.. title: Quantum Class 2, Thurs 2022-09-01
.. slug: class02
.. date: 2022-09-01
.. tags: class
.. category:
.. link:
.. description:
.. type: text
.. has_math: true
.. sectnum::
.. contents:: Table of contents
..
Class 1
=======
I edited the blog to show what we actually did.
Homework 2
==========
is online, due Tues.
Theory vs Experiment
====================
#. Sometimes the theoreticians posit something new, then the experimentalists try to build it.
a. atom bomb
#. classical computer
#. quantum computer
#. Other times the experimentalists (aka hackers) build something new.
a. bridges
#. airplanes
#. medieval cathedrals
#. steam engines
#. calculus
#. Then those may become so successful that bigger and bigger ones are built until those collapse / crash / fall down / blow up / have paradoxes.
#. Then the theoreticians have to come in and clean up the mess to allow more progress.
#. They may look for unifying themes in apparently separate problems.
#. Group theory in abstract (modern) algebra happened that way.
#. Anything discovered about groups was then valid in all the applied areas.
#. All theories have limits that may or may not be relevant.
#. Paradoxes expose limits. "All triangles are isosceles" error exposes something not covered by Euclid's axioms.
#. Physics Nobels tend to go to theoretical explanations of surprising experiments. Although, there is nothing in common among all Nobel winners, not even intelligence (according to Enrico Fermi).
#. Very rarely, experimentalists do something that the theoreticians had proven was impossible.
a. Galileo seeing sunspots.
#. Marconi radioing across Atlantic.
#. Michaelson-Morley. (However several other contemporaneous inexplicable observations all proved to have classical explanations.)
and something new is discovered / invented. Unfortunately the crackpots then seize on these rare examples...
Video
=====
#. Quantum Computing in Under 11 Minutes daytonellwanger https://www.youtube.com/watch?v=TAzZKAdX2Tw 10:56 more technical
Intro to quantum computing
==========================
#. This is from
a. *Yanofsky and Mannucci, Quantum Computing for Computer Scientists*,
#. *Hidary, 2nd edition*, and
#. my opinions.
#. Isomorphism between geometry and algebra. Work in whichever domain is easier. Results carry over.
a. 2D: x+ij -> (x,y)
#. 3D: quaternions. 3D rotations are not commutative, and so quaternions are not. There's a memorial on a bridge in Trinity College Dublin where William Rowan Hamilton thought of them. Quaternions are equivalent to 3D vector algebra.
#. qbits - Bloch sphere.
#. qbits vs qubits? Above my pay grade.
#. Evidence for quanta:
a. 1905 photo-electric effect explanation. Einstein Nobel.
#. Ultraviolet catastrophe.
#. 1922 Stern Gerlach experiment. Very influential.
https://en.wikipedia.org/wiki/Stern%E2%80%93Gerlach_experiment
#. Hidary 1.1 Quantum Computer Definition, p 3
A quantum computer is a device that leverages specific properties de- scribed by quantum mechanics to perform computation.
#. State vector
a. completely describes a system
#. cannot be directly observed, only measured...
#. which changes it.
#. Hidary 1.1 Superposition and Entanglement, p 4
2 big properties.
#. bra-ket notation.
#. can rewrite a state vector in a different basis
#. Hidary 1.3 The Superposition Principle, p 4
a. "The linear combination of two or more state vectors is another state vector in the same Hilbert space and describes another state of the system."
#. Generally false in classical domain.
Particle can go thru only 1 of 2 slits.
However vibration states in a string add.
#. Hidary entanglement p 7
description is confusing, defer till later.
#. Yanovsky p 40, vector space review
a. One qbit is a simple vector space.
#. Can change basis, e.g., to Hadamard basis. p 51.
#. Eigenvalues and eigenvectors, p 60
#. Hermetian matrices, p 63
#. Classical 2 slit experiment, p 86.
Probabilities add.
#. Quantum 2 slit experiment, p 93.
Complex waves add.
Probabilities might reduce.
Quantum properties - Entanglement
=================================
#. Crazy counterintuitive idea that's the basis for quantum speedup.
#. Classical metaphor for entanglement:
a. Start with a piece of paper.
#. Tear it into two halves.
#. Put each half into an envelope, seal them, and mix them up, so that you can't tell which half is in which envelope.
#. Address and mail one envelope to a friend in Australia, and the other to a friend in Greenland.
#. When the Australian opens his envelope, he knows what the Greenlander will find in his.
#. However that doesn't let the Australian send any info to the Greenlander, or vv.
#. This **has been demonstrated** with real qbits transported 1000 miles apart.
#. Entanglement means that if you measure one qbit then what you observe restricts what would be observed when you measure the other qbit.
#. However that **does not let you communicate**.
#. The above metaphor is inaccurate in ways that don't affect us now. (It assumes a hidden variable, which is false.)
#. Entanglement and superposition do funny things to operations. Consider the `Controlled NOT gate `_. It has 2 inputs, x and y.
a. Classically, y is negated iff x=1. x doesn't change.
#. If x and y are superposed with a Hadamard basis, then y can affect x.
Video to watch on your own
==========================
#. `Quantum Computing 2022 Update `_, 15:12, July 24 2022.
#. You prepare discussion points and questions for next class.
Misc intro to quantum computing stuff
=====================================
This is misc stuff that you might find interesting, which I'm drawing from.
Intro sites - 2
---------------
#. `"Spooky" physics | Leo Kouwenhoven | TEDxDelft (18:00) `_
#. A beginner's guide to quantum computing | Shohini Ghose https://www.youtube.com/watch?v=QuR969uMICM 10:04
#. https://towardsdatascience.com/introduction-to-quantum-programming-a19aa0b923a9?gi=69d861e26d80
#. https://medium.com/@jonathan_hui/qc-programming-with-quantum-gates-8996b667d256
#. https://medium.com/@jonathan_hui/qc-programming-with-quantum-gates-2-qubit-operator-871528d136db
#. https://www.cl.cam.ac.uk/teaching/0910/QuantComp/notes.pdf
a. They have a nice description of measurement starting at slide 10.
#. Each measurement operator has a *basis* vector set.
#. The operator represents the qbit as a linear combo of the basis vectors.
#. Then it projects the qbit onto one of the basis vectors, with probability being the length of that component.
#. It is possible for two different qbits to measure the same in some basis, but measure different in a different basis.
#. `Can we make quantum technology work? | Leo Kouwenhoven | TEDxAmsterdam (18:19) `_
#. `Quantum Computing Concepts – Quantum Hardware (3:22) `_
#. `Experiment with Basic Quantum Algorithms (Ali Javadi-Abhari, ISCA 2018) `_ (19:05)
#. `Quantum Computing for Babies `_
Current status sites
--------------------
#. https://www.telegraph.co.uk/technology/2020/09/02/britain-must-act-fast-prevent-brain-drain-quantum-computing/ - good summary of programs around the world.
#. `Quantum startup CEO suggests we are only five years away from a quantum desktop computer `_
No new homework
===============
Finish 1 and enjoy Labor Day.
Videos to watch for Tues
=========================
#. Watch `A Beginner’s Guide to Quantum Computing `_, 18 min, by Dr. Talia Gershon, IBM Research.