Talk:Quantum computation

Article Checklist for "Quantum computation"

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Checklist last edited by	Charles Blackham 14:00, 5 June 2007 (CDT)

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Question. The article says: "Throughout this article The Many Worlds Interpretation (MWI) of quantum mechanics is used." Why so? Is that a feature of quantum computation as a topic? Or is it a debatable interpretation? Cf. Neutrality Policy. --Larry Sanger 14:05, 20 April 2007 (CDT)

MWI is a useful interpretation of quantum mechanics to enable the explanation and understanding of the basic concepts of quantum computations in a less abstract way. The particular interpretation which one wishes to use when examining quantum computation does not really affect the subject itself, unless one is looking at it from a solely philosophical point of view. In the finished article, MWI will only be used as an aide to explanation and not a vehicle to drive a particular point of view. Charles Blackham 17:23, 20 April 2007 (CDT)

There's a new book (I just finished it last night) entitled Schrödinger's Rabbits that discusses the MWI in some detail. It's probably fair to say that there is a debate here, but a civil one, not at all reminiscent of some of the so-called debates we've seen on Citizendium. To understand what it's all about you need to know a little quantum mechanics, and in particular, that both particles (like electrons) and light exhibit both particle-like and wave-like behavior. The classic demonstration of this phenomenon is the two-slit experiment where electrons (or photons) are made to pass through one of two slits. If no attempt is made to detetrmine which of the two slits the electron (for definiteness, let's use electrons) passes through, you will see a classic interference pattern. What is this? Well, if you drop a pebble in a perfectly still pond, you'll see waves emenating in a circular pattern. Now, if you drop two pebbles simultaneously, you'll see two patterns of circles, but sometimes the ridges from each will coincide making the water level even higher, sometimes the troughs will coincide making even lower, and sometimes a ridge and trough will effectively cancel eachother out. Now, if you imagine two point light sources at a fixed frequency nd the waves they generate, you get the same kind of pattern, and it can actually be measured, say, with an unexposed film, which will reveal a kind of "banding" effect. Returning to electrons, if you make no attempt to determine which slit the electron goes through, you will get the same type interference pattern, even if there is only one electron. Now, if you "watch" to see which slit the electron passes through (e.g., by shining a bright light above a slit) the pattern disappears. This is known as wave function collapse, and in the Copenhagen interpretation of quantum mechanics (a term retrospectively applied to the formulation of QM by early researchers), this collapse follows directly from the act of observation. There have been attempts to explain this phenomenon by arguing that the physical act of observation somehow modifies the system, but more refined experiments have made this argument difficult to sustain. The most notable physicist arguing for something approaching classical collapse is Sir Roger Penrose, but in any case, the Copenhagen interpretation is widely considered to be of historical interest only. The many-worlds intetpretation takes a different approach. Every possible "history" of a system occurs in an alternate universe. That sounds rather fantastic, but in a sense, it's just a different way of talking about the same mathematics. Now, different "worlds" or "wave functions" that are compatible (or geometrically close) are coherent, meaning that observables can represent a variety of states with a high probability, but when those worlds diverge we have a phenomenon known as decoherence, which is the more modern replacement for the older idea of wave function collapse. Now, the fascinating thing is that time frequirfed for dechonrence can actually be measured. The MWI is often preferred because it allows us to maintain a property of physical systems called locality: no instantaneous communication is required, but rather decoherence occurs through propogation of local effects. Think of two electrons in opposite spin states, but where the spin of one is not measured or modified for a long time. When it does occur, does this allow us to "teleport" information? The answer is no, but only because we can't actually use it! Anyway, David Deutch, the Oxford physicist who pioneered quantum computing and quantum information theory, has used the MWI, but you could argue that it provides a convenient or "natural" framework for quantum computation. It is still an open question (so far as I know) whether MWI can be verified by experiment. Greg Woodhouse 13:17, 5 June 2007 (CDT)

As I say in my above comment, the interpretation of QM used, and the philosophical baggage associated with it, matters very little when it comes to the actual physics of what's happening during a computation. However, the various interpretations do provide a way to try to understand what is happening and overcome some of the abstract nature of the mathematics involved. MWI, as you note, has many advantages when it comes to quantum computation. It does not really matter whether MWI is verifiable or not, or whether it is true. MWI will only be used in the finished article as a pedagogical tool, which I believe is valid, like the use of the Bohr atom when one is introduced to atomic theory. I also appreciate that MWI, like all such philosophical questions about the nature of reality, brings with it its controversies and thus I shall in the introduction explain more clearly the main reason for using MWI: as a clear pedagogical tool, and not because it is the right interpretation. Charles Blackham 14:15, 5 June 2007 (CDT)

Definition of qubit

I'm a little surprised by your definition of qubit. A single qubit is superposition of two mutually exclusive states conventionally called |0> and |1>. Your definition makes it sound to me like you're allowing multiple qubits. Am I misunderstanding your intent? Greg Woodhouse 10:32, 6 June 2007 (CDT)

A qubit is an actual physical system, not a boolean observable, with states which may be denoted by |0> and |1>. The qubit has a infinite number of observables, all of which are boolean, each corresponding to a different 2x2 Hermitian matrix. One does not of course have to be concerned with the evolution of all these observables - only the ones one wishes to observe. This idea will become clearer when I have written the simple computation section. Charles Blackham 12:27, 6 June 2007 (CDT)

Diagrams

Does anyone know of software (ideally for OS X) that can be used to draw diagrams of quantum circuits (or classical circuits, for that mattetr)? Greg Woodhouse 11:34, 6 June 2007 (CDT)

Paint does the job well enough on Windows. Charles Blackham 12:27, 6 June 2007 (CDT)

Try out the program inkscape, it's a pretty good mostly cross platform application (uses the GTK2 libraries). That's what I use for line drawings. --Paul Derry 12:48, 9 June 2007 (CDT)

Notation

Where can I find a reference as to what the algorithm notation presented in the article means? Coming from someone that has no experience with this material I find it rather cryptic... --Paul Derry 12:50, 9 June 2007 (CDT)

The notation will be explained most naturally, I think, in articles outlining the Schrodinger and Heisenberg pictures, which I hope to start shortly. You might also find helpful the article on Dirac's Bra-ket notation. Charles Blackham 02:52, 11 June 2007 (CDT)

Oracle

You might want to compare the concept of oracle you have introduced to the classical concept (oracle Turing machines and relative computability). The concept seems rather similar, though you are obviously talking about unitary dynamics. Greg Woodhouse 08:56, 12 June 2007 (CDT)