Contents:
3:18 Quantum & IT
7:50 Classical vs quantum programming
12:40 The quantum world – For programmers
21:53 The qubit
35:48 General pattern (classical states / superposition / collapse)
41:12 State as a vector
56:04 Programming!
1:04:33 Environment & Interpretations
1:11:30 Quantum gates, isolation, and information
1:34:29 Quantum impracticality
ERRATUM:
The D-Wave machine is a qubit-based quantum computer. I wanted to contrast it with gate-based, universal quantum computers.
At “The role of information” slide, the qubit collapsing to state |0> means that the cat survives.
ADDITIONS:
“The core idea” slide: Note that according to our everyday intuition, classical states of an object shouldn’t co-exist simultaneously. Also, isolation is very important: quantum mechanics guarantees only that isolated physical systems can be assigned a state (vector). The quantum-state concept can be extended to include non-isolated physical systems as well (see the EPR pair below for justification), using the so-called density-matrix formalism instead of vectors, but that is out of scope for this talk.
“Entanglement – The EPR pair” slides: Quantum mechanics guarantees that every isolated system has a quantum state (vector) of its own. To make the example clearer, suppose that the EPR-pair system is isolated. Then, the fact that the two individual qubits cannot have their own states implies that they are NOT isolated from each other (within the EPR-pair system). Curiously, this means that a single qubit of an EPR pair isn’t isolated but isn’t in a classical state either… the density-matrix formalism mentioned above was invented to be able to assign a quantum state even in such situations. (However, the shortcoming is that density-matrix states of individual parts won’t capture the “non-local connection” between those parts. In other words, the whole of an entangled system is more than the sum of its parts.)
“Quantum gates & information” slides: We assume that before applying the gate U, the state of the environment is independent of |ψ>. So if our “detective” is only allowed to examine the environment to figure out |ψ>, then applying a quantum gate won’t help her, as she still won’t be able to correlate |ψ> with the new state of the environment (what’s more, she won’t be able to correlate |ψ’> either).
