Introduction to Quantum Computing

Desiree Vogt-Lee

About Me

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

Classical Bits

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

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

Gates - Hadamard

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

Example Coding on a Quantum Computer

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

From Quantum Annealing amid Local Ruggedness and Global Frustration (2017).

(Not officially released or peer reviewed!)

The task:

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.