OK so school's about to start. New schedule includes wave motion, sound, fluid dynamics, electromagnetism, optics, and proofs.

My past few months of study have included topological quantum computing, quantum gravity, condensed matter physics, statistical mechanics (mostly entropy), superposition, and what all of that means...inside, outside, on the surface of a black hole, and in infinite dimensions.

I have to do some gear-switching :(

Throughout some course of my life, after reading the Commonwealth Saga by Peter F. Hamilton (check it out if you haven't, it's a great space opera), I have gotten a drive to build...well, really fucking good computers. Not things limited by transistor size, or by classical computation theory - I mean the stuff that quantum mechanics brought in, the stuff that shattered the idea of computation by bringing in physical systems that are simply unable to be simulated within the framework of classical computation for one simple reason: You might be able to say that your theory-puter can simulate quantum physics with classical computation, but in reality any classical computer you build will be 150% unable to simulate any quantum system bigger than a few dozen qubits; beyond that, its processing time, no matter how powerful the computer is, will take longer than the age of the observable universe.

Yet, you don't have to simulate these things; you can MAKE them because the world allows you to do so. The problem of simulation then switches around; can we build a computer capable of simulating...well, all the physics we know and love today...or more? Theoretically, a quantum computer should be able to simulate quantum point computations (QPCs) of any kind of quantum mechanical interaction, down to the particle physics. Understanding the computational side of field theories is a subject which doesn't have a lot of exploration; after all, one of the fundamental parts of quantum field theories is the ability to distinguish identical states, and even split their components, increasing the particle number. A many-body Schrodinger is limited to the number of bodies you put into it initially; even if you make that infinite, a single-quanta particle cannot split, instead it must influence the particles around it.

Thus, from quantum mechanics, and particle physics, we have an interesting new picture: Particles are not individual quanta. We already know this to some extent; quantum mechanics isn't all about how particles must be quantized, it's about how things in general are quantized. An electron has spin up, spin down, charge negative, and even components of positive charge and negative mass; on top of all this it has more an angular momentum, it has positional momentum with respect to the space around it. We also know that if an electron and positron collide with enough energy, their annihilation will actually produce more particles - ones with properties such as color and flavor.

How to classify these particle states which have underlying quantum states which for the large part hide themselves? There's also an oddity which might help the picture: Fermions and bosons may have non-integer or integer spin, but they are still quantized values...and while an electron (spin +-1/2) is a fermion, so are the spin +-1/3, +-2/3 up and down quarks. Additionally, in an atom, we have m_s, m_l, and m_j - where m_j is the atom's composite angular momentum number, a quantized yet composite entity. Are all quantum states composite ones? Is the only elementary unit of universal construction, a qubit? Qudits also fit into this framework, but even they may be represented by their smaller partner, the qubit.

How to make these particle states, though? Raw data is simply raw data; with enough construction perhaps a real system of physics is grown, but we have some particular quantities that need to be true. For one, we have all these constants, hbar, c, G, Λ, etc which all have to arise somehow. Is there a more fundamental constant in a data-centric theory of qubits, which leads directly to particle physics?

This is a question that David Deutsch thinks has no obvious answer; there are an infinite set of possible constructions that might happen, and even if you apply Fermi's golden rule of state rate-change limits, it just leaves you with an infinite dimensional 0-dimensional space; even if ALL qubits can interact with one another instantaneously, and their phase speed limit is Planck's constant, there is simply too much to try and build.

There is a hope in the AdS-CFT correspondence, in that we might think of this fundamental field of qubits to be the constructor of a quantum, fractal-like space in which, from infinite-dimensional anti de sitter space, holographic projection may (eventually) paint a 3-dimensional picture, through some number theoretic methodology. These are things that begin to stray from my knowledge...but I see some method of looking into the real numbers as a way forward.

We can look at topological quantum computation as a way to visualize the growth of composite qubit states - of geometric timelike constructions - as systematic realities. Ideally, we may be able to build a topological computer in which we target a particle physics quantum geometry, and simulate it in a way that is even impossible for high-energy particle accelerators; a way in which we may prepare pure states out of computational structures, and run them into another to allow those computational structures to interact. We would base our initial structures off what we know of these field theories, involving a substrate of exotic construction - an actively programmable construction, such as a quantum FPGA of large dimension - and through error, correct it, gaining a picture known by our design, which mimics the physical reality. This is the next experimental venture which humanity will undertake, giving us a picture into reality which is not only a simulation, but a reconstruction; we will mimic low-lying physics by imitating it on a larger structure.

This might also be how we escape from our reality into higher dimensions; these computers will reconstruct dimensions larger than their own physical construction, building those dimensions out of both timelike qudits and inverse holographic projectors, entangling large-scale geometries to sort entropy before knitting it into superposition dimensions. This relies, of course, upon the fundamentals of the AdS/CFT correspondence.

Einstein and de Sitter were both able to see down into a more fundamental construction, beyond the initial building blocks of quantum mechanics. They did not know how to make the connection, although Einstein realized that it had to be possible somehow; God does not play dice, not in the reality which we know, at least. There are infinite dimensions, but many of them overlap; their overlap and interference eventually draws a 4-dimensional spacetime at some point, somewhere in there.

Someplace, in the two theories we know, they collide, and from that point onward the quantized knitting draws physical reality. That reality is one we know. It is both a probabilistic computation, and a deterministic one; it will go someplace, but that pathway involves structures beyond our current comprehension. Only ingenuity, creativity, and application will get us there. Then hilariously enough, computational applications (ie google chrome) will be identical, physically, to the way we view "application" to any physical process such as a saw to woodworking. Woodworking is the OS, and if you apply a saw, it is naught but an API from the woodworking meme to the reality network.

Blah, so this is probably going to be a ranting location with nobody reading it for a while, but hey it's on the internet, so eventually someone will come by!

Anyways. Alice and Bob have always been rather secretive folk, trying to hide messages from Eve, even introducing third parties such as Charlie just to figure out ways to prevent Eve from figuring out what they're doing. They try and communicate with quantum information, which means that any time Eve wants to listen in, she has to stand in the way of the channel, take some of the data out, and corrupt it; Alice and Bob notice this, and they'll shut up until Eve goes away.

In the world of Quantum Information Theory, Alice and Bob usually communicate using "qubits" or quantum bits; these are super useful not because Alice can send some value in between zero and one as many talk about, but because if she sends a lot of them, and their angle between zero and one is dependent on the angle of some other qubit that she holds, she can encode lots of data in that angle. It's complicated, but suffice to say, if Alice and Bob can communicate normally ("classically") then Alice can tell Bob how to interpret his qubits based on what her set of entangled qubits looks like; this is also the principle behind Quantum Key Distribution, which is a very secure future communications technology. It also described Superdense Coding, which allows us to use the many superpositioned states of a quantum system to perform lots of operations at once.

What exactly do I mean by any of all that anyways? Well, QIT is a great source of interest because in the future, Quantum Computers may outperform regular computers, and the degree to which they may do this (with respect to certain problems, such as cybersecurity) is pretty intense. They are, however, really difficult to conceptualize, much less realize. A great book on Quantum Computation is here, and it goes into tremendous detail on how quantum physics may be used to build a unique sort of (binary, in the case of this book) computer. I won't waste your time by expecting you to read an entire book though:

Quantum Mechanics postulates that quantum states come in fundamental units, called quanta. Quanta fundamentally refers to how we make sure our wave equation is smooth and continuous; for some reason, in the mathematics, when we do this, only solutions with integer (1,2,3...) values with respect to allowed energy levels come out. If we want to think about QM even more abstractly though, we can generalize it to Quantum Field Theory, which lets us track how the quanta of particles interact with one another to produce other quantized effects. These quantized effects are of course, qubits in a sense, and Alice/Bob can communicate using them, but how do they come about?

Well, let's consider a basic example of how Alice and Bob could communicate. Alice is an electron sitting up in a high, uncomfortable energy level of an atom, so it wants to hop down to one of the lower seats. Bob is a nearby lazy electron that could use a kick up within his atom, but needs a certain amount of energy; specifically, he needs at least the amount of energy that Alice loses as she changes seats, in order to go up. If Alice goes down, she emits a photon equivalent to the change in energy her seat change represents, and if this photon carries enough energy to knock Bob's lazy electron ass up, it will likely do so (if it's passing that way). But, what if Alice only goes down one seat, or if she goes down too many seats? If Bob doesn't get enough energy, obviously he can't haul his butt up to that spot, so that's out of the question, but if he has too much energy, then the photon might bounce off after giving him enough energy to get up. It might also get him up there, then make his atom go flying wildly.

Alice might, or might not, change seats. Bob might, or might not, be bumped up; his atom might, or might not be, knocked about; Alice's photon might, or might not, continue on its way to interact with Charlie. Technically speaking, all these events happen, and we simply pick the event which happens in order to define the classical mechanics which guide reality. That event is the one that's most likely. In this case, is Alice happiest at a low seat? Then Bob will probably end up in his high seat. Alice tells Bob her feeling on seat choice by probabilistically emitting a photon; Bob, in all futures, sees that Alice really likes going lower, but he probably doesn't see that she is picky sometimes, going to middle seats (which don't convey any information to Bob). So, Alice communicates information to Bob by going down enough seats to actually have a noticeable quantum effect on Bob. Obvious, right?

Well, let's consider a bigger system. We have Alice, Bob, Charlie, David, and Eve. Going in order, Bob takes more energy than David or Eve to get bumped up a seat. Alice has 4 seats of which she can hop down to, and she's equally far from B C D and E. It's most likely that she'll go down to the lowest seat, but in order of decreasing likelihood she'll hit up the higher ones. So, if she goes down all the way, everyone might get a kick up - but it might give Eve enough energy to abandon her atom entirely, whereas Bob only barely absorbs it. Who's the most likely candidate for absorption? Well, all events happen. Bob gets maybe-kicked up his energy level; Charlie gets mostly maybe-kicked up, and his atom is maybe-kicked sideways, with a maybe-photon sent off sideways; David gets maybe-kicked up, his atom is mostly maybe-kicked sideways, a maybe-photon is sent off sideways, and he in fact maybe-flies-off. Eve is maybe-kicked up, her atom is mostly maybe-kicked sideways, a maybe-photon is sent off sideways, and she mostly maybe-flies-off.

Whoa! That's nonsense! Well, it's Quantum Mechanics. Let's reconcile that with ourselves by following out what happens afterwards. ABCD&E meet afterwards to share what happened to them. Bob says he got kicked up. What does everyone else say? Well, that nothing happened! Photons come in fundamental quanta. Although the symmetrical electromagnetic wave produced by Alice might seem to imply that everyone should have some energy, it actually only comes out as a boson, a fundamental force carrier representing a quantum state transition's conservation of energy.

This happens all the time though, and there are reasons why it's not nonsense. Consider what happens after all these events happen. Bob, Charlie, David, and Eve all go about their business afterwards, but if they've been kicked up an energy level, they do things a little differently. Let's say that the increase in energy level is an apple which is given. If Bob or Charlie is given an apple, they give is to Eve; if Eve is given an apple, she eats it; if David is given an apple, he eats it. We now have four possible futures which are mostly equivalent to two final options. Alternatively, David could give the apple back to Alice, who then gives it out randomly again; now we have four futures, one of which contains all four in a consecutive loop. Obviously David's option happens infinitely many times, and the remaining options which exit the loop consist of Bob, Charlie and Eve; these reduce to just Eve, but with a slightly stranger set of final states depending on how the Alice-David loop radiated energy to the environment (atom, scattering photon).

If we take all these differing futures and we sum them up to figure out the most probable thing, then the scary concept of total randomness all the time fades away a bit; the overlap of end events makes a lot of things (mostly) identical, and this mostly-identical-ness can be exploited in the sense that we only care about a single quantum state (Eve's electron energy level) rather than the system at large. If we look at the system at large, one of the entire universe of evolving quantum fields, we see something like a turbulent probabilistic nonsense structure...but with enough overlap that it seems like a fuzzy ocean of matter, light, and cosmological goodness.

If we want to use this concept in a computer, we just hitch a ride on the universe: We shape a section of that turbulent nonsense structure to be something with some form of sense (to us) and let it interact with itself & the universe for long enough that its probabilistic structure converges to our answer. We're interested in real-world answers to real-world problems, which means "classical" questions with "classical" answers; in the quantum world, this means we take BIG chunks of cosmological goodness, encode our classical question in the quantum structure of all this stuff (ie by sticking lots of electrons onto a transistor) and then allow quantum processes to take hold.

All that turbulent nonsense occurs, shuffling the electrons, EM waves propagating through silicon and bumping electrons throughout, heat dissipating into the environment...but throughout all of it, the "most probable" thing is for the computation to happen (in the case of a regular computer, for the transistor let current through or not) and thus as all the crazy-nonsense, mostly-normal (but erroneous) and totally normal quantum processes add up to give us our classical answer.

Leonard Susskind refers to this process of environment field turbulence "scrambling" and often applies it to wormholes. Quantum data at its finest is something more fundamental than the classical questions we ask computers, and so we wouldn't usually think of a classical computer performing scrambling, but nonetheless - it does. It does so in an interesting way...but I'll leave that for later.

For now, this is my first blog post evar :D total ranting and nonsense, but I hope someone out there enjoys it. My later ones will hopefully be more organized, better edited, shorter, and have more technical info while being more readable by a non-scientific audience, but we'll see where this goes.