Beyond my reply to Jon, I could suggest looking at this slide set as an introduction...
https://www.cl.cam.ac.uk/teaching/0910/QuantComp/notes.pdf
John
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From : [log in to unmask]
Date : 22/02/2019 - 15:26 (GMT)
To : [log in to unmask]
Subject : Re: London Quantum Networking Meetup
Dear Jon,
From what I know of it, there is a way of thinking about superpositions (i.e a combination of the two basis states that form the current state of a qb it) by using the Bloch Sphere, the surface of which provides points allowing all of the possibilities. But this wouldn't be a countably infinite number. It would be the infinity of the real numbers.
This may not bounce back from the NGN reflector as I think it deleted me.
Regards
John
----Original message----
From : [log in to unmask]
Date : 22/02/2019 - 12:08 (GMT)
To : [log in to unmask]
Subject : Re: London Quantum Networking Meetup
which reminds me, was visiting the quantum dot folks a the cavendish
lab earlier this week and one of the physicists was talking about
superpositions of states, and said there's literally infinitely many
possible (e.g. you have a particle can be spin up or down, so you have
a system in state a*up and b*down (actually a+b have to sum to 1:)
so i said "do you mean countably infinite" and he said he didn't
know...
so actually, i'm not convinced its any kind of infinite - firstly, in
practice, you can't measure infinitessimally different mixes of states
- the system for doing measurement uses (e.g.) photons or soemthing to
interact, and they have discrete size (hey, quantized, right:)
secondly, maybe, entanglement might involve virtual particles and
mean that the distributions of states are themselves quantized anyhow,
so there could be a finite number (kind of related argument to
ultraviolet catastrophe:)
but computationally, this matters, since the size of the state space
is what gives qbits their magic extra complexity so they can explore
algorithmic stuff "faster" - so if it was countably (i.e. a&b are
rational) or uncoutnably (bigger) this would mean different
theoretical things for quantum computability/complexity than finite
(which would just be a speed up)....
anyone know the right answer?
cheers
>
> May be of interest to those on this group:
>
> https://skillsmatter.com/meetups/12146-quantum-networks
>
> David
>
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