Quantum Computing: how information is encoded

[slakker]

I did some quick searches and couldn't find any discussions on this topic. Anyone with background or ability to describe the basics to a novice. I understand the high level basic concepts, but don't know how information is encoded and how the qubits are operated on. Unlike boolean logic gates as the basis of classical computing, how and what are the "operators" of a qubit?

 

[phinds]

Magic, near as I can tell

Saw an interesting article in a major magazine a few weeks back about what was billed as the largest quantum computer yet built. The thrust of the article was that it had the potential to revolutionize computing, but they problem was that no one actually knew how it worked. Weird. There are even critics who content that it isn't ever a quantum computer. Also weird.

Id you look at "Related Discussions" at the bottom of this page you will find there are some threads on quantum computing

 

[Routaran]

There's a few youtube videos that get the basic ideas involved in quantum computing across. Check this playlist out
http://www.youtube.com/playlist?list=PLkahZjV5wKe_dajngssVLffaCh2gbq55_

I recommend watching all the videos as it goes over classical computing, its drawbacks and how quantum computing can make it better.

 

[phinds]

The computer I referenced in post #2 is called the DWave. Just saw another article on it. Not impressive.

 

[Routaran]

Yeah, with all the stuff that I have read about D-Wave in the past, I was skeptical as well.

That said, I saw this at phys.org a few days back.
http://phys.org/news/2014-03-d-wave-chip-rigorous.html

The challenge is that the tests we can perform on the USC-based D-Wave processor can't directly 'prove' that the D-Wave processor is quantum – we can only disprove candidate classical models one at a time," said QCC Director Prof. Daniel Lidar. "But so far we find that the D-Wave processor is always consistent with our quantum models. Our tests continually get more rigorous and complex.

I thought it was a scam for sure when I first heard about them and the way they avoided letting anyone test their stuff but I'm not sure anymore. I'm hoping they're the real thing, or at least a significant step in the right direction maybe?

 

[slakker]

@Routarans: That's interesting about the D-Wave, I live in the Vancouver area where this company is based and heard them in the news a few times in the last few years. Also the You tube link is very useful! Great primer, now I understand the concept at a 100,000 foot level...

 

[DonQubito]

Quantum gates are generalizations of reversible gates. An example of a reversible gate is the Toffoli gate. The Toffoli gate acts on blocks of three bits. T(a,b,c)=(a,b,(c XOR (a AND b))). T is reversible because if you apply it twice in a row, you get the original bit string back, i.e. T(T(a,b,c))=(a,b,c). T can also simulate an AND operation because T(a,b,0)=(a,b, a and b). If you add the not operator X, where X(a)=NOT a, then the combination of T and X is universal for computing because AND and NOT are universal gates for computing.

If you want to make the system universal for quantum computation, then you need to add a single gate called the Hadamard. (Actually, if you add the Hadamard, you don't even need the NOT gate anymore) The Hadamard sends a 0 bit to and equal superposition of 0 and 1 with a positive phase and Hadamard sends the 1 bit to and equal superposition with a negative phase. If it wasn't for the phase information, then the Hadamard would be equivalent to a coin toss and thus the same as a randomized computer. The extra phase makes it quantum mechanical. Normally the phase of a quantum state is a complex number, but the combination of T, X and H can simulate a complex phase using a single auxiliary qubit and so T, X and H ends up being universal for quantum computation.

On universal gate sets: http://en.wikipedia.org/wiki/Functional_completeness
On quantum superposition: http://en.wikipedia.org/wiki/Quantum_superposition
On the Hadamard gate: http://en.wikipedia.org/wiki/Quantum_gate#Hadamard_gate
Universality of Toffoli and Hadamard: http://arxiv.org/pdf/quant-ph/0301040v1.pdf

 

[.Scott]

The computer I referenced in post #2 is called the DWave. Just saw another article on it. Not impressive.

Here's what DWave says about programming their device:
from page 3 of:
http://www.dwavesys.com/sites/default/files/D-Wave-brochure-102013F-CA.pdf

Programming the Computer
A user interfaces with the quantum computer by connecting to it over a network, as you would with a traditional computer. The user’s problems are sent to a server interface, which turns the optimization program into machine code to be programmed onto the chip. To program the system a user maps a problem into a search for the “lowest point in a vast landscape” which corresponds to the best possible outcome.
The processor considers all the possibilities simultaneously to determine the lowest energy required to form those relationships. The computer returns many very good answers in a short amount of time - 10,000 answers in one second. This gives the user not only the optimal solution or a single answer, but also other alternatives to choose from.

There's a lot more at this link:
http://www.dwavesys.com/software
But here is the critical quote:

Using this hybrid system is simple. The developer provides the generating function, initiates the computation, and then the system starts 'thinking' about the generating function in the following, iterative way:

1 - A series of random solutions are generated by the conventional computing system.
2 - The quality of these guesses is evaluated by passing them into the generating function.
3 - The real numbers characterizing the fitness of the solutions are sent to the D-Wave system.
4 - The D-Wave system automatically adjusts itself based on this feedback, and then generates a new series of parameters, based on the results received.
5 - These new parameters are sent back to the conventional system, where their they are evaluated.
6 - Steps 3-5 are repeated until exit criteria are met.

The "D-Wave system" is the 512-qubit processor. Please note exactly what information is presented to the D-Wave system. The quantum processor never gets the generator function - only samplings of the generators output. So if the generator function returns 0% for all 2^512 input combinations except one, it's going to be completely useless in finding that 1 combination.
Moreover, there will never be any guarantee that as it works on the problem it will ever fully discover what the generator function is doing. And when I say "fully", I am being very generous.