Re: How does quantum computing work ?

Hi Vidya!

I will try to expand on the basic ideas and then I refer you back to the
articles posted by Xiao Chen http://www.madsci.org/posts/archives/feb2001/982422986.Cs.r.html
and Mark
Huber http://www.madsci.org/posts/archives/dec2000/977413412.Ph.r.html
which hopefully will then be more understandable. I especially recommend
the tutorials (as Mark does) at http://www.qubit.org.

There are four basic concepts that you need to understand to see how a
quantum computer might work:

1) Superposition:

Since you have already mentioned it we can start with superposition. In
conventional ("classical") computers there is no such thing as
superposition (where the system can be in two states at once). It makes no
sense for a machine to be in two states at once since this would involve
the switching devices to be both on and off at the same time.

Quantum mechanics however allows the system to (effectively) be in two
states at once. This is mainly because a set of states in quantum mechanics
not only have a probability(*), but also another parameter which is like a
phase between the states. The fact that a state has a phase is probably
more strange than it having a probability. It is the combination of these
that allows quantum computers to be good at certain problems. So the basic
unit of quantum computing is the qubit where the two states, 0 and 1, each
have a certain probability and a certain phase between them which we can
set.

2) Interaction:

In a conventional ("classical") computer operations are performed by the
interaction of electrical currents (which are just the electrons moving
around). 

Quantum computers perform operations in a similar way, but would typically
involve the interaction of single particles (the states of which form the
qubits). Now the interaction is very much more complex since it will change
both the probability and relative phase of the states. The interactions
that are used are called unitary since they conserve probability and are
reversible. They are _not_ measurements which are (normally) irreversible
and non-unitary. This is where the computing is done _without_ measuring
the state. It is kind of like closing your eyes and letting the system get
on with what you have programmed it to do. We can choose the interaction
very carefully to perform the right operation.

3) Communication:

Communication is required to decide what the sequence of operations is.
Classically, communication between logic elements is done by sending
currents down wires. In a quantum computer particles could be transferred
around or interactions could be turned on and off by applied fields.
However, the principle of communication is pretty much the same in both
cases. Note that we still don't make a measurement at this point so the
states remains unchanged.

4) Measurement:

This (I think) is where most of the confusion arises. The measurement of
the state (and the result of the computation) is performed at the end of
the sequence of interactions. Only then do we look to see what state the
system is in. The measurement does not produce a random result, but gives
us an answer dictated by the probability of the various states of the
system that we measure. In most cases we would expect the final state of
the calculation to be in either the 0 or 1 state and not a superposition
state since the superposition state can give us no information when we
measure it. Measurement is actually a very special type of interaction.

Above I have only talked about a single qubit, but the principles apply
equally to an array of qubits. Then the only other thing that I think you
should know is that a quantum computer is only good for certain types of
problem. In most cases it is no better and no worse than a classical
computer.

I hope this allows you to delve a little deeper into the both understanding
how quantum computing might work and also let you explore some of the more
subtle and beautiful features of quantum mechanics and specifically quantum
information theory that I have desperately tried to sweep under the carpet
in writing this so that I could keep it (fairly) simple.

Regards,

Phil.

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Phil Marsden
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Department of Microelectronics and Information Technology (IMIT)
Laboratory of Optics, Photonics and Quantum Electronics (OPQ)
Royal Institute of Technology (KTH) Stockholm
Email: phil.marsden@physics.org    http://www.ele.kth.se/~phil
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(*) Note that this is not really a probability. The late Richard Feynman
refers to this as an amplitude which incorporates both the probability part
and the phase. It doesn't really have a classical analogue.