Olivia Di Matteo
April 27, 2019

Logistics
Lectures will take place from 12:00 - 1:30pm in the TRIUMF auditorium on May 9, 10, 13, and 14.

Prerequisites
Basic quantum mechanics and linear algebra (superposition of states, measurement, spin 1/2 systems, Hamiltonians,eigenvalues/eigenvectors). Experience with Python is helpful for following the demonstrations and playing with the software on your own. No quantum computing experience is necessary.

May 9th/10th: gate model quantum computing
Day 1: Theory

• Motivation behind quantum computing
• Mathematical representation of qubits
• Unitary operations; common quantum gates and universal gate sets; quantum circuits
• Measurements; measurement bases; projectors
• Visualizing qubits on the Bloch sphere
• Multi-qubit systems; tensor products and entanglement
• Applications: superdense coding, quantum teleportation, Deutsch's algorithm

Day 2: Hardware and applications

• Overview of major classes of algorithms
• Visual walk-through of Grover's search algorithm
• Computational speedups and quantum advantage
• How do I build a qubit? How do I manipulate it?
• Curernt state of noisy intermediate-scale quantum devices (NISQ devices): qubit hardware graphs, error
• rates, technical challenges
• Full-stack quantum computing'; see the work ow of solving a problem on a quantum computer
• Overview of Hamiltonian simulation
• HEP application: Calculating neutrino oscillation probabilities on a quantum processor
• HEP application: Finding ground states of molecules with the variational quantum eigensolver

May 13th/14th: quantum annealing
Day 1: Theory

• The adiabatic theorem
• Equivalence of adiabatic and gate-model quantum computing
• Simulated annealing and the Ising model; transverse-eld Ising model
• Quadratic unconstrained binary optimization problems (QUBOs)
• Equivalence of QUBOs and Ising Hamiltonians
• D-Wave quantum annealers: what are they? How do they work?
• Formulation of problems as QUBOs; what kinds of problems have people solved using D-Wave?

Day 2: Hardware and applications

• Brief overview of superconducting qubit hardware
• D-Wave topology; the chimera and Pegasus qubit hardware graphs
• Technological limitations: noise, precision restrictions, problem size and graph minor embeddings
• Application Solving a simple graph theory problem (hopefully using the actual quantum processor!)
• Graph embedding; how do I couple two qubits that aren't directly connected?
• HEP application: classifying Higgs decay signals
• HEP application: particle tracking with LHC data
• Brief survey of ideas in quantum machine learning

Software demonstrations
I will be doing demonstrations live, but will also distribute the code and Jupyter notebooks so you can follow along
or play with it afterwards. You will need to install:

• Python 3 (I recommend the Anaconda distribution since it comes pre-installed with Jupyter and the scientic
• packages you will need),
• Qiskit, IBM's software platform, installable from their Github page or via pip,
• D-Wave's Ocean SDK, installable via pip with instructions here

I recommend doing the installation before the lectures start. If at any point you're stuck, feel free to message me (odimatteo@triumf.ca) or even better, drop by my oce (MOB 284) with your laptop and I will help.