Qubits

[Afghan]

Just have a swift question about quantum information theory. I'm sure one of you smart people can help me out...

A qubit (as I understand it) has C possible configurations where C is the cardinality of the continuum. Two qubits therefore should be able to store twice as much information... approximately 2*C different configurations.

So the qubit is not a very good unit to measure the amount of information you have, right?

[Dark Knight Bob]

1 qubit = 1^1 bits of informtaion

2 qubits =2^2 bits of information

3 = 3^3

4 = 4^4

and so forth.

You get to apoint where if you could build a quantum computer the size and normal 'bit' equivalent power of a standard pc you could calculate more information than every particle in the entire known universe.

Of course this doesn't mean you could measure the universe just simulate it... in theory.

[Anglican]

A qubit just has two basic states, it differs from the claasical bit in that it can be in a superpostion of these two states.

[Afghan]

A qubit just has two basic states, it differs from the claasical bit in that it can be in a superpostion of these two states.

Yeah, but the possible superpositions of the two states form a continuum.

[cpollett]

Just have a swift question about quantum information theory. I'm sure one of you smart people can help me out...

A qubit (as I understand it) has C possible configurations where C is the cardinality of the continuum. Two qubits therefore should be able to store twice as much information... approximately 2*C different configurations.

So the qubit is not a very good unit to measure the amount of information you have, right?

The easiest way to think of a qubit of information is to think of having two vectors [1 0] and [0 1] (I would normally write these as column vectors but I am trying to avoid typing). Then consider sums like:
a*[1 0] + b*[0 1] where |a|^2 + |b|^2 =1 and a and b are complex numbers. This is one qubit. To have more than one qubit you use tensor products [a b] @ [c d] is the four dimensional vector [a*c a*d b*c b*d].
So a general 2 qubit state is a complex sum of the four vectors:
[1 0 0 0], [0 1 0 0], [0 0 1 0], and [0 0 0 1] such that the sum of the length squares of these complex numbers is 1.

Usually a quantum circuit performs some computation and then we might get some complex sum of vectors. We perform a measurement and read off which vector the wave function collapses to. For an n qubit state this would in general be one of 2^n vectors. Although as you pointed out the coefficients before we do the measurement are complex numbers so there could be quite a lot of them, the amount of information you can feasibly and reliably extract about their value turns out to be substantially less.
You might want to google search quantum advice and look at some papers by Scott Aaronson.

[Anglican]

Yeah, but the possible superpositions of the two states form a continuum.

Yes, but that's not so interesting in the context of how much informtaion can be stored, after all we could just use any old analogue storage device without having to introduce all the practical diffculties of quantum computing, it is the fact that we have basic states which may be in a superpostin that is importnat (infact when you've got a computer with only a few qubits, it's not really that different from a classicla computer with the same number of bits certainly the parctical diffculties outweigh any advantage in this case).

[Dark Knight Bob]

The other important thing about qubits is that it can run parallel threads simultaneously.

That is with a standard serial processing. If you had a deck of cards and you wanted to see which was the 4 of hearts. You'd have to go through the cards on at a time. With quantum computer of 4 qubits (256 bit) you could in one cycle test all 52 cards instantaneously and come out with the answer.

The advantages come from being able to run through the qubit number of operations in one cycle.

That's a simplistic analogy ( i can't remember the exact mathematical specifics. I'm recalling this from memory from lectures) but I hope it explains the benefit.

The real benefit from that is the exponential increase in processing power with just a few qubits.

[OdysseusTheInnkeeper]

Some of the information on spintronics, which is actually being engineered now, indicate that the "processing state' of the electron is when its entangled- or in its 'Schrodinger-like' state, which means in transition from positive to negative one-half spin. The research also indicates that these subatomic processing systems have inherent fractal attributes.

There are designs being worked on for 2 to 8 qubit processors.

Cheers, Odysseus

[Dark Knight Bob]

8 qubits!? That's like a 16777216 bit processor!!!

:D

even a 5 qubit would rock. 3125 bit equivalent!

[Anglican]

The other important thing about qubits is that it can run parallel threads simultaneously.

That is with a standard serial processing. If you had a deck of cards and you wanted to see which was the 4 of hearts. You'd have to go through the cards on at a time. With quantum computer of 4 qubits (256 bit) you could in one cycle test all 52 cards instantaneously and come out with the answer.

The advantages come from being able to run through the qubit number of operations in one cycle.

That's a simplistic analogy ( i can't remember the exact mathematical specifics. I'm recalling this from memory from lectures) but I hope it explains the benefit.

The real benefit from that is the exponential increase in processing power with just a few qubits.


I don't belive it's quite that simple, as of course when you make measurement of a quantum computer your result will not be a superpostion of states, so running classical algorithms will not give you any advatnge over classical computers.

[Dark Knight Bob]

Oh I agree. The real world implication are that you can't run standard code on a quantum computer. To have any form of real world computation you'd need some sort of hybrid. Or an entirely different form of computational logic.