAT IT MEANS TO COMPUTE
(And maybe, even build one someday)
Plus, this is a great problem domain for
building Mathematica skill!