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Quantum Computing
Hacking Nature's Computer
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About Presenter James Weaver
Java Champion, JavaOne Rockstar, plays well with others, etc :-)
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Author of several Java/JavaFX/RaspPi books
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Developer Advocate & International Speaker for Pivotal
Mission: "Transform how the world builds software"
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Mission: "Transform how the world builds software"
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You are cordially invited to ...
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Concepts we'll address today
Introduction to quantum computing
Axioms of quantum mechanics (with cats)
- Superposition principle
- Measurement
- Unitary evolution
Quantum mechanical demo (with photons)
Abstracting cats and photons with qubits
Quantum computing algorithms
Quantum entanglement
More algorithms
Supplementary resources
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Deutsch's algorithm (1985)
Literally the Hello World of quantum algorithms
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Deutsch's algorithm
Determine if function is constant or balanced
Input a | Constant f(a) | Constant f(a) | Balanced f(a) | Balanced f(a) |
---|---|---|---|---|
0 | 0 | 1 | 0 | 1 |
1 | 0 | 1 | 1 | 0 |
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Deutsch's algorithm
How many queries of the oracle to solve?
Classical:
This oracle requires 2 queries classically
Quantum:
We create a superposition of inputs to the oracle for constructive/destructive interference.
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Querying the oracle classically
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example: f (0) = 0 and f (1) = 1 balanced
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Quantum parallelism
what is it, really?
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Double-slit experiment
constructive and destructive interference
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Text
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Choreographing interference
to increase the chance of getting the right answer
Text
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Excerpts from “THE TALK” by Scott Aaronson and Zach Weinersmith
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Querying the oracle quantumly
example: f (0) = 0 and f (1) = 1 balanced
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Lecture 3: One Qubit, Two Qubit by Dave Bacon, University of Washington (Deutsch slightly modified)
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Deutsch (slightly modified)
Why constant vs. balance require only one query
Inp | Con |
---|---|
0 | 0 |
1 | 0 |
Inp | Con |
---|---|
0 | 1 |
1 | 1 |
Inp | Bal |
---|---|
0 | 0 |
1 | 1 |
Inp | Bal |
---|---|
0 | 1 |
1 | 0 |
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Deutsch's algorithm
with oracle having constant function
Leverages phase-kickback from the bottom wire to choreograph constructive and destructive interference
Expected result is 100% probability of measuring
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Deutsch's algorithm
with oracle having balanced function
Expected result is 0% probability of measuring
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Leverages phase-kickback from the bottom wire to choreograph constructive and destructive interference
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Deutsch-Jozsa algorithm
exponentially faster than classical
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Deutsch-Jozsa algorithm, 1992
Determine if function is constant or balanced
Input | Constant | Constant | Balanced | Balanced |
---|---|---|---|---|
000 | 0 | 1 | 0 | 1 |
001 | 0 | 1 | 1 | 0 |
010 | 0 | 1 | 0 | 1 |
011 | 0 | 1 | 1 | 0 |
100 | 0 | 1 | 0 | 1 |
101 | 0 | 1 | 1 | 0 |
110 | 0 | 1 | 0 | 1 |
111 | 0 | 1 | 1 | 0 |
Results when querying our example oracle
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Deutsch-Jozsa algorithm
How many invocations of the oracle to solve?
Classical:
Our oracle (black box) requires 5 invocations classically
Quantum:
We create a superposition of inputs to the oracle, and use the phase-kickback trick, for constructive/destructive interference. See:
see also: Wikipedia Deutsch-Jozsa Decoherence section
(Exponentially faster!)
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Deutsch-Jozsa algorithm
with oracle having constant function
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Deutsch-Jozsa algorithm
example oracle with constant function
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Deutsch-Jozsa algorithm
with oracle having balanced function
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Deutsch-Jozsa algorithm
example oracle with balanced function
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Deutsch-Jozsa implemented in Quil
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Deutsch-Jozsa implemented in Quil
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Concepts we'll address today
Introduction to quantum computing
Axioms of quantum mechanics (with cats)
- Superposition principle
- Measurement
- Unitary evolution
Quantum mechanical demo (with photons)
Abstracting cats and photons with qubits
Quantum computing algorithms
Quantum entanglement
More algorithms
Supplementary resources
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Quantum entanglement
Alice and Bob's long running relationship
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Quantum entanglement
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basic circuit
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Quantum teleportation
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and the no cloning theorem
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Superdense coding
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example circuit
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Bell inequality test
(CHSH game)
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Concepts we'll address today
Introduction to quantum computing
Axioms of quantum mechanics (with cats)
- Superposition principle
- Measurement
- Unitary evolution
Quantum mechanical demo (with photons)
Abstracting cats and photons with qubits
Quantum computing algorithms
Quantum entanglement
More algorithms
Supplementary resources
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Bernstein-Vazirani algorithm
basic circuit
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Simon's algorithm
the quantum portion
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Shor's algorithm
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Period finding
using Quantum Fourier Transform
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Grover's search
finding a needle in a haystack
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Concepts we'll address today
Introduction to quantum computing
Axioms of quantum mechanics (with cats)
- Superposition principle
- Measurement
- Unitary evolution
Quantum mechanical demo (with photons)
Abstracting cats and photons with qubits
Quantum computing algorithms
Quantum entanglement
More algorithms
Supplementary resources
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Complex numbers
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aren't complicated
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Complex numbers encode
amplitude and phase
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Roots of unity
are useful for Shor
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Matrices
think two-dimensional arrays
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Vector spaces
a home for vectors and scalars
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Classic textbook on Quantum Computing
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by "Mike & Ike"
By Source (WP:NFCC#4), Fair use,
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Quantum Computing
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Quantum Computing Exposed: Hacking Nature's Computer
By javafxpert
Quantum Computing Exposed: Hacking Nature's Computer
Part two of a gentle introduction to quantum computing
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