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Topic: Quantum logic


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 Quantum computer - Wikipedia, the free encyclopedia
Quantum computers are different from classical computers such as DNA computers and computers based on transistors, even though these may ultimately use some kind of quantum mechanical effect (for example covalent bonds).
In quantum mechanics, the state of a physical system (such as an electron or a photon) is described by an element of a mathematical object called a Hilbert space.
Qubits for a quantum computer can be implemented using particles with two spin states: "up" and "down"; in fact any system, possessing an observable quantity A which is conserved under time evolution and such that A has at least two discrete and sufficiently spaced consecutive eigenvalues, is a suitable candidate for implementing a qubit.
en.wikipedia.org /wiki/Quantum_computer   (3223 words)

  
 Quantum logic -- Facts, Info, and Encyclopedia article   (Site not responding. Last check: 2007-10-20)
Quantum logic has been proposed as the correct logic for propositional inference generally, most notably by the philosopher (Click link for more info and facts about Hilary Putnam) Hilary Putnam, at least at one point in his career.
The similarities of the quantum logic formalism to a system of (Click link for more info and facts about deductive) deductive logic is regarded more as a curiosity than as a fact of fundamental philosophical importance.
Quantum logic provides a satisfactory foundation for a theory of (A garment (especially a coat) that can be worn inside out (with either side of the cloth showing)) reversible quantum processes.
www.absoluteastronomy.com /encyclopedia/q/qu/quantum_logic.htm   (2723 words)

  
 UO Research to Create 'Quantum Computer' Building Block
A second, though more speculative, use of the quantum logic gate would be as the building block for a "quantum computer" in much the same way as a transistor is the basic building block of today's computer.
Quantum computing has been recognized in the past five or so years as one of the most exciting areas of research, combining computer science theory and quantum physics.
Raymer notes that while the development of the quantum computer is still perhaps 20 years in the future, if one were ever built, it would be used "for certain special tasks and might operate thousands to millions of times faster than the largest parallel processor computer" available today.
www.uoregon.edu /newscenter/quantum.html   (559 words)

  
 Quantum Logic Explorer Home Page
Quantum logic can be conveniently broken down into 3 sets of axioms: the ortholattice axioms, the orthomodular law (which holds in those ortholattices that are also orthomodular lattices), and stronger axioms (that we discuss at the end of this page).
In the Quantum Logic Explorer database we have called the first one an axiom, and the other two are derived from it using only the axioms for ortholattices (look at the line called "The theorem was proved from these axioms" at the end of each proof listing, and there will be no mention of ax-r3).
Quantum logic is often expressed and studied as a propositional calculus.
us.metamath.org /qlegif/mmql.html   (3303 words)

  
 Quantum computing FAQ
This would also be a Quantum logic gate, because a radio pulse can also put an atom in a superposition of states, both spin up and spin down at the same time, and anything coupled to that state would also be in a superposition of states.
Quantum Information Program at NIST quantum information science project at NIST http://qubit.nist.gov/ A near-term goal of this program is to produce the first (prototype) quantum logic processor consisting of approximately 10 qubits.
Quantum Physics Division of the Physics Laboratory of NIST http://physics.nist.gov/Divisions/Div848/div848.html [- ] develops the laser as a precise measurement tool; [- ] investigates new ways to direct and control atoms and molecules; [- ] studies the interaction of ultrashort light pulses with matter; and [- ] measures nanometer scale motion of biological molecules.
www.rdrop.com /~cary/html/quantum_c_faq.html   (7848 words)

  
 D.J. Foulis, Dept. of Mathematics & Statistics University of Massachusetts, 'A Half Century of Quantum ...
Quantum logic offers the possibility of reestablishing some of the close bonds between physics and philosophy that existed before the exploitation of powerful techniques of mathematical analysis changed not only the methods of physical scientists, but their collective mindset as well.
Quantum logic is a recognized, autonomous, and rapidly developing field of mathematics (note 3) and it has engendered related research in a number of fields such as measure theory [11,14,
Birkhoff and von Neumann proposed that the specific quantum logic of projection operators on a Hilbert space should be replaced by a general class of quantum logics governed by a set of axioms, much in the same way that Boolean algebras had already been characterized axiomatically.
www.quantonics.com /Foulis_On_Quantum_Logic.html   (11210 words)

  
 NIST: Physics Laboratory's - Quantum Information
The starting point for quantum information at NIST was in 1995 when the Ion Storage Group demonstrated the first quantum-logic gate.
Quantum Computers May Be Easier to Build Than Predicted, NIST Work Suggests.
Josephson junction-based quantum bits for performing quantum measurements, quantum logic operations, and studying decoherence in solid state material systems, led by Ray Simmonds.
qubit.nist.gov   (943 words)

  
 Quantum Logic and Probability Theory
It is uncontroversial (though remarkable) that the formal apparatus of quantum mechanics reduces neatly to a generalization of classical probability in which the role played by a Boolean algebra of events in the latter is taken over by the "quantum logic" of projection operators on a Hilbert space.
Quantum mechanics is, on this view, a theory about the possible statistical distributions of outcomes of certain measurements, and its non-classical ‘logic’ simply reflects the fact that not all observable phenomena can be observed simultaneously.
Quantum logic has played a large role in shaping (and clarifying) this discussion, in particular by allowing us to be quite precise about what we mean by a classical explanation.
plato.stanford.edu /entries/qt-quantlog   (7961 words)

  
 BIBLIOGRAPHY OF REVERSIBLE AND QUANTUM LOGIC AND COMPUTING   (Site not responding. Last check: 2007-10-20)
A magnetic bubble logic element is the multiple-output logic element whose number of '1''s of the output is equal to that of corresponding input, and fanout of each output terminal of the element is restricted to one.
AB = A conservative logic element (CLE) is a multiple-output logic element whose weight of an input vector is equal to that of the corresponding output vector, and is a generalized model of magnetic bubble logic elements, fluid logic elements, and so on.
A conservative logic element is a multiple-output logic element whose number of '1s' of the input is equal to that of the corresponding output, and whose fan out of each output terminal is restricted to one.
www.ece.pdx.edu /~mperkows/PQLG/biblio.html   (1739 words)

  
 CQC Intros: Quantum Computing   (Site not responding. Last check: 2007-10-20)
On the atomic scale matter obeys the rules of quantum mechanics, which are quite different from the classical rules that determine the properties of conventional logic gates.
A quantum logic gate, like a classical gate, is a very simple computing device that performs one elementary quantum operation, usually on two qubits, in a given period of time[4].
The quantum theory of computation must in any case be an integral part of the world view of anyone who seeks a fundamental understanding of the quantum theory and the processing of information.
www.qubit.org /library/intros/comp/comp.html   (2952 words)

  
 Quantum logic: to be, or NOT to be? (October 2002) - News - PhysicsWeb
Although it is impossible to build perfect logic gates for quantum bits of information, a team led by Francesco De Martini of the University of Rome “La Sapienza” and INFM in Italy has achieved almost the maximum theoretical fidelity with its device (F De Martini et al 2002 Nature 419 815).
Physicists have long believed that such binary information could also be stored in certain two-state quantum systems, such as the horizontal and vertical polarization states of photons, or the spin-up and spin-down states of electrons.
Although this demonstration of a quantum NOT gate is an important step in the field of quantum computation, it is not certain that optical methods would be used in a real quantum computer.
physicsweb.org /article/news/6/10/15   (522 words)

  
 Gravitational vs. Quantum Logic: Virtually Left-handed Trinary Logic
The radically binary 2-based nature of right-handed trinary logic is further manifest in the fact that the sequence of the number of U's constituting the edges of the edge-sharing triangles of U's whose hypotenuses extend to the edges of the major infinitely expanding triangle is 2, 5, 14, 41, 122,.
Contrast with this situation the tripling (trinary) pattern of horizontally-based triangles of 1's in the infinitely expanding triangle produced by the real trinary logic geometric series infinite iterative sequential summing, where the sequence of such triangles is 1, 3, 9, 27, 81,.
It is the exemplary instance of the right-handed ternary logic illustrated in the text.
dgleahy.com /dgl/p19.html   (760 words)

  
 NIST Ion Storage Group   (Site not responding. Last check: 2007-10-20)
When extended to many quantum bits, the parallelism of quantum superpositions allows exponential increase in speed relative to classical computers in certain algorithms, most notably an algorithm for factoring large numbers (P. Shor, ATandT) which is of interest in the field of cryptography.
In such a computer, the quantum bits are "wired" together by virtue of their collective motion in the trap, and externally applied laser light entangles quantum bits and allows the construction of quantum logic gates.
Quantum logic operations with trapped ions are limited by the coupling between the ion motion and the environment, resulting in quantum decoherence.
tf.nist.gov /ion/qucomp/intro.htm   (476 words)

  
 Quantum dot logic advances TRN 101100
Efforts to make computers using quantum dots, which are microscopic specks of material that behave like atoms, have taken two steps forward with the development of a switch that needs no leads to the external environment and a clocking function that controls the switch.
In theory, quantum dots can be grouped into cells that in turn can be combined to form the logic gates, memory units and wires that are the building blocks of computers.
The Notre Dame researchers have succeeded in building a QCA cell out of four metallic islands that are physically isolated from each other and the environment, said Ravi K. Kummamuru, a graduate student at Notre Dame and researcher on the project.
www.trnmag.com /Stories/101100/Quantum_Dot_Computing_101100.htm   (999 words)

  
 Quantum Information Dynamics
In quantum information dynamics (1,3,7), we are trying to understand the basic principles of quantum Information Theory and its application to processes involving the interaction of qubits: the quantum carriers of information.
Subsequently, we showed how the quantum mutual entropy (the "mutual entanglement") is at the heart of a natural definition of the von Neumann capacity of noisy quantum channels (6).
Quantum information theory is a statistical theory of information, and as such can be useful to examine non-equilibrium processes in quantum statistical mechanics.
www.krl.caltech.edu /~adami/quantum.html   (548 words)

  
 Encyclopedia: Quantum logic   (Site not responding. Last check: 2007-10-20)
Birkhoff and J. von Neumann, The Logic of Quantum Mechanics, vol 37, 1936.
Mackey, Mathematical Foundations of Quantum Mechanics, W. Benjamin, 1963 (paperback reprint by Dover 2004).
Putnam, Is Logic Empirical, Boston Studies in the Philosophy of Sciencevol V, 1969
www.nationmaster.com /encyclopedia/Quantum-logic   (2638 words)

  
 Quantum logic
The quantum bus between the atomic qubits in our system will be the single photon quantum field of a high-finesse optical cavity.
  Quantum logic gates between arbitrary atoms can be performed by first linearly translating one or both of the standing waves in the vertical direction to bring the two atoms of interest into the cavity mode.
We have proposed an implementation of a quantum logic scheme utilizing the direct magnetic spin-spin interaction between individually trapped neutral atoms.
www.physics.gatech.edu /ultracool/Quantum_logic.htm   (1012 words)

  
 NIST Ion Storage Group   (Site not responding. Last check: 2007-10-20)
In a quantum computer, data can be stored in qubits, each of which is a two-level quantum mechanical system, with basis states 0> and 1> (for example).
However, there is a drawback to this sort of computation: according to quantum mechanics, whenever we read the state of a quantum register, we effectively collapse the superposition to one particular value and immediately destroy the parallelism.
A quantum logic gate is a fundamental building block of a quantum computer, just as conventional logic gates (AND, OR, Exclusive-OR, etc.) are the building blocks for traditional digital logic.
tf.nist.gov /ion/qucomp/quan_log.htm   (992 words)

  
 Quantum Physics, Logic And Spacetime: Variations On Finkelsteins Quantum Relativity; Author: Selesnick, S. A.; Author: ...
In this highly interesting monograph, a brief description of Finkelstein's approach to quantum theory and some of its ramifications is first given.
Specifically, his suggestion that some sort of quantum-set-like structure should underlie our macroscopic perception of spacetime is developed to the point where a fair slice of fundamental physics (for a massless world) may be formally derived in an elementary fashion from the ground up.
In detail, a model of what Finkelstein has called a quantum net, in conjunction with a single Schwinger-like dynamical principle, gives rise to the standard Langrangians for: massless Dirac fermions, general relativity, and Yang-Mills fields for the gauge groups SU(n), n = 3, 4.
www.netstoreusa.com /mabooks/981/9810232551.shtml   (311 words)

  
 The universal quantum logic matrix - Physics Help and Math Help - Physics Forums
This means that the question of the correctness of this area of quantum theory -- the reality of "quantum entanglement" and the special logic required to derive it -- is currently an open question.
As a matter of fact it is the conservation of quantum spin that causes a violation of Bell's inequality.
Whereas logical OR for sets is simply union, in the linear case it must be the smallest subspace containing a and b.
www.physicsforums.com /showthread.php?p=420785   (1437 words)

  
 Exogenous Quantum Logic - Mateus, Sernadas (ResearchIndex)   (Site not responding. Last check: 2007-10-20)
Note that the endogenous approach to probabilistic logic is also useful and, actually, widely used.
Fibring Of Logics As A Universal Construction - Caleiro, Carnielli, Rasga..
2 A half-century of quantum logic (context) - Foulis - 1999
citeseer.ist.psu.edu /660726.html   (444 words)

  
 RAPID SINGLE-FLUX-QUANTUM LOGIC
In the latching logics, this periodic reset of all gates is achieved by using an rf rather than a dc current supply for all the gates; this waveform performs also a global synchronization of the whole device.
Thus, an elementary cell of the RSFQ family is equivalent to a usual asynchronous logic circuit coupled with a latch (flip-flop) storing its output bit(s) until the end of the clock period.
Mukhanov, O.A., Rylov, S.V., Semenov, V.K, and Vyshenskii, S.V. (1989 a) 'RSFQ logic arithmetic', IEEE Trans.
pavel.physics.sunysb.edu /RSFQ/Research/WhatIs/rsfqre2m.html   (10171 words)

  
 Quantum Logic with an Optical Lattice
PRL describes a new type of quantum logic gate that might, at least in theory, meet those seemingly contradictory requirements.
In the quantum version, the quantum state of one atom determines its affect on the other.
According to quantum computing theory, the complete set of logic operations can be built up from this and a few other basic operations.
focus.aps.org /story/v3/st7   (554 words)

  
 Quantum logic gate lights up (August 2003) - News - PhysicsWeb
Quantum computers, on the other hand, exploit the ability of quantum particles to be in two or more states at the same time.
A quantum bit or “qubit” can therefore be “0” or “1” or any combination of the two.
This means that a quantum computer could, in principle, outperform a classical computer for certain tasks.
physicsweb.org /article/news/7/8/5   (528 words)

  
 Amazon.com: Books: An Introduction to Hilbert Space and Quantum Logic (Problem Books in Mathematics)   (Site not responding. Last check: 2007-10-20)
A logic of events is then developed in the next section, where quantum logic is defined explicitly.
Quantum systems have states that are ontologically uncertain according to the author.
The structure of the collection of these subspaces is defined in terms of the quantum logic defined earlier.
www.amazon.com /exec/obidos/tg/detail/-/0387968709?v=glance   (1023 words)

  
 [No title]   (Site not responding. Last check: 2007-10-20)
An introduction to the principle of correcting quantum information without direct measurement (and consequent wavefunction collapse).
An introduction to the phenomenon of quantum entanglement, which quantum computers would exploit to achieve their superiority over ordinary 'classical' computers.
A brief overview of the evolution of computing toward the "nanometre" scale where quantum mechanics may be exploited.
www.qubit.org /library/introductions.html   (220 words)

  
 Quantum Philosophy Theories
Quantum Physics and Classical Physics in the Light of Quantum Logic by Prof.
Yvon Gauthier -The Mathematical Foundations Of Quantum Mechanics by Hilbert and Von Neuman- 10) Prof.
Abner Shimony - The Logic of EPR- 35) Prof.
www.qpt.org.uk   (688 words)

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