James L. Weaver
Developer Advocate


jweaver@pivotal.io
JavaFXpert.com

@JavaFXpert

Dr. Johan Vos
Co-founder & CTO


johan.vos@gluonhq.com
gluonhq.com

@JohanVos

Quantum Computing

Hacking into Nature's Computer

About Presenter James Weaver

Java Champion, JavaOne Rockstar, plays well with others, etc :-)

Author of several Java/JavaFX/RaspPi books

Developer Advocate & International Speaker for Pivotal

Mission: "Transform how the world builds software"

Mission: "Transform how the world builds software"

About Presenter Dr. Johan Vos

Developer / Physicist / Writer / Speaker -  Gluon

About Gluon

Gluon CloudLink

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

History repeating itself

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!

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

Breaking RSA crypto

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

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

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

Leveraging quantum computing for chemistry

Quantum communication and cryptography

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 

Qubit geometry

Representing qubits

ket notation, vectors, and geometrically

Hardware representation of qubits

Physical support Type
Photon Polarization Horizontal Vertical
Electrons Spin Up Down
Superconductor Charge Uncharged Charged
\vert0\rangle
0\vert0\rangle
\vert1\rangle
1\vert1\rangle

Superconducting qubits on a chip

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

Measuring in the computational basis

Visualizing quantum measurement

Polarized lenses blocking light

Vertically polarized photon

won't pass through horizontally polarized filter

Superposition collapse

Why does adding a lens let more light through?

Measuring in an alternative basis

Orchestrating superpositions

Measuring in various basis states

Double-slit experiment

constructive and destructive interference

Text

Classic logic gates

a quick review for comparison to quantum gates

Some quantum gates

matrix operations model quantum mechanical behavior

More quantum gates

just going though a phase

Quantum gate hardware

example using photons

NOT / Pauli-X / Bit flip gate

Pauli-Z / Phase flip gate

Hadamard gate

CNOT gate

Strange?

Java-based quantum simulator

Exploring the quantum simulator

e.g. visualize states of multiple qubits: |00>

Exploring the quantum simulator

e.g. visualize states of multiple qubits: |01>

Simple quantum circuit

collapses to 8 random states with equal probability

Quantum superpositions

and observability

Measuring qubits

collapses to a basis state, discarding superposition

Measuring quantum state

a Java analogy

Measuring quantum state

Hitchhiker's Guide to the Galaxy analogy

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

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

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.

 

1
11
2
22

Querying the oracle classically

\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \end{bmatrix} \cdot \begin{bmatrix} 0 \\ 1 \\ 0 \\ 0 \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \\ 0 \\ 1 \end{bmatrix}
[1000000100100100][0100]=[0001]\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \end{bmatrix} \cdot \begin{bmatrix} 0 \\ 1 \\ 0 \\ 0 \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \\ 0 \\ 1 \end{bmatrix}
\vert01\rangle
01\vert01\rangle
\vert11\rangle
11\vert11\rangle

example: f (0) = 0 and f (1) = 1   balanced

Quantum parallelism

what is it, really?

Double-slit experiment

constructive and destructive interference

Text

Choreographing interference

to increase the chance of getting the right answer

Text

Querying the oracle quantumly

\begin{bmatrix} +\frac{1}{2} & +\frac{1}{2} & +\frac{1}{2} & +\frac{1}{2} \\ +\frac{1}{2} & -\frac{1}{2} & +\frac{1}{2} & -\frac{1}{2} \\ +\frac{1}{2} & +\frac{1}{2} & -\frac{1}{2} & -\frac{1}{2} \\ +\frac{1}{2} & -\frac{1}{2} & -\frac{1}{2} & +\frac{1}{2} \end{bmatrix} \cdot \begin{bmatrix} 0 \\ 0 \\ 1 \\ 0 \end{bmatrix} = \begin{bmatrix} +\frac{1}{2} \\ +\frac{1}{2} \\ -\frac{1}{2} \\ -\frac{1}{2} \end{bmatrix}
[+12+12+12+12+1212+1212+12+121212+121212+12][0010]=[+12+121212]\begin{bmatrix} +\frac{1}{2} & +\frac{1}{2} & +\frac{1}{2} & +\frac{1}{2} \\ +\frac{1}{2} & -\frac{1}{2} & +\frac{1}{2} & -\frac{1}{2} \\ +\frac{1}{2} & +\frac{1}{2} & -\frac{1}{2} & -\frac{1}{2} \\ +\frac{1}{2} & -\frac{1}{2} & -\frac{1}{2} & +\frac{1}{2} \end{bmatrix} \cdot \begin{bmatrix} 0 \\ 0 \\ 1 \\ 0 \end{bmatrix} = \begin{bmatrix} +\frac{1}{2} \\ +\frac{1}{2} \\ -\frac{1}{2} \\ -\frac{1}{2} \end{bmatrix}

example: f (0) = 0 and f (1) = 1   balanced

\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \end{bmatrix} \cdot \begin{bmatrix} +\frac{1}{2} \\ +\frac{1}{2} \\ -\frac{1}{2} \\ -\frac{1}{2} \end{bmatrix} = \begin{bmatrix} +\frac{1}{2} \\ -\frac{1}{2} \\ -\frac{1}{2} \\ +\frac{1}{2} \end{bmatrix}
[1000000100100100][+12+121212]=[+121212+12]\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \end{bmatrix} \cdot \begin{bmatrix} +\frac{1}{2} \\ +\frac{1}{2} \\ -\frac{1}{2} \\ -\frac{1}{2} \end{bmatrix} = \begin{bmatrix} +\frac{1}{2} \\ -\frac{1}{2} \\ -\frac{1}{2} \\ +\frac{1}{2} \end{bmatrix}
\begin{bmatrix} +\frac{1}{2} & +\frac{1}{2} & +\frac{1}{2} & +\frac{1}{2} \\ +\frac{1}{2} & -\frac{1}{2} & +\frac{1}{2} & -\frac{1}{2} \\ +\frac{1}{2} & +\frac{1}{2} & -\frac{1}{2} & -\frac{1}{2} \\ +\frac{1}{2} & -\frac{1}{2} & -\frac{1}{2} & +\frac{1}{2} \end{bmatrix} \cdot \begin{bmatrix} +\frac{1}{2} \\ -\frac{1}{2} \\ -\frac{1}{2} \\ +\frac{1}{2} \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \\ 0 \\ 1 \end{bmatrix}
[+12+12+12+12+1212+1212+12+121212+121212+12][+121212+12]=[0001]\begin{bmatrix} +\frac{1}{2} & +\frac{1}{2} & +\frac{1}{2} & +\frac{1}{2} \\ +\frac{1}{2} & -\frac{1}{2} & +\frac{1}{2} & -\frac{1}{2} \\ +\frac{1}{2} & +\frac{1}{2} & -\frac{1}{2} & -\frac{1}{2} \\ +\frac{1}{2} & -\frac{1}{2} & -\frac{1}{2} & +\frac{1}{2} \end{bmatrix} \cdot \begin{bmatrix} +\frac{1}{2} \\ -\frac{1}{2} \\ -\frac{1}{2} \\ +\frac{1}{2} \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \\ 0 \\ 1 \end{bmatrix}
= \begin{bmatrix} \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}} \end{bmatrix}
=[12121212]= \begin{bmatrix} \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}} \end{bmatrix}

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

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

\vert0\rangle
0\vert0\rangle

Deutsch's algorithm

with oracle having balanced function

Expected result is 0% probability of measuring

\vert0\rangle
0\vert0\rangle

Leverages phase-kickback from the bottom wire to choreograph constructive and destructive interference

Deutsch-Jozsa algorithm

exponentially faster than classical

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:

Lecture 5: A simple searching algorithm; the Deutsch-Jozsa algorithm by John Watrous, University of Calgary

see also: Wikipedia Deutsch-Jozsa Decoherence section

 

2^{(n-1)}+1
2(n1)+12^{(n-1)}+1
1
11

(Exponentially faster!)

Deutsch-Jozsa algorithm

with oracle having constant function

Deutsch-Jozsa algorithm

example oracle with constant function

Deutsch-Jozsa algorithm

with oracle having balanced function

Deutsch-Jozsa algorithm

example oracle with balanced function

Deutsch-Jozsa implemented in Quil

Deutsch-Jozsa implemented in Quil

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

Quantum entanglement

basic circuit

Quantum teleportation

and the no cloning theorem

Superdense coding

example circuit

Bell inequality test 

(CHSH game)

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

Simon's algorithm

the quantum portion

Shor's algorithm

Period finding

using Quantum Fourier Transform

Grover's search

finding a needle in a haystack

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

aren't complicated

Complex numbers encode

amplitude and phase

Roots of unity

are useful for Shor

Matrices

think two-dimensional arrays

Vector spaces

a home for vectors and scalars

James L. Weaver
Developer Advocate


jweaver@pivotal.io
JavaFXpert.com

@JavaFXpert

Dr. Johan Vos
Co-founder & CTO


johan.vos@gluonhq.com
gluonhq.com

@JohanVos

Quantum Computing

Quantum Computing Exposed: Deep Dive

By javafxpert

Quantum Computing Exposed: Deep Dive

Helping developers get started with quantum computing

  • 3,807