@DanielSank, where would be a good place to learn about how quantum computers are constructed? I know some general things, but I can't seem to find any specifics.
@heather There are several aspects of that question.
Are you interested in the physical realization of qubits, how qubits are thought to be connected up to form a useful system, or about the whole system including the classical computer algorithms needed for error correction?
@DanielSank, well, probably all of that. I understand that qubits can be realized as electrons, or photons, or other elementary particles, using spin. But I don't know much else about it.
@DanielSank, well, I know that data in the computer is represented as bits, and that bits can be represented as differences in voltage or magnetic field (I'm pretty sure the magnetic field is used in memory, which just might be why it's bad to have a phone and a magnet in the same pocket).
@heather Yeah, good. Each bit is a single physical system with two possible states. Those can be voltage states, charge states, magnetic dipole orientation...
Of course, note that you can use an abacus to do computations too. In that case, the physical information is the position of beads on a wire.
The point is that information is physical.
okay, so you know that in a computer you have data stored in bits.
So it would be transferred, maybe converted from a mangetic dipole orientation to a voltage state because it is leaving the memory (how would that work?) and then passed through a gate, where the charge is changed somehow (how would that work?) and then passed back to the memory where it is converted back again.
Well, let's not get into too much detail. The point is that somehow we need a physical system in which the two voltages interact in a way that manifests a NAND gate.
Like, you have to actually build a physical system where the voltage at one point is the NAND of the voltages at two other points.
You have to build a physical system which is quantum mechanical and in which you can get the state of the qubits to transform based on your desired logic.
"Coherent" essentially means "stays quantum", and in the end that really means "doesn't interact with the environment against my will".
If a quantum system interacts with random stuff that you don't know about, the quantum state "leaks" into the surrounding degrees of freedom and your qubit is no longer in a nice quantum state.
There are always these articles coming out about some latest and greatest qubit with amazing coherence, but in so many cases, those qubits aren't so great because they don't interact well.
It actually works! The approach there is essentially to start with something very, very coherent (the atoms) and force them to interact using insanely strong electromagnetic fields (the laser) and very close distances.
This is an important note: much of real life experimental physics is decided by engineering capabilities.
What can and cannot be built in the lab by the people in that lab is very important. It's important for physicists, both theorists and experimentalists, to understand what can be built, and for experimentalists to train hard in good building skills.
@heather Well, consider a normal computer. Suppose your computer program says this:
x = 4
y = 1
z = x + y
Suppose x and y happen to be stored in parts of memory that are physically very far away.
This question may be a bit dumb, but what exactly is the problem with a path-dependent potential? I am not quite sure about this one, I think besides it will be a mutlivalued function, maybe things are just too complicated if you are dealing with a path dependent potential.
@DanielSank, at the bottom it says Models, and it lists Shor's first, and the rest improve on his (for example, the second one uses 7 qubits instead of 9) which suggests that his was first. Of course, I'm not sure.
Well I guess for starters is that such potential will be defined by an integral $$\Phi(\mathcal{C})=\int_{\mathcal{C}}\textrm{blahblahblah} d\mu$$ thus doing calculus on it will automatically be functional calculus stuff, which is a lot less straightforward than the usual calculus as the whole path have to be taken account of in order to define the potential
It basically will mean that the value of $\Phi$ will be determined by the set of points in a path in some kind of state space. I think Feymann path integrals has a similar logic
NB googling "path dependent potentials" found a bunch of interesting papers related to feymann integral stuff. I am guessing such potential is the norm in QFT
@DanielSank, how exactly do these four approaches compare in terms of success? I mean, what is, for example, the largest number of qubits set up using each method?
1) Quantum computing = processing information using quantum systems.
2) Gate model quantum computing = doing #1 by making the qubits do logic gates.
3) Quantum annealing = doing #1 by letting a quantum system fall into the ground state, measuring that state, and taking the result as the answer to a minimization problem.
Oh, so 1 is the overarching thing and then 2 and 3 are ways to do that thing. 2 is what uses things like Hadamard gates and CNOT gates, and what we've been talking about.
For quantum annealing, then, would the structure of the information processing be different? Because you don't have a gate changing the bit/qubit state?
Another approach would be to literally build a physical system with three degrees of freedom, $x$, $y$, and $z$, whose energy is given by our expression.
Then you'd just let the system fall to its low energy state and measure the values of the parameters.
Done.
However, this doesn't actually work because there can be local minima: arrangements of the system that have lower energy than other nearby arrangements, but which are not actually the lowest overall energy arrangement.
So, "annealing" is where you start the system off in some random arrangement, but at a high temperature. The thermal motion causes the system to bounce around. The idea is that if the system gets stuck in a local minimum, the thermal motion should un-stuck it.
Then you slowly lower the temperature and eventually when the temperature is low enough you should be in the ground state.
This has problems too though because thermally escaping a local minimum can be slow.
etc. etc.
Now, "quantum annealing" is actually a misnomer. I'm not going to go into the exact details, but we don't actually change the temperature... we change something else.
Okay. So, what's an example of a problem that can be represented as a minimization problem? Would, say, the traveling salesman problem be a minimization problem?
Anyway, the point of quantum annealing is that quantum tunneling should help your system escape local minima without having to go over the energy barriers.
They're initial idea was that maybe coherence doesn't matter much for quantum annealing, so they built a system with lots and lots of qubits, but they're all very not coherent.
@dmckee Yes, although note that MCMC may not be known to our young participant here.
@DanielSank I'm trying to figure how to explain it in a few words. I mean "step-wise random exploration of the configuration space" is accurate but perhaps not very clear.
Oh geesh. I've clicked through three times (Markov chain, stochastic process, markov property) and I still have no idea what in the universe it is talking about.
@dmckee, so it is sort of like having a function, and then picking a random x, and seeing what the y is, and then picking another random x to get another random y?
Or do I misunderstand the "under some configuration" part?
In the real problem the function depends on many variable $f = f(x,y,z,w,u,v,s,t,p,r,q,...)$ and may take quite a lot of (classical) processing to evaluate.
