## Quantum Party Tricks

\vert\space\space\space\rangle

### featuring grumpy cat

Java Champion

Developer / Author / Speaker

james.weaver@ibm.com
JavaFXpert.com

CulturedEar.com

### History repeating itself

Massive hardware, limited bits, software infancy

Quantum computers make direct use of quantum-mechanical phenomena, such as superposition, interference and entanglement, to perform operations on data.

Feasible on classical computers

Feasible on quantum computers

Solutions to problems

### Why use a quantum computer?

Some problems may be solved exponentially faster

## My microscopic cat is often grumpy

\vert\space\space\space\rangle
\vert\space\space\space\rangle

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

\vert\space\space\space\rangle
= \begin{bmatrix} 1 \\ 0 \end{bmatrix}
\vert\space\space\space\rangle
= \begin{bmatrix} 0 \\ 1 \end{bmatrix}
= \begin{bmatrix} \sqrt{\frac{1}{3}} \\ \sqrt{\frac{2}{3}} \end{bmatrix}
\sqrt{\frac{1}{3}}
\vert\space\space\space\rangle
+
\sqrt{\frac{2}{3}}
\vert\space\space\space\rangle
\vert\space\space\space\rangle
\vert\space\space\space\rangle

## Axiom 1: Superposition principle

### Cat can be in any combination of grumpy and happy

\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\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}

NOT gate (Pauli/X, bit-flip)

## Making Grumpy Cat happy with an X gate

After measurement

Before measurement

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### 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}

\sqrt{\frac{1}{2}}
\vert\space\space\space\rangle
+
\sqrt{\frac{1}{2}}
\vert\space\space\space\rangle

## Making Grumpy Cat happy about half the time

After measurement

Before measurement

\sqrt{\frac{1}{3}}
\vert\space\space\space\rangle
+
\sqrt{\frac{2}{3}}
\vert\space\space\space\rangle

## Axiom 3: Measurement

### probability is amplitude squared

When observed there is a:

\frac{1}{3}
\frac{2}{3}

probability of being grumpy

probability of being happy

\vert\space\space\space\rangle

## Quantum entanglement

### spooky actions at a distance

H

\vert\space\space\space\rangle

CNOT gate

\sqrt{\frac{1}{2}}
+
\vert\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\rangle
\sqrt{\frac{1}{2}}
\sqrt{\frac{1}{2}}
+
\vert\space\space\space\space\space\space\space\rangle
\vert\space\space\space\space\space\space\space\rangle
\sqrt{\frac{1}{2}}

Mars - ESA

Alice Cat

Bob Cat

Venus - NASA

\vert\space\space\rangle
=
\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \end{bmatrix}
\begin{bmatrix} \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}} \end{bmatrix}

## Entangling Alice Cat and Bob Cat

After measurement

Before measurement

## Running on an IBM quantum computer

Right-click the Q block and paste QASM into IBM Quantum Experience Circuit Composer

### IBM Q Experience Qiskit notebooks

Qiskit open source quantum computing framework

## Quantum Party Tricks

\vert\space\space\space\rangle

By javafxpert

# JJUG Lightning Talk: Grumpy and Happy Cats

Learn some Quantum Party Tricks!

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