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quantum.html
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<!DOCTYPE html>
<html>
<head>
<title>Quantum Computing</title>
<meta charset="utf-8" />
<link href="https://cdn.rawgit.com/Ilia-Kosenkov/UTU-slides/81794612/style.css" rel="stylesheet" type="text/css">
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</head>
<body>
<textarea id="source">
layout: true
---
class: title-slide, utu-back-title
# Quantum Computing
## **Comp Coffee** @ Tuorla, 2017-11-29
---
class: utu-back-content
# What is quantum computing?
- Quantum computers operate on qubits [*CUE*-bits]
- Two fundamental properties of qubits - superposition and entanglement\
- States are represented as vectors in Hilbert space
(product `\(\langle\phi|\psi\rangle= \sum_i \phi_i^*\psi_i\)`)
- Two states: `\(|0\rangle\)` (zero-ket) and `\(|1\rangle\)` (one-ket)
`\(|0\rangle = \begin{bmatrix}1 \\ 0\end{bmatrix}\)`, `\(|1\rangle = \begin{bmatrix}0 \\ 1\end{bmatrix}\)`, `\(|+\rangle = \frac{1}{\sqrt{2}}\begin{bmatrix}1 \\ 1\end{bmatrix}\)`, `\(|-\rangle = \frac{1}{\sqrt{2}}\begin{bmatrix}1 \\ -1\end{bmatrix}\)`,
`\(|\circlearrowright\rangle = \frac{1}{\sqrt{2}}\begin{bmatrix}1 \\ i\end{bmatrix}\)`, `\(|\circlearrowleft\rangle = \frac{1}{\sqrt{2}}\begin{bmatrix}1 \\ -i\end{bmatrix}\)`
---
class: utu-back-content
# What is quantum computing?
- Entangled state of two qubit system
`\(\frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)\)`
- Classical gates: **NOT, AND, OR**, also **XOR, NAND**
- Another important gate: **CNOT**, or controlled **NOT**
---
class: utu-back-content
# Quantum gates
- *Pauli* gates `\(\mathbf{X, Y, Z}\)` (unary)
- *Clifford* gates `\(\mathbf{S, H, S^\dagger}\)` (superpositions)
- Other gates from non-*Clifford* group
- Measurement gate that sends qubit value to a respective normal bit
---
class: utu-back-content
# Quantum gates
.double[
.column[
- `\(\mathbf{X} = \begin{bmatrix}0 & 1 \\ 1 & 0\end{bmatrix}\)`, rotation on `\(\pi\)` around x
- `\(\mathbf{Y} = \begin{bmatrix}0 & -i \\ i & 0\end{bmatrix}\)`
- `\(\mathbf{Z} = \begin{bmatrix}1 & 0 \\ 0 & -1\end{bmatrix}\)`
- Note that `\(|\psi\rangle = \cos\left(\frac{\theta}{2}\right)|0\rangle + e^{i\phi}\sin\left(\frac{\theta}{2}\right)|1>\)` and
`\(\)`
]
.column[
]
]
---
class: utu-back-content
# Quantum gates
.double[
.column[
- `\(\mathbf{H} = \frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\ 1 & -1\end{bmatrix}\)`,
`\(\mathbf{H}\)` applied to `\(|0\rangle\)` gives `\(|+\rangle\)`
- `\(\mathbf{S} = \begin{bmatrix}1 & 0 \\ 0 & i\end{bmatrix}\)`
- `\(\mathbf{S^\dagger} = \begin{bmatrix}1 & 0 \\ 0 & -i\end{bmatrix}\)`
]
.column[
]
]
---
class: utu-back-content
# **CNOT** two-qubit gate
.double[
.column[
`\(\begin{bmatrix}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0\end{bmatrix}\)`
- `\(|00\rangle \rightarrow |00\rangle\)`
- `\(|10\rangle \rightarrow |10\rangle\)`
- `\(|01\rangle \rightarrow |11\rangle\)`
- `\(|11\rangle \rightarrow |01\rangle\)`
]
.column[
]
]
---
class: utu-back-content, middle, center
# Go on and check it out!
## [IBM Quantum Experience](https://quantumexperience.ng.bluemix.net/)
</textarea>
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