First published on MSDN on Feb 28, 2018
Already understand the basics and just want to get stuck in? Can't quite remember what the CSWAP matrix looks like? This post is for you.
Here you will find a collection of all the main states/gates/matrices/useful maths bits/etc. covered so far in this blog series. This cheat-sheet will be updated as important new things are introduced in posts :smiling_face_with_smiling_eyes:
Any unitary transformation we do on |𝜓〉 can be visualised as simply moving the point (marked |𝜓〉) around the Bloch Sphere*. Sadly, this visualisation can only be used for single qubit states, as there is no known (simple) generalisation that applies to multi-qubit systems. You may also see it referred to in places as the Unit Sphere.
Bell States/EPR pairs - these are the simplest examples of quantum entanglement between two qubits:
GHZ (Greenberger-Horne-Zeilinger) states, shown below both in general form (for
qubits) and in its simplest (three-qubit) form:
Gates, Matrices and Operations
Below is a summary of the key gates as introduced in my
previous post about Gates and Circuits
. Operations have been included for all single- and two-qubit gates (three plus becomes too big for display). For controlled gates, the identity matrix (𝕀) has been higlighted red and the original gate matrix blue, as seen