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Quantum Computing
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/3998732/johan-round-300x300.png)
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Hacking into Nature's Computer
About Presenter James Weaver
Java Champion, JavaOne Rockstar, plays well with others, etc :-)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/2305520/Screen_Shot_2016-03-03_at_3.30.04_PM.png)
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Author of several Java/JavaFX/RaspPi books
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/3090105/jim-weaver-fretboard.png)
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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About Presenter Dr. Johan Vos
Developer / Physicist / Writer / Speaker - Gluon
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/3998735/Screen_Shot_2017-07-20_at_11.32.30_AM.png)
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About Gluon
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4304298/Screen_Shot_2017-11-07_at_10.05.41_AM.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/3998735/Screen_Shot_2017-07-20_at_11.32.30_AM.png)
Gluon CloudLink
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4304300/Screen_Shot_2017-11-07_at_10.06.16_AM.png)
Concepts we'll address today
Introduction to quantum computing
Representing qubits
Axioms of quantum mechanics
- Superposition principle
- Measurement
- Unitary evolution
Quantum computing algorithms
Quantum entanglement
More algorithms
Supplementary resources
Intro to Quantum Computing
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4137734/2000px-Bloch_Sphere.png)
History repeating itself
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4137779/Eniac.jpg)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4137793/ibm-q-hardware.png)
massive hardware, limited bits, software infancy
Quantum computers make direct use of quantum-mechanical phenomena, such as superposition and entanglement, to perform operations on data.
Some QC proofs of concept
mini-universe in your garage
Don't try this at home, kids!
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4180050/sussex-qc.jpg)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4180052/delft-qc.jpg)
Why use a quantum computer?
Feasible on classical computers
Feasible on quantum computers
Solutions to problems
some problems may be solved exponentially faster
Transistors can't get much smaller
the quantum tunneling struggle is real
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4260017/quantum-tunneling-transistors.jpeg)
Breaking RSA crypto
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4086250/peter-shor.jpg)
someday maybe, using Shor's algorithm
“If you start factoring 10-digit numbers then it’s going to start getting scary”
Dr. Peter Shor, 2013
Related paper published 25 Jan 1997 by Dr. Shor:
Note: Shor's algorithm was formulated in 1994
Quickly searching unsorted data
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4086792/lov-grover-whiteboard.jpg)
using Grover's algorithm
"Programming a quantum computer is particularly interesting since there are multiple things happening in the same hardware simultaneously. One needs to think like both a theoretical physicist and a computer scientist."
Dr. Lov Grover, 2002
Related paper published 17 Jul 1997 by Dr. Grover:
Simulating nature
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4086175/Richard_Feynman_Nobel.jpg)
complex chemical reactions, for example
“Nature isn't classical, dammit, and if you want to make a simulation of nature, you'd better make it quantum mechanical, and by golly it's a wonderful problem, because it doesn't look so easy.”
Dr. Richard Feynman, 1981
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4086220/Feynman_and_Sheldon_playing_the_bongos.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4138000/Screen_Shot_2017-09-18_at_11.27.57_PM.png)
Leveraging quantum computing for chemistry
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4279108/Screen_Shot_2017-10-30_at_12.54.44_PM.png)
Quantum communication and cryptography
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4138083/Screen_Shot_2017-09-19_at_12.05.39_AM.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4138099/Screen_Shot_2017-09-19_at_12.18.57_AM.png)
Concepts we'll address today
Introduction to quantum computing
Representing qubits
Axioms of quantum mechanics
- Superposition principle
- Measurement
- Unitary evolution
Quantum computing algorithms
Quantum entanglement
More algorithms
Supplementary resources
Classical bits vs. qubits
two discrete states vs. infinite superpositions
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4137855/classical-bits-qubits.png)
Qubit geometry
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4302934/desmos-qubit-circle.png)
Representing qubits
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4129985/Screen_Shot_2017-09-15_at_5.05.57_PM.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4130004/Screen_Shot_2017-09-15_at_5.15.41_PM.png)
ket notation, vectors, and geometrically
Hardware representation of qubits
Physical support | Type | ||
---|---|---|---|
Photon | Polarization | Horizontal | Vertical |
Electrons | Spin | Up | Down |
Superconductor | Charge | Uncharged | Charged |
Superconducting qubits on a chip
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4302572/Rigetti_Tech_2017_HR--54-lower-res.jpg)
Concepts we'll address today
Introduction to quantum computing
Representing qubits
Axioms of quantum mechanics
- Superposition principle
- Measurement
- Unitary evolution
Quantum computing algorithms
Quantum entanglement
More algorithms
Supplementary resources
Diagonally polarized photon
collapsing to a measurement basis state
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4129361/Screen_Shot_2017-09-15_at_12.28.18_PM.png)
Measuring in the computational basis
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4179968/qubit-measure-standard-basis-some-psi.png)
Visualizing quantum measurement
Polarized lenses blocking light
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4129324/Screen_Shot_2017-09-15_at_12.09.44_PM.png)
Vertically polarized photon
won't pass through horizontally polarized filter
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4141717/ninety-degree-filters.png)
Superposition collapse
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4129263/Screen_Shot_2017-09-15_at_11.45.07_AM.png)
Why does adding a lens let more light through?
Measuring in an alternative basis
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4179957/qubit-measure-plus-minus-basis-zero-psi.png)
Orchestrating superpositions
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4129263/Screen_Shot_2017-09-15_at_11.45.07_AM.png)
Measuring in various basis states
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4129418/Screen_Shot_2017-09-15_at_12.55.22_PM.png)
Double-slit experiment
constructive and destructive interference
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4278421/2000px-Two-Slit_Experiment_Light.svg.png)
Text
Classic logic gates
a quick review for comparison to quantum gates
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4167045/classic-logic-gates.png)
Some quantum gates
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4129873/some-quantum-gates.png)
matrix operations model quantum mechanical behavior
More quantum gates
just going though a phase
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4207546/Screen_Shot_2017-10-10_at_8.41.24_AM.png)
Quantum gate hardware
example using photons
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4304581/photon-based-gate.png)
NOT / Pauli-X / Bit flip gate
from video: Single qubit gates - Umesh Vazirani
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4130981/Screen_Shot_2017-09-16_at_9.59.26_AM.png)
Pauli-Z / Phase flip gate
from video: Single qubit gates - Umesh Vazirani
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4130998/Screen_Shot_2017-09-16_at_10.07.02_AM.png)
Hadamard gate
from video: Single qubit gates - Umesh Vazirani
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4131016/Screen_Shot_2017-09-16_at_10.15.54_AM.png)
CNOT gate
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4204581/Screen_Shot_2017-10-09_at_2.03.15_PM.png)
Strange?
Java-based quantum simulator
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4304566/Screen_Shot_2017-11-07_at_11.25.31.png)
Exploring the quantum simulator
e.g. visualize states of multiple qubits: |00>
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4141525/Screen_Shot_2017-09-19_at_4.03.20_PM.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4141562/Screen_Shot_2017-09-19_at_4.12.25_PM.png)
Exploring the quantum simulator
e.g. visualize states of multiple qubits: |01>
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4141573/Screen_Shot_2017-09-19_at_4.21.41_PM.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4141576/Screen_Shot_2017-09-19_at_4.18.07_PM.png)
Simple quantum circuit
collapses to 8 random states with equal probability
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4141297/Screen_Shot_2017-09-19_at_2.51.14_PM.png)
Quantum superpositions
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4084855/dilbert-quantum.gif)
and observability
Measuring qubits
collapses to a basis state, discarding superposition
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4137899/Screen_Shot_2017-09-18_at_10.47.48_PM.png)
Measuring quantum state
a Java analogy
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4300150/harnessing-the-power-of-java-8-streams-22-638.jpg)
from an IndicThreads slide deck
Measuring quantum state
Hitchhiker's Guide to the Galaxy analogy
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4302694/hg2g-deep-thought.jpg)
Deep Thought after 7.5 million years of calculation
Concepts we'll address today
Introduction to quantum computing
Representing qubits
Axioms of quantum mechanics
- Superposition principle
- Measurement
- Unitary evolution
Quantum computing algorithms
Quantum entanglement
More algorithms
Supplementary resources
Deutsch's algorithm (1985)
Literally the Hello World of quantum algorithms
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4281709/deutsch-circuit-watrous.png)
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 |
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4281676/deutsch-oracle.png)
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.
Querying the oracle classically
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4281676/deutsch-oracle.png)
example: f (0) = 0 and f (1) = 1 balanced
Quantum parallelism
what is it, really?
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4279381/try-all-answers-meme.jpg)
Double-slit experiment
constructive and destructive interference
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4278421/2000px-Two-Slit_Experiment_Light.svg.png)
Text
Choreographing interference
to increase the chance of getting the right answer
Text
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4283459/Screen_Shot_2017-10-31_at_7.49.22_PM.png)
Excerpts from “THE TALK” by Scott Aaronson and Zach Weinersmith
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4283686/aaronson-the-talk-beginning.png)
Querying the oracle quantumly
example: f (0) = 0 and f (1) = 1 balanced
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4283058/deutsch-modified-bacon.png)
Lecture 3: One Qubit, Two Qubit by Dave Bacon, University of Washington (Deutsch slightly modified)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4287166/Screen_Shot_2017-11-01_at_6.10.53_PM.png)
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 |
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4279912/Screen_Shot_2017-10-30_at_4.52.30_PM.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4279920/Screen_Shot_2017-10-30_at_4.53.23_PM.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4279983/Screen_Shot_2017-10-30_at_4.54.26_PM.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4280026/Screen_Shot_2017-10-30_at_4.55.11_PM.png)
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
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4283758/Screen_Shot_2017-10-31_at_10.51.15_PM.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4283388/Screen_Shot_2017-10-31_at_8.07.41_AM.png)
Deutsch's algorithm
with oracle having balanced function
Expected result is 0% probability of measuring
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4283765/Screen_Shot_2017-10-31_at_10.54.11_PM.png)
Leverages phase-kickback from the bottom wire to choreograph constructive and destructive interference
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4283388/Screen_Shot_2017-10-31_at_8.07.41_AM.png)
Deutsch-Jozsa algorithm
exponentially faster than classical
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4130887/Deutsch-Jozsa_Algorithm.png)
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
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!)
Deutsch-Jozsa algorithm
with oracle having constant function
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4141317/Screen_Shot_2017-09-19_at_2.57.05_PM.png)
Deutsch-Jozsa algorithm
example oracle with constant function
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4130829/dj-algo-const-oracle.png)
Deutsch-Jozsa algorithm
with oracle having balanced function
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4141329/Screen_Shot_2017-09-19_at_3.03.34_PM.png)
Deutsch-Jozsa algorithm
example oracle with balanced function
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4130872/dl-algo-balanced-oracle.png)
Deutsch-Jozsa implemented in Quil
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4130887/Deutsch-Jozsa_Algorithm.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4259172/Screen_Shot_2017-10-24_at_2.09.16_PM.png)
Deutsch-Jozsa implemented in Quil
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4130887/Deutsch-Jozsa_Algorithm.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4259151/Screen_Shot_2017-10-24_at_2.06.06_PM.png)
Concepts we'll address today
Introduction to quantum computing
Representing qubits
Axioms of quantum mechanics
- Superposition principle
- Measurement
- Unitary evolution
Quantum computing algorithms
Quantum entanglement
More algorithms
Supplementary resources
Quantum entanglement
Alice and Bob's long running relationship
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4300349/quantum_entanglement.jpg)
Quantum entanglement
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4176662/Screen_Shot_2017-09-29_at_7.45.29_PM.png)
basic circuit
Quantum teleportation
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4176671/Screen_Shot_2017-09-29_at_7.51.51_PM.png)
and the no cloning theorem
Superdense coding
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4176676/Screen_Shot_2017-09-29_at_7.59.47_PM.png)
example circuit
Bell inequality test
(CHSH game)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4176692/Screen_Shot_2017-09-29_at_8.20.20_PM.png)
Concepts we'll address today
Introduction to quantum computing
Representing qubits
Axioms of quantum mechanics
- Superposition principle
- Measurement
- Unitary evolution
Quantum computing algorithms
Quantum entanglement
More algorithms
Supplementary resources
Bernstein-Vazirani algorithm
basic circuit
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4215387/Screen_Shot_2017-10-11_at_10.09.05_PM.png)
Simon's algorithm
the quantum portion
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4223694/Screen_Shot_2017-10-14_at_10.08.46_AM.png)
Shor's algorithm
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4304248/Screen_Shot_2017-11-07_at_9.29.46_AM.png)
Period finding
using Quantum Fourier Transform
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4223777/Screen_Shot_2017-10-14_at_10.57.24_AM.png)
Grover's search
finding a needle in a haystack
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4176684/Screen_Shot_2017-09-29_at_8.14.09_PM.png)
Concepts we'll address today
Introduction to quantum computing
Representing qubits
Axioms of quantum mechanics
- Superposition principle
- Measurement
- Unitary evolution
Quantum computing algorithms
Quantum entanglement
More algorithms
Supplementary resources
Complex numbers
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4109914/1000px-Complex_number_illustration.svg.png)
aren't complicated
Complex numbers encode
amplitude and phase
Roots of unity
are useful for Shor
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4110300/1000px-One5Root.svg.png)
Matrices
think two-dimensional arrays
![](https://s3.amazonaws.com/media-p.slid.es/uploads/396450/images/4110446/Matrix.svg.png)
Vector spaces
a home for vectors and scalars
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Quantum Computing
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Quantum Computing Exposed: Deep Dive
By javafxpert
Quantum Computing Exposed: Deep Dive
Helping developers get started with quantum computing
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