# Introduction to Quantum Computing

Desiree Vogt-Lee

• Physics student
• Data scientist at NTI
• Recently returned from a quantum computing workshop and hackathon in Zurich

### Quantum Bits (qubits)

$| \psi \rangle = \alpha | 0 \rangle + \beta | 1 \rangle$

From Wikicommons (2009).

Classical Computation: checking all possibilities in rapid succession

Quantum Computation: checking all possibilities in parallel

Qubits Possibilities Power $(2^N)$
1 0, 1 2
2 00, 10, 01, 11 4
3 000, 001, 011, 110, 010, 100, 101, 111 8

For each qubit added, the compute power doubles.

## Quantum Computers

Computers that use qubits instead of bits.

Quantum properties: superposition, entanglement, interference

Different types of QCs: annealers, adiabatic, universal, Noisy Intermediate Scale Quantum (NISQ)

Usually when we refer to QCs, we mean fault tolerant devices, but currently we only have NISQ devices.

## Unitary Operators

Operations are performed on universal QCs by applying unitary gates.

Gates must be unitary in order to be reversible and preserve the normalisation of the quantum state.

$UU^{\dagger} = I$

From Wikicommons (2009).

## Gates - Pauli X

Equivalent to a classical NOT gate

Performs a bit flip operation

$X=\begin{bmatrix} 0 & 1\\ 1 & 0 \end{bmatrix}$

No equivalent classical gate

Puts qubit into superposition state between 0 and 1

$H=\frac{1}{\sqrt{2}}\begin{bmatrix} 1 & 1\\ 1 & -1 \end{bmatrix}$

## Gates - Controlled NOT (CNOT)

Performs a bit flip operation based on the value of the first qubit

$CNOT=\begin{bmatrix} 1 &0 &0 &0 \\ 0 &1 &0 &0 \\ 0 &0 &0 &1 \\ 0 &0 &1 &0 \end{bmatrix}$

Before After
00 00
01 01
10 11
11 10

## Quantum Algorithms - Shor's Algorithm

Factoring algorithm that runs in polynomial time

From Wikicommons (2014).

Could be used to break public key cryptography (RSA)

## Quantum Algorithms - Grover's Algorithm

Searching algorithm that runs in $O(\sqrt{N})$ evaluations

From Wikicommons (2009).

## Applications of Quantum Computing

Chemical Simulation

• Molecular design
• Drug discovery
• Protein structure prediction

Cryptography

• Breaking RSA
• Breaking Diffie-Hellman

Artificial Intelligence

• Prediction
• Classification

Scenario Simulation

• Risk Analysis
• Disruption Management

## Biggest Issue with Current Quantum Computing

Decoherence/Noise: the loss of coherence, where a quantum system reverts to a classical state due to interactions with the environment.

It is an issue as to perform computation, qubits need to be in an entangled or in superposition.

Overcome using quantum error correcting (QEC) codes such as repetition codes, and circuits are designed to not spread error.

## Hardware Designs

Silicon Spin Superconducting Ion Traps Diamond
Pros High stability, reproducible, manufacturable Fast, easy to fabricate, flexible One of the first qubit designs, very stable Can operate at room temperature, interacts with light
Cons Difficult to interconnect: only two entangled Unstable, low temperatures required Requires large vacuum, many lasers and slow Difficult to entangle and fabricate reproducibility
Number Entangled 2 53 14 2
Coherence Time 30s 50$\mu s$ 1000s 2s
Developers Intel, UNSW, Princeton, TUDelft D-Wave, IBM, Google, Rigetti, TUDelft IonQ, MIT TUDelft, Harvard

## D-Wave 2000Q

2000 qubit quantum annealer (not a universal quantum computer!)

From D-Wave (2009).

From Ars Technica (2017).

## D-Wave Annealer Speedup

DW: D-Wave   SA: Simulated Annealing   SVMC: Spin Vector Monte Carlo   QMC: Quantum Monte Carlo   HFS: Hamze-de Freitas-Selb Algorithm

(Not officially released or peer reviewed!)

Sampling the output of pseudo-random quantum circuits. The circuits entangle a set of qubits by repeated application of single and two qubit operations which produce a set of bitstrings. The output is a probability distribution of the bitstrings.

#### Result:

Sampling the random circuit 1 million times