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

@JavaFXpert

Mission: "Transform how the world builds software"

@JavaFXpert

Mission: "Transform how the world builds software"

@JavaFXpert

About Presenter Dr. Johan Vos

Developer / Physicist / Writer / Speaker -  Gluon

@JohanVos

@JohanVos

About Gluon

@JohanVos

Gluon CloudLink

Concepts we'll address today

Introduction to quantum computing

Axioms of quantum mechanics (with cats)

  • Superposition principle
  • Measurement
  • Unitary evolution

Abstracting cats with qubits

Quantum computing gates and circuits

Java and quantum computing

@JavaFXpert

History repeating itself

ENIAC computer circa 1947

IBM Research quantum computer circa 2017

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.

@JavaFXpert

Some QC proofs of concept

University of Sussex

Professor Winfried Hensinger spoke at Devoxx/UK

Delft University of Technology

mini-universe in your garage

Don't try this at home, kids!

@JavaFXpert

Why use a quantum computer?

Feasible on classical computers

Feasible on quantum computers

Solutions to problems

some problems may be solved exponentially faster

@JavaFXpert

Transistors can't get much smaller

the quantum tunneling struggle is real

spectrum.ieee.org/semiconductors/devices/the-tunneling-transistor

@JavaFXpert

Breaking RSA crypto

someday maybe, using Shor's algorithm

newscientist.com/article/mg22029445-100-my-quantum-algorithm-wont-break-the-internet-yet/

“If you start factoring 10-digit numbers then it’s going to start getting scary”

Dr. Peter Shor, 2013

Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer

Related paper published 25 Jan 1997 by Dr. Shor:

Note: Shor's algorithm was formulated in 1994

@JavaFXpert

Quickly searching unsorted data

using Grover's algorithm

outlookindia.com/magazine/story/ring-o-stars/220719

"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

Quantum Mechanics helps in searching for a needle in a haystack

Related paper published 17 Jul 1997 by Dr. Grover:

@JavaFXpert

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

en.wikipedia.org/wiki/Richard_Feynman

bigbangtheory.wikia.com/wiki/Richard_Feynman

@JavaFXpert

Nature journal issued 14 September 2017

Leveraging quantum computing for chemistry

arxiv.org/abs/1710.07629

@JavaFXpert

Quantum communication and cryptography

arxiv.org/abs/1707.00542

arxiv.org/abs/1707.00934

@JavaFXpert

Machine learning

estimating gradients using quantum computing

@JavaFXpert

Keri McKiernan: Computing gradients using Forest

Concepts we'll address today

Introduction to quantum computing

Axioms of quantum mechanics (with cats)

  • Superposition principle
  • Measurement
  • Unitary evolution

Abstracting cats with qubits

Quantum computing gates and circuits

Java and quantum computing

@JavaFXpert

Axioms of Quantum Mechanics

\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle

featuring grumpy cat (or is it grumpy ket)? 

@JavaFXpert

My microscopic cat is often grumpy

@JavaFXpert

\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle
\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle

sometimes he is actually happy

but I've never observed him in-between those states

desmos.com/calculator/0rpttswx6s​

Axiom 1: Superposition principle

@JavaFXpert

my cat can be in any combination of grumpy and happy

\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle
= \begin{bmatrix} 1 \\ 0 \end{bmatrix}
=[10]= \begin{bmatrix} 1 \\ 0 \end{bmatrix}
\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle
= \begin{bmatrix} 0 \\ 1 \end{bmatrix}
=[01]= \begin{bmatrix} 0 \\ 1 \end{bmatrix}
= \begin{bmatrix} \sqrt{\frac{1}{3}} \\ \sqrt{\frac{2}{3}} \end{bmatrix}
=[1323]= \begin{bmatrix} \sqrt{\frac{1}{3}} \\ \sqrt{\frac{2}{3}} \end{bmatrix}
\sqrt{\frac{1}{3}}
13\sqrt{\frac{1}{3}}
\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle
+
++
\sqrt{\frac{2}{3}}
23\sqrt{\frac{2}{3}}
\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle
\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle
\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle

Representing quantum states

geometrically, ket notation, and vectors

\vert\space\space\space\space\rangle
∣    ⟩\vert\space\space\space\space\rangle
\vert\space\space\space\space\rangle
∣    ⟩\vert\space\space\space\space\rangle
\vert\space\space\space\space\rangle
∣    ⟩\vert\space\space\space\space\rangle
\vert\space\space\space\space\rangle
∣    ⟩\vert\space\space\space\space\rangle
\vert\space\space\space\space\rangle
∣    ⟩\vert\space\space\space\space\rangle
\vert\space\space\space\space\rangle
∣    ⟩\vert\space\space\space\space\rangle

@JavaFXpert

\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle
\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle

Axiom 2: Unitary evolution

gates modeled as matrices

X

\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \cdot \begin{bmatrix} 1 \\ 0 \end{bmatrix} = \begin{bmatrix} 0 \\ 1 \end{bmatrix}
[0110]⋅[10]=[01]\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \cdot \begin{bmatrix} 1 \\ 0 \end{bmatrix} = \begin{bmatrix} 0 \\ 1 \end{bmatrix}

NOT gate (Pauli/X, bit-flip)

@JavaFXpert

\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle

Hadamard gate

great for putting cats in equal superpositions

H

\begin{bmatrix} \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}} \end{bmatrix} \cdot \begin{bmatrix} 1 \\ 0 \end{bmatrix} = \begin{bmatrix} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{bmatrix}
[121212−12]⋅[10]=[1212]\begin{bmatrix} \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}} \end{bmatrix} \cdot \begin{bmatrix} 1 \\ 0 \end{bmatrix} = \begin{bmatrix} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{bmatrix}

Hadamard gate

\sqrt{\frac{1}{2}}
12\sqrt{\frac{1}{2}}
\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle
+
++
\sqrt{\frac{1}{2}}
12\sqrt{\frac{1}{2}}
\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle

@JavaFXpert

\sqrt{\frac{1}{3}}
13\sqrt{\frac{1}{3}}
\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle
+
++
\sqrt{\frac{2}{3}}
23\sqrt{\frac{2}{3}}
\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle

Axiom 3: Measurement

probability is amplitude squared

When observed there is a:

\frac{1}{3}
13\frac{1}{3}
\frac{2}{3}
23\frac{2}{3}

probability of being grumpy

probability of being happy

@JavaFXpert

Multiple cats

\vert\space\space\space\space\space\space\space\rangle
∣       ⟩\vert\space\space\space\space\space\space\space\rangle
\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle
\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle
=
==
\vert\space\space\space\space\space\space\space\space\rangle
∣        ⟩\vert\space\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\space\rangle
∣        ⟩\vert\space\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\space\rangle
∣        ⟩\vert\space\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\space\rangle
∣        ⟩\vert\space\space\space\space\space\space\space\space\rangle
= \begin{bmatrix} 1 \\ 0 \end{bmatrix}
=[10]= \begin{bmatrix} 1 \\ 0 \end{bmatrix}
\otimes \begin{bmatrix} 1 \\ 0 \end{bmatrix}
⊗[10] \otimes \begin{bmatrix} 1 \\ 0 \end{bmatrix}

Composite quantum states

= \begin{bmatrix} 1 \\ \\ \\ \end{bmatrix}
=[1]= \begin{bmatrix} 1 \\ \\ \\ \end{bmatrix}
= \begin{bmatrix} 1 \\ 0 \\ \\ \end{bmatrix}
=[10]= \begin{bmatrix} 1 \\ 0 \\ \\ \end{bmatrix}
= \begin{bmatrix} 1 \\ 0 \\ 0 \\ \end{bmatrix}
=[100]= \begin{bmatrix} 1 \\ 0 \\ 0 \\ \end{bmatrix}
= \begin{bmatrix} 1 \\ 0 \\ 0 \\ 0 \end{bmatrix}
=[1000]= \begin{bmatrix} 1 \\ 0 \\ 0 \\ 0 \end{bmatrix}

@JavaFXpert

Multiple cats

\vert\space\space\space\space\space\space\space\rangle
∣       ⟩\vert\space\space\space\space\space\space\space\rangle
\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle
\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle
=
==
= \begin{bmatrix} 0 \\ 1 \\ 0 \\ 0 \end{bmatrix}
=[0100]= \begin{bmatrix} 0 \\ 1 \\ 0 \\ 0 \end{bmatrix}
= \begin{bmatrix} 1 \\ 0 \end{bmatrix}
=[10]= \begin{bmatrix} 1 \\ 0 \end{bmatrix}
\otimes \begin{bmatrix} 0 \\ 1 \end{bmatrix}
⊗[01] \otimes \begin{bmatrix} 0 \\ 1 \end{bmatrix}

Composite quantum states

\vert\space\space\space\space\space\space\space\space\rangle
∣        ⟩\vert\space\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\space\rangle
∣        ⟩\vert\space\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\space\rangle
∣        ⟩\vert\space\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\space\rangle
∣        ⟩\vert\space\space\space\space\space\space\space\space\rangle

@JavaFXpert

Multiple cats

\vert\space\space\space\space\space\space\space\space\space\space\space\rangle
∣           ⟩\vert\space\space\space\space\space\space\space\space\space\space\space\rangle
\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle
=
==
= \begin{bmatrix} 0 \\ 0 \\ 0 \\ 1 \\ 0 \\ 0 \\ 0 \\ 0 \end{bmatrix}
=[00010000]= \begin{bmatrix} 0 \\ 0 \\ 0 \\ 1 \\ 0 \\ 0 \\ 0 \\ 0 \end{bmatrix}
= \begin{bmatrix} 1 \\ 0 \end{bmatrix}
=[10]= \begin{bmatrix} 1 \\ 0 \end{bmatrix}
\otimes \begin{bmatrix} 0 \\ 1 \end{bmatrix}
⊗[01] \otimes \begin{bmatrix} 0 \\ 1 \end{bmatrix}

Composite quantum states

@JavaFXpert

\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle
\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle
\otimes \begin{bmatrix} 0 \\ 1 \end{bmatrix}
⊗[01] \otimes \begin{bmatrix} 0 \\ 1 \end{bmatrix}
\vert\space\space\space\space\space\space\space\space\space\space\space\space\rangle
∣            ⟩\vert\space\space\space\space\space\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\space\space\space\space\space\rangle
∣            ⟩\vert\space\space\space\space\space\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\space\space\space\space\space\rangle
∣            ⟩\vert\space\space\space\space\space\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\space\space\space\space\space\rangle
∣            ⟩\vert\space\space\space\space\space\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\space\space\space\space\space\rangle
∣            ⟩\vert\space\space\space\space\space\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\space\space\space\space\space\rangle
∣            ⟩\vert\space\space\space\space\space\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\space\space\space\space\space\rangle
∣            ⟩\vert\space\space\space\space\space\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\space\space\space\space\space\rangle
∣            ⟩\vert\space\space\space\space\space\space\space\space\space\space\space\space\rangle
\sqrt{\frac{1}{2}}
12\sqrt{\frac{1}{2}}
+
++

Superpositions, evolution & measurement

putting the three axioms together

\vert\space\space\space\space\space\space\space\rangle
∣       ⟩\vert\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\rangle
∣       ⟩\vert\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\rangle
∣       ⟩\vert\space\space\space\space\space\space\space\rangle
\sqrt{\frac{1}{2}}
12\sqrt{\frac{1}{2}}
\sqrt{\frac{1}{2}}
12\sqrt{\frac{1}{2}}
+
++
\vert\space\space\space\space\space\space\space\rangle
∣       ⟩\vert\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\rangle
∣       ⟩\vert\space\space\space\space\space\space\space\rangle
\sqrt{\frac{1}{6}}
16\sqrt{\frac{1}{6}}
+
++
\vert\space\space\space\space\space\space\space\rangle
∣       ⟩\vert\space\space\space\space\space\space\space\rangle
\sqrt{\frac{1}{3}}
13\sqrt{\frac{1}{3}}
\vert\space\space\space\space\space\space\space\rangle
∣       ⟩\vert\space\space\space\space\space\space\space\rangle

@JavaFXpert

quantum gates

quantum gates

measure

\downarrow
↓\downarrow
\downarrow
↓\downarrow
\downarrow
↓\downarrow
\vert\space\space\space\space\space\space\space\rangle
∣       ⟩\vert\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\rangle
∣       ⟩\vert\space\space\space\space\space\space\space\rangle

with 1/2 probability

with 1/6 probability

with 1/3 probability

\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle

Quantum entanglement

spooky actions at a distance

H

Hadamard gate

\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle

CNOT gate

\sqrt{\frac{1}{2}}
12\sqrt{\frac{1}{2}}
+
++
\vert\space\space\space\space\space\space\space\rangle
∣       ⟩\vert\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\rangle
∣       ⟩\vert\space\space\space\space\space\space\space\rangle
\sqrt{\frac{1}{2}}
12\sqrt{\frac{1}{2}}
\sqrt{\frac{1}{2}}
12\sqrt{\frac{1}{2}}
+
++
\vert\space\space\space\space\space\space\space\rangle
∣       ⟩\vert\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\rangle
∣       ⟩\vert\space\space\space\space\space\space\space\rangle
\sqrt{\frac{1}{2}}
12\sqrt{\frac{1}{2}}

Mars - ESA

Alice Cat

Bob Cat

Venus - NASA

@JavaFXpert

\vert\space\space\rangle
∣  ⟩\vert\space\space\rangle
=
==

Concepts we'll address today

Introduction to quantum computing

Axioms of quantum mechanics (with cats)

  • Superposition principle
  • Measurement
  • Unitary evolution

Abstracting cats with qubits

Quantum computing gates and circuits

Java and quantum computing

@JavaFXpert

Hardware representation of qubits

Physical support Type
Microscopic cats Mood Grumpy Happy
Photon Polarization Horizontal Vertical
Electrons Spin Up Down
Superconductor Energy levels Ground Excited
\vert0\rangle
∣0⟩\vert0\rangle
\vert1\rangle
∣1⟩\vert1\rangle

from wikipedia.org/wiki/Qubit​

@JavaFXpert

Classical bits vs. qubits

two discrete states vs. infinite superpositions 

from: The Future of Computing – Quantum & Qubits by Sam Sattel

@JavaFXpert

Qubit geometry

desmos.com/calculator/hjpqghdeat​

@JavaFXpert

Representing qubits

The Mathematics of Quantum Computers | PBS Infinite Series

ket notation, vectors, and geometrically

@JavaFXpert

Superconducting qubits on a chip

Rigetti Computing

@JavaFXpert

Video explanation

Concepts we'll address today

Introduction to quantum computing

Axioms of quantum mechanics (with cats)

  • Superposition principle
  • Measurement
  • Unitary evolution

Abstracting cats with qubits

Quantum computing gates and circuits

Java and quantum computing

@JavaFXpert

Classic logic gates

a quick review for comparison to quantum gates

imgur.com/M59IOZQ

@JavaFXpert

Some quantum gates

krishnakumarsekar/awesome-quantum-machine-learning

matrix operations model quantum mechanical behavior

@JavaFXpert

Quantum gate hardware

sending pulses to superconducting qubits

@JavaFXpert

Video explanation

Quantum software development

  • Classic computing -> classic algorithms (classic gates)
  • Quantum computing -> quantum algorithms (quantum gates)
    • Operations on a single qubit may affect other qubits
    • Qubits can in different states at the same moment

@JohanVos

Quantum software development

  • In many cases, the best approach to a problem is a combination of classic algorithms and quantum algorithms
  • Quantum algorithms leverage quantum gates, taking into account entanglement

@JohanVos

Shor’s algorithm

  • “IT WILL BREAK ALL ENCRYPTION”
  • It allows faster integer factorization (52 = 2 * 2 * 13)
    • quantum: polynomial time
    • classic: sub-exponential time
  • The problem is decomposed in a number of steps, including finding the periodicity of a function f(x) = f(x + r)
  • This problem can relatively fast be solved using a quantum algorithm

@JohanVos

Shor's algorithm

Hacking at Quantum Speed with Shor's Algorithm | Infinite Series

@JavaFXpert

Multiple cats

\vert\space\space\space\space\space\space\space\rangle
∣       ⟩\vert\space\space\space\space\space\space\space\rangle
\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle
\vert\space\space\space\rangle
∣   ⟩\vert\space\space\space\rangle
=
==
\vert\space\space\space\space\space\space\space\space\rangle
∣        ⟩\vert\space\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\space\rangle
∣        ⟩\vert\space\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\space\rangle
∣        ⟩\vert\space\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\space\rangle
∣        ⟩\vert\space\space\space\space\space\space\space\space\rangle
= \begin{bmatrix} 1 \\ 0 \end{bmatrix}
=[10]= \begin{bmatrix} 1 \\ 0 \end{bmatrix}
\otimes \begin{bmatrix} 1 \\ 0 \end{bmatrix}
⊗[10] \otimes \begin{bmatrix} 1 \\ 0 \end{bmatrix}

Composite quantum states

= \begin{bmatrix} 1 \\ \\ \\ \end{bmatrix}
=[1]= \begin{bmatrix} 1 \\ \\ \\ \end{bmatrix}
= \begin{bmatrix} 1 \\ 0 \\ \\ \end{bmatrix}
=[10]= \begin{bmatrix} 1 \\ 0 \\ \\ \end{bmatrix}
= \begin{bmatrix} 1 \\ 0 \\ 0 \\ \end{bmatrix}
=[100]= \begin{bmatrix} 1 \\ 0 \\ 0 \\ \end{bmatrix}
= \begin{bmatrix} 1 \\ 0 \\ 0 \\ 0 \end{bmatrix}
=[1000]= \begin{bmatrix} 1 \\ 0 \\ 0 \\ 0 \end{bmatrix}

@JavaFXpert

Exploring the quantum simulator

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

from Lecture 2: Overview of quantum information by John Watrous, University of Calgary

open in Quirk quantum circuit simulator

@JavaFXpert

Exploring the quantum simulator

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

from Lecture 2: Overview of quantum information by John Watrous, University of Calgary

open in Quirk quantum circuit simulator

@JavaFXpert

Simple quantum circuit

collapses to 8 random states with equal probability

open in Quirk quantum circuit simulator

@JavaFXpert

Quantum entanglement

basic circuit

open in Quirk quantum circuit simulator

@JavaFXpert

Quantum superpositions

and observability

http://dilbert.com/strip/2012-04-17

@JavaFXpert

Measuring qubits

The Mathematics of Quantum Computers | PBS Infinite Series

collapses to a basis state, discarding superposition

@JavaFXpert

Measuring quantum state

a Java analogy

from an IndicThreads slide deck

@JavaFXpert

Concepts we'll address today

Introduction to quantum computing

Axioms of quantum mechanics (with cats)

  • Superposition principle
  • Measurement
  • Unitary evolution

Abstracting cats with qubits

Quantum computing gates and circuits

Java and quantum computing

@JavaFXpert

Quantum Computer simulators

  • With some matrix algebra, a quantum computer can be simulated by a classic computer
    • This requires heaps of memory, increasing with increasing number of qubits
  • Cloud-based quantum simulators can deal with more qubits
  • Different languages:

@JohanVos

Quantum Computing simulators in Java

@JohanVos

StrangeFX

Java-based quantum simulator by Gluon / Johan Vos

@JavaFXpert

github.com/gluonhq/strangefx

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

Quantum Computing Exposed: Hacking Nature's Computer

By javafxpert

Quantum Computing Exposed: Hacking Nature's Computer

Gentle introduction to quantum computing by James Weaver and Dr. Johan Vos

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