Desiree Vogt-Lee

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

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

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.

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.

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).

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 |

Factoring algorithm that runs in polynomial time

From Wikicommons (2014).

Could be used to break public key cryptography (RSA)

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

From Wikicommons (2009).

**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

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.

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 |

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

From Ars Technica (2017).

**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!)

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.

Sampling the random circuit 1 million times

Google Sycamore (53 qubits): 200s

Classical supercomputer (Summit, Julich): 10,000yrs on 10M cores

Does *not* mean we can now break encryption!

- Slides: https://desireevl.com/slides
- Bernstein-Vazirani IPYNB: https://github.com/desireevl/desireevl.github.io/blob/master/images/intro-qc/Bernstein-Vazirani.ipynb
- List of QC resources: https://github.com/desireevl/awesome-quantum-computing
- Michelle Simmons talk: https://www.youtube.com/watch?v=FnPp73F5cnE
- D-Wave hardware: https://arxiv.org/pdf/1611.04528.pdf, https://arxiv.org/pdf/1701.04579.pdf
- Google quantum supremacy paper: https://t.co/TVgiNS54FK?amp=1
- Google quantum supremacy supplementary materials: https://t.co/8m8NHBbcDK?amp=1