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Parallel Quantum Computers

  1. Nov 24, 2007 #1
    Quantum Turing Machine
    NP-hard problems, such as the 'subset sum problem', or Travelling Salesman Problem (TSP) where n is large have lengthy solutions for a Turing Machine since n can be arbitarily set at a high value.
    Assume that the whole Universe were made into a Turing computer to solve a cryptographical subset sum
    problem such that every atom were made into a computer register then the value of n could still be set too high for the problem to be solved in a practically appropriate time span.

    But such a monstrous computer (the size of the Universe!) would be the equivalent of a Q computer with just one little tiny 40 qubit register. Role on Q Computers eh?
    I am wondering if a Q computer could manage infinite parallel computing power?, since entangled particles can have an infinite number of values (Heisenberg etc) all deriving from just one particle. For example, one fixed frequency photon has an exactly known momentum and therefore its position is completely unknown, and could be any. Its position would then provide our bit value range (infinity). This computer would not need
    all the atoms in the Universe to solve NP-Hard problems, one photon could do it. (oh no, I'm going mad now, somebody correct me pls!)

    The other interesting question is - could a computer come up with NP-Complete theory itself, could it come up with Pythagoras?
    Evolution of life was a process that required a long time. The Universe could not just produce a complex human from random atom collisions let alone one that knows Shakespeare plays and plays Mario well. In the same way, I believe, maths & physics theorums themselves need an evolutionary process to appear in the Universe as epistemological entities. A computer cannot just conjure them up without masses of supporting information available to it. In other words maths thoeries cannot just appear from basic axioms and operators, just as humans cannot just appear from random collisions between atoms, although Math would disagree. Is there a quanta of probablity, below which the Universe cannot possibly go?
     
  2. jcsd
  3. Nov 24, 2007 #2
    But one quantum particle does not a quantum computer make.
    They have managed to entangle a handful of different qubits -which can be lots of things, and also achieved 'multi-entanglement': where more than one quantum state -say electric polarisation, and spin, are superposed simultaneously, and stay coherent for a while, but so far, only in labs...
     
  4. Nov 25, 2007 #3
    it is often said that a quantum computer calculates in polynomial time- but in actuality this is the limit of the 'bandwidth' of the observer-QC interface- you can extract the answer as fast as polynomial time [with an ultimate limit within the Beckenstein bound]- but the nature of a quantum computer says that it actually computed all the possible answers at once- which includes all possible states- and some of those in principle must correspond to the n-qubit quantum computer in a state of an n-qubit quantum interface to an unlimitedly larger quantum computer or network lying in one of the infinte states of the multiverse- [and that to a larger- and so on ad infinitum]essentially there are paths of computation which ultimately harness the entire quantum multiverse if needed- so the upper limit of accessing the answer is the Beckenstein Bound- but the computation itself is virtually limitless in a sense- because fundamentally the quantum computer is like a logic structure which connects to an already existing infinite hilbert space of 'all possible answers to all possible problems' it could perform most if not all forms of hypercomputation and non-turing computations-
     
    Last edited: Nov 25, 2007
  5. Nov 26, 2007 #4
    this is an obvious possibility that comes from one of the oldest philosophical ideas in the history of rational thought: Pythagoras' Monad: that the universe and all it's complexity emerges from the self-interaction of one thing- this idea has been given physical power through the discovery of Universal Turing Machines- simple algorithms that can produce all possible causal sets- recently the simplest Tm was proved to be a 2 state-3 color cellular automaton this corresponds to any 2 state- or 1 bit system in a logic gate with 3 inputs/outputs-

    now consider that a qubit is a bit in superposition- if a qubit where placed in a feedback logic gate- a gate in which outputs feed back into the input- the qubit would form a virtually infinite qubit logic lattice- like standing in a room where all the walls are mirrors- as any interaction with itself should be the same as an interaction with another qubit [as long as the system is not 'observed' from outside- the superposition should endure allowing the lattice to form]- and with each interaction both of the qubit's states are generated branching into states that correspond to all possible permutations of bits- and with 3 or more I/O channels it would be universal and correspond to the phase space of possible universes thus emerging as the multiverse- this could be mapped as a 2D hexagonal logic lattice with qubits at each vertex extending toward infinity- such as the sort of lattices in loop quantum gravity models-

    interestingly photons at maximum energy- the Planck energy- shrink to the Planck area and are said to form an event horizon around themselves as too much energy is confined to too small a space- it has been suggested that these photon/black holes are the froth of the 'quantum foam'- since the photon can act as a qubit and the warped spacetime around it forces all it's signals to return to itself providing any number of I/O channels- a Planck scale photon/ black hole might allow a physical substrate for this feedback qubit logic gate- each one computing it's own copy of the entire multiverse by definition- and our own multiverse also a computation of some self-trapped photon in a parent universe- or the photon itself is "The Monad" and all things emerge from it's self-interactions through universal computation
     
    Last edited: Nov 26, 2007
  6. Nov 26, 2007 #5
    Another concept to get the ol' head around is that quantum processing isn't like ordinary computation: a quantum processor doesn't do a calculation, it is a calculation... it depends on how it gets set up.
     
    Last edited: Nov 26, 2007
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