Request For Article: Many-Worlds Quantum Computing

First of all consider a computer is incomplete without a program, so lets just think of a programmed computer - whether in hardware or software doesn't matter for our purposes.

This gives us a system that goes from some known start state to some outcome state through a series of intermediate steps. If each of these steps is deterministic, then the entire system reaches the same outcome in all universes where it had the same starting point.

If those steps were stochastic, perhaps because there is chance of memory corruption in our computer or because of a random guess, than in some universes the system arrives as a different outcome, based on the probability of that branch of the intermediate states. This can produce many branches, but because each of these branches cannot affect the others the result is tree of intermediate states, leading to the outcomes of our computer and its program.

Now, both of these are classical computers, but it helps to know what a classical computer looks like in a many worlds interpretation, before mapping a quantum computer there. This is because all computers, classical or quantum share a property - they are computers. This means there must be a path from the starting state to the outcome state. We can influence that path in many ways, but the path is part of how we define and build a computer and a program.

In quantum mechanics, there is a phenomena called entanglement, which loosely means that the events in very similar worlds can affect the probabilities of events in all of those worlds. You can think of this as the boundaries between the many worlds smoothing out as you get to a small scale.

This means that unlike our stochastic tree of states, the quantum computer can have a more complex structure. It is even possible, for two branches to converge back into one and to have branches cancel out.* In practice, these are more approximate than precise, so you will find a dominant combination of two branches or a near cancellation. Using this interaction a skilled quantum algorithm designer can use a variety of tricks to make correct answers more likely, by canceling wrong answers, and by increasing the probability of correction ones.

There is no uniform solution to this problem, for example, the best known quantum algorithm, the Shor algorithm for prime factorization exploits frequency of a possible prime factorization using number theory. This works well on quantum computers because the frequency difference is also a critical value for determining the probability of the combination of two quantum variables.

In each case, a computer and its program produce a path of execution, but by exploiting the features of or needing to deal with the problems of non-determinism and quantum mechanics, the nature of that computation becomes more complex and difficult to see. Any one world's view is not sufficient, especially in the case of quantum computing where the probabilities which govern a world's execution are not derived solely from within that world.

• I'm fairly sure one this, but I'm a little rusty, so I could be wrong.

I'm about to start writing up my doctoral thesis in experimental quantum computing.

If people are interested I might be able to write a few posts introducing quantum computing/quantum algorithms and many worlds over the next couple of months. I'm by no means an expert in the theory side, but I'll try to chat about it with people who are.

From a personal perspective it might help me to start the words flowing.

Voted down for being off-topic. Feel free to delve into a deep discussion about the merits of doing this and what should be considered off-topic. Meanwhile, I'll say what I have to say anyway. Feel free to delve into a deep discussion about the merits of doing this as well.

The thing is, quantum mechanics looks like the Copenhagen interpretation. That's why Copenhagen hasn't been falsified. We've barely managed to produce any evidence against it. (I'm not considering its low-ish prior probability to be evidence, of course.) Therefore, if you want to explain an observed phenomenon, it's perfectly valid to explain it in terms of wavefunction collapse.

Note to self: ponder, and write something about, when it makes sense to explain something in terms of a mechanism you don't know exists.

Saying that a quantum algorithm is "simultaneously sampling all possibilities and choosing the best one" has always been, I've found, a strange way of putting it, since it suggests that quantum computing can do a lot more than it actually can. (Quantum superintelligence: simultaneously sample every possible process of reasoning and choose the most interesting one. Unfortunately, you can't actually do that.)

A quantum algorithm such as Grover's algorithm simply works by changing the probability amplitudes (i.e. the heights of the wavefunctions, the things that can interfere constructively and destructively, the things that determine the probability of each outcome) in such a way that the probability of the desired answer is much higher than the probability of any other answer. ("Probability" here is just a specific function of probability amplitude, which happens to be consistent with both quantum evolution and the laws of probability.) When you perform the observation, then, the majority of Bornstuff goes to the world where the answer observed is the desired one.

How does Grover's algorithm work, specifically? Well, there's a plane where one line is the algorithm's starting point, and another line is the correct answer; it uses reflections to rotate the point for a certain amount of time, until it's very close to the correct answer. I dunno. For details, see Wikipedia.

Thanks folks, sounds like the entire point of quantum computing is to avoid the kinda differences in interpretation that Copenhagen/MWI are concerned with, so my suspicion that a MW computational image would help is mistaken. Which is good, read around some Quantum Algorithms a bit. Have a better grasp of how that actually works than the terrible "explore all possibilities and pick the best" line that seems to come up so much.

Still leaves me a bit at a loss with these quantum effects in photosynthesis though:

We have obtained the first direct evidence that remarkably long-lived wavelike electronic quantum coherence plays an important part in energy transfer processes during photosynthesis,” said Graham Fleming, the principal investigator for the study. “This wavelike characteristic can explain the extreme efficiency of the energy transfer because it enables the system to simultaneously sample all the potential energy pathways and choose the most efficient one.”

Seems likely that line about "simultaneously sampling all the potential energy pathways and choosing the most efficient one" is just as misleading as the similar line in explaining how to quantumly factor a number.

Humm. Oh well. Can't expect to clear up all my confusion in one day. It's Friday Night, I should go find something fun to do.

The key to a quantum algorithm is getting wrong answers to cancel out (opposing complex amplitudes) and right answers to build up (harmonizing complex amplitudes). Exploring all branches simultaneously is easy. The hard part is getting the evolution of a linear, unitary quantum process to make "wrong" configuration amplitudes cancel and "correct" configuration amplitudes add. Peter Shor's critical insight in the quantum-factoring algorithm had something to do with the circularity of something to do with factors (I don't know the details).

Okay, here is how I think it might work - I am not a quantum computer programmer, so take my ideas with lots of salt.

Imagine a completely classical world. Imagine a bit (e.g. a coin faceup or facedown) inside of a container (e.g. a cup). Imagine a fundamental physical operation something like shaking the cup. If you don't know whether the bit is faceup or facedown, then you might imagine that inside the cup are two superimposed worlds. That is, you can imagine that the world is one possibility thin where you are, and then bubbles out to be two possibilities thin inside the cup.

When you shake the cup and then open the cup, one way to describe what happens is that the superimposed worlds "collapse", nondeterministically, into one of the possibilities. This is something like popping the bubble. Another way to describe what happens is that the bubble expands through you, splitting you, and one of the copies sees one of the possibilities, and the other copy sees the other possibility.

We can model entanglement in this classical world - imagine taking the cup-coin combination, and passing it through a duplicator. You still don' t know whether the coin is heads or tails, but "collapsing" one will also "magically" collapse the other.

This is all well and good, you say - but it isn't quantum computation.

My understanding here is fuzzier. As I understand it, there's an additional "imaginary" dimension in the quantum computation than there is in the classical possibility-worlds that we've been talking about. Sometimes, the bubble or stack of possible worlds, when viewed from the outside, can have constructive or destructive interference, as if the different worlds were transparencies that one can stack and look through.

To the QC novices - does that make sense? To the QC experts - is that even roughly true?

Ugh. To be honest, quantum computing is a waste. A complete dead end. So you can do a few calculations a little faster. Big deal. The same efforts would be better spent on improving manufacturing methods so that we can turn out products faster, especially those that involve shaping of scrap metal.