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1.
The Quantum Speed up as Advanced Cognition of?the?Solution 总被引:1,自引:1,他引:0
Giuseppe Castagnoli 《International Journal of Theoretical Physics》2009,48(3):857-873
Solving a problem requires a problem solving step (deriving, from the formulation of the problem, the solution algorithm)
and a computation step (running the algorithm). The latter step is generally oblivious of the former. We unify the two steps
into a single physical interaction: a many body interaction in an idealized classical framework, a measurement interaction
in the quantum framework. The many body interaction is a useful conceptual reference. The coordinates of the moving parts
of a perfect machine are submitted to a relation representing problem-solution interdependence. Moving an “input” part nondeterministically
produces a solution through a many body interaction. The kinematics and the statistics of this problem solving mechanism apply
to quantum computation—once the physical representation is extended to the oracle that produces the problem. Configuration
space is replaced by phase space. The relation between the coordinates of the machine parts now applies to a set of variables
representing the populations of the qubits of a quantum register during reduction. The many body interaction is replaced by
the measurement interaction, which changes the population variables from the values before to the values after measurement
(and the forward evolution into the backward evolution, the same unitary transformation but ending with the state after measurement).
Quantum computation is reduction on the solution of the problem under the problem-solution interdependence relation.
The speed up is explained by a simple consideration of time-symmetry, it is the gain of information about the solution due
to backdating, to before running the algorithm, a time-symmetric part of the reduction on the solution. This advanced cognition
of the solution reduces the solution space to be explored by the algorithm. The quantum algorithm takes the time taken by
a classical algorithm that knows in advance 50% of the information acquired by reading the solution (i.e. by measuring the
content of the computer register at the end of the quantum algorithm).
From another standpoint, the notion that a computation process is condensed into a single physical interaction explains the
fact that we perceive many things at the same time in the introspective “present” (the instant of the interaction in the classical
case, the time interval spanned by backdated reduction in the quantum case). 相似文献
2.
The Mechanism of Quantum Computation 总被引:1,自引:1,他引:0
Giuseppe Castagnoli 《International Journal of Theoretical Physics》2008,47(8):2181-2194
3.
L. S. Schulman 《Foundations of Physics》1997,27(12):1623-1636
The quantum Zeno effect (QZE) is often associated with the ironic maxim, “a watched pot never boils”, although the notion
of “watching” suggests a continuous activity at odds with the usual (pulsed measurement) presentation of the QZE. We show
how continuous watching can provide the same halting of decay as the usual QZE, and, for incomplete hindrance, we provide
a precise connection between the interval between projections and the response time of the continuous observer. Thus, watching
closely, but not so closely as to halt the “boiling”, is equivalent to—gives the same degree of partial hindrance as—pulsed
measurements with a particular pulsing rate. Our demonstration is accomplished by treating the apparatus for the continuous
watching as a fully quantum object. This in turn allows us a second perspective on the QZE, in which it is the modified level
structure of the combined system/apparatus Hamiltonian that slows the decay. This and other considerations favor the characterization
“dominated time evolution” for the QZE. 相似文献
4.
Giuseppe Castagnoli 《International Journal of Theoretical Physics》2009,48(12):3383-3395
Quantum algorithms require less operations than classical algorithms. The exact reason of this has not been pinpointed until
now. Our explanation is that quantum algorithms know in advance 50% of the solution of the problem they will find in the future.
In fact they can be represented as the sum of all the possible histories of a respective “advanced information classical algorithm”.
This algorithm, given the advanced information (50% of the bits encoding the problem solution), performs the operations (oracle’s
queries) still required to identify the solution. Each history corresponds to a possible way of getting the advanced information
and a possible result of computing the missing information. This explanation of the quantum speed up has an immediate practical
consequence: the speed up comes from comparing two classical algorithms, with and without advanced information, with no physics
involved. This simplification could open the way to a systematic exploration of the possibilities of speed up. 相似文献
5.
Thomas Filk 《International Journal of Theoretical Physics》2006,45(6):1166-1180
The famous “spooky action at a distance” in the EPR-scenario is shown to be a local interaction, once entanglement is interpreted as a kind of “nearest neighbor” relation among quantum systems. Furthermore, the wave function itself is interpreted as encoding the “nearest neighbor” relations between a quantum system and spatial points. This interpretation becomes natural, if we view space and distance in terms of relations among spatial points. Therefore, “position” becomes a purely relational concept. This relational picture leads to a new perspective onto the quantum mechanical formalism, where many of the “weird” aspects, like the particle-wave duality, the non-locality of entanglement, or the “mystery” of the double-slit experiment, disappear. Furthermore, this picture circumvents the restrictions set by Bell’s inequalities, i.e., a possible (realistic) hidden variable theory based on these concepts can be local and at the same time reproduce the results of quantum mechanics.
PACS: 03.65.Ud, 04.60.Nc 相似文献
6.
M. Combescot O. Betbeder-Matibet F. Dubin 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,52(2):181-189
We have recently constructed a many-body theory for composite excitons, in
which the possible carrier exchanges between N excitons can be treated
exactly through a set of dimensionless “Pauli scatterings” between two
excitons. Many-body effects with free excitons turn out to be rather
simple because these excitons are the exact one-pair
eigenstates of the semiconductor Hamiltonian, in the absence of localized
traps. They consequently form a complete orthogonal basis for one-pair
states. As essentially all quantum particles known as bosons are
composite bosons, it is highly desirable to
extend this free exciton many-body theory to other kinds of
“cobosons” — a contraction for composite bosons — the physically
relevant ones being possibly not the exact one-pair eigenstates of
the system Hamiltonian. The purpose of this paper is
to derive the “Pauli scatterings” and the “interaction scatterings” of
these cobosons in terms of their wave functions and the interactions
which exist between the fermions from which they are
constructed. It is also explained how to calculate many-body effects in
such a very general composite boson system. 相似文献
7.
M. C. Land 《Foundations of Physics》1997,27(1):19-41
Despite the many successes of the relativistic quantum theory developed by Horwitz et al., certain difficulties persist in
the associated covariant classical mechanics. In this paper, we explore these difficulties through an examination of the classical.
Coulomb problem in the framework of off-shell electrodynamics. As the local gauge theory of a covariant quantum mechanics
with evolution paratmeter τ, off-shell electrodynamics constitutes a dynamical theory of ppacetime events, interacting through
five τ-dependent pre-Maxwell potentials. We present a straightforward solution of the classical equations of motion, for a
test event traversing the field induced by a “fixed” event (an event moving uniformly along the time axis at a fixed point
in space). This solution is seen to be unsatisfactory, and reveals the essential difficulties in the formalism at the classical
levels. We then offer a new model of the particle current—as a certain distribution of the event currents on the worldline—which
eliminates these difficulties and permits comparison of classisical off-shell electrodynamics with the standard Maxwell theory.
In this model, the “fixed” event induces a Yukawa-type potential, permitting a semiclassical identification of the pre-Maxwell
time scale λ with the inverse mass of the intervening photon. Numerical solutions to the equations of motion are compared
with the standard Maxwell solutions, and are seen to coincide when λ≳10−6 seconds, providing an initial estimate of this parameter. It is also demonstrated that the proposed model provides a natural
interpretation for the photon mass cut-off required for the renormalizability of the off-shell quantum electrodynamics. 相似文献
8.
Giuseppe Castagnoli 《International Journal of Theoretical Physics》2009,48(8):2412-2426
The oracle chooses a function out of a known set of functions and gives to the player a black box that, given an argument,
evaluates the function. The player should find out a certain character of the function (e.g. its period) through function
evaluation. This is the typical problem addressed by the quantum algorithms. In former theoretical work, we showed that a
quantum algorithm requires the number of function evaluations of a classical algorithm that knows in advance 50% of the information
that specifies the solution of the problem. This requires representing physically, besides the solution algorithm, the possible
choices of the oracle.
Here we check that this 50% rule holds for the main quantum algorithms. In structured problems, a classical algorithm with the advanced information, to identify
the missing information should perform one function evaluation. The speed up is exponential since a classical algorithm without
advanced information should perform an exponential number of function evaluations. In unstructured database search, a classical
algorithm that knows in advance n/2 bits of the database location, to identify the n/2 missing bits should perform O(2
n/2) function evaluations. The speed up is quadratic since a classical algorithm without advanced information should perform
O(2
n
) function evaluations. The 50% rule allows to identify in an entirely classical way the problems solvable with a quantum
sped up.
The advanced information classical algorithm also defines the quantum algorithm that solves the problem. Each classical history,
corresponding to a possible way of getting the advanced information and a possible result of computing the missing information,
is represented in quantum notation as a sequence of sharp states. The sum of the histories yields the function evaluation
stage of the quantum algorithm. Function evaluation entangles the oracle’s choice register (containing the function chosen
by the oracle) and the solution register (in which to read the solution at the end of the algorithm). Information about the
oracle’s choice propagates from the former to the latter register. Then the basis of the solution register should be rotated
to make this information readable. This defines the quantum algorithm, or its iterate and the number of iterations. 相似文献
9.
Clare Hewitt-Horsman 《Foundations of Physics》2009,39(8):869-902
The interpretation of quantum mechanics is an area of increasing interest to many working physicists. In particular, interest
has come from those involved in quantum computing and information theory, as there has always been a strong foundational element
in this field. This paper introduces one interpretation of quantum mechanics, a modern ‘many-worlds’ theory, from the perspective
of quantum computation. Reasons for seeking to interpret quantum mechanics are discussed, then the specific ‘neo-Everettian’
theory is introduced and its claim as the best available interpretation defended. The main objections to the interpretation,
including the so-called “problem of probability” are shown to fail. The local nature of the interpretation is demonstrated,
and the implications of this both for the interpretation and for quantum mechanics more generally are discussed. Finally,
the consequences of the theory for quantum computation are investigated, and common objections to using many worlds to describe
quantum computing are answered. We find that using this particular many-worlds theory as a physical foundation for quantum
computation gives several distinct advantages over other interpretations, and over not interpreting quantum theory at all. 相似文献
10.
Robert Oeckl 《Czechoslovak Journal of Physics》2001,51(12):1401-1406
The natural generalization of the notion of bundle in quantum geometry is that of bimodule. If the base space has quantum
group symmetries, one is particularly interested in bimodules covariant (equivariant) under these symmetries. Most attention
has so far been focused on the case with maximal symmetry — where the base space is a quantum group and the bimodules are
bicovariant. The structure of bicovariant bimodules is well understood through their correspondence with crossed modules.
We investigate the “next best” case — where the base space is a quantum homogeneous space and the bimodules are covariant.
We present a structure theorem that resembles the one for bicovariant bimodules. Thus, there is a correspondence between covariant
bimodules and a new kind of “crossed” modules which we define. The latter are attached to the pair of quantum groups which
defines the quantum homogeneous space.
We apply our structure theorem to differential calculi on quantum homogeneous spaces and discuss a related notion of induced
differential calculus.
Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June
2001.
This work was supported by a NATO fellowship grant. 相似文献
11.
12.
M. B. Mensky 《Optics and Spectroscopy》2007,103(3):461-467
Conceptual problems in quantum mechanics result from the specific quantum concept of reality and require, for their solution,
including the observer’s consciousness into the quantum theory of measurements. Most naturally, this is achieved in the framework
of Everett’s “many-world interpretation” of quantum mechanics. According to this interpretation, various classical alternatives
are perceived by consciousness separately from each other. In the Extended Everett Concept (EEC) proposed by the present author,
the separation of the alternatives is identified with the phenomenon of consciousness. This explains the classical character of the alternatives and unusual manifestations
of consciousness arising “at the edge of consciousness” (i.e., in sleep or trance) when its access to “other alternative classical
realities” (other Everett’s worlds) becomes feasible. Because of reversibility of quantum evolution in EEC, all time moments
in the quantum world are equivalent, while the impression of flow of time appears only in consciousness. If it is assumed
that consciousness may influence the probabilities of alternatives (which is consistent in case of infinitely many Everett’s
worlds), EEC explains free will, “probabilistic miracles” (observing low-probability events), and decreasing entropy in the
sphere of life.
The text was submitted by the author in English. 相似文献
13.
U. Mohrhoff 《Foundations of Physics》2009,39(2):137-155
This paper offers a critique of the Bayesian interpretation of quantum mechanics with particular focus on a paper by Caves,
Fuchs, and Schack containing a critique of the “objective preparations view” or OPV. It also aims to carry the discussion
beyond the hardened positions of Bayesians and proponents of the OPV. Several claims made by Caves et al. are rebutted, including
the claim that different pure states may legitimately be assigned to the same system at the same time, and the claim that
the quantum nature of a preparation device cannot legitimately be ignored. Both Bayesians and proponents of the OPV regard
the time dependence of a quantum state as the continuous dependence on time of an evolving state of some kind. This leads
to a false dilemma: quantum states are either objective states of nature or subjective states of belief. In reality they are
neither. The present paper views the aforesaid dependence as a dependence on the time of the measurement to whose possible
outcomes the quantum state serves to assign probabilities. This makes it possible to recognize the full implications of the
only testable feature of the theory, viz., the probabilities it assigns to measurement outcomes. Most important among these
are the objective fuzziness of all relative positions and momenta and the consequent incomplete spatiotemporal differentiation
of the physical world. The latter makes it possible to draw a clear distinction between the macroscopic and the microscopic.
This in turn makes it possible to understand the special status of measurements in all standard formulations of the theory.
Whereas Bayesians have written contemptuously about the “folly” of conjoining “objective” to “probability,” there are various
reasons why quantum-mechanical probabilities can be considered objective, not least the fact that they are needed to quantify
an objective fuzziness. But this cannot be appreciated without giving thought to the makeup of the world, which Bayesians
refuse to do. Doing this on the basis of how quantum mechanics assigns probabilities, one finds that what constitutes the
macroworld is a single Ultimate Reality, about which we know nothing, except that it manifests the macroworld or manifests
itself as the macroworld. The so-called microworld is neither a world nor a part of any world but instead is instrumental
in the manifestation of the macroworld. Quantum mechanics affords us a glimpse “behind” the manifested world, at stages in
the process of manifestation, but it does not allow us to describe what lies “behind” the manifested world except in terms
of the finished product—the manifested world, for without the manifested world there is nothing in whose terms we could describe
its manifestation. 相似文献
14.
We argue that it is fundamentally impossible to recover information about quantum superpositions when a quantum system has
interacted with a sufficiently large number of degrees of freedom of the environment. This is due to the fact that gravity
imposes fundamental limitations on how accurate measurements can be. This leads to the notion of undecidability: there is
no way to tell, due to fundamental limitations, if a quantum system evolved unitarily or suffered wavefunction collapse. This
in turn provides a solution to the problem of outcomes in quantum measurement by providing a sharp criterion for defining
when an event has taken place. We analyze in detail in examples two situations in which in principle one could recover information
about quantum coherence: (a) “revivals” of coherence in the interaction of a system with the measurement apparatus and the
environment and (b) the measurement of global observables of the system plus apparatus plus environment. We show in the examples
that the fundamental limitations due to gravity and quantum mechanics in measurement prevent both revivals from occurring
and the measurement of global observables. It can therefore be argued that the emerging picture provides a complete resolution
to the measurement problem in quantum mechanics. 相似文献
15.
Andrei Khrennikov Masanori Ohya Naboru Watanabe 《Journal of Russian Laser Research》2010,31(6):589-598
We continue the study of similarities between quantum information theory and theory of classical Gaussian signals. The possibility
of using quantum entropy for classical Gaussian signals was explored a long time ago. Recently we demonstrated that some basic
quantum channels can be represented as linear transforms of classical Gaussian signals. Here we consider bipartite quantum
systems and show that an important quantum channel given by the partial trace operation has a simple classical representation,
namely, a coordinate projection of a classical “prequantum signal.” We also consider the classical signal realization of quantum
channels corresponding to state transforms in the process of measurement. The latter induces a difficult interpretational
problem — the output signal corresponding to one system depends on a measurement that has been done on the second system.
This situation might be interpreted as a sign of quantum nonlocality, action at a distance. Although we do not exclude such
a possibility, i.e., that, in complete accordance with Bell, the creation of a realistic prequantum model is impossible without
action at a distance, we found another interpretation of this situation that is not related to quantum nonlocality. 相似文献
16.
M. Combescot O. Betbeder-Matibet 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,55(1):63-76
The purpose of this paper is to show how the diagrammatic expansion
in fermion exchanges of scalar products of N-composite-boson
(“coboson”) states can be obtained in a practical way. The hard
algebra on which this expansion is based, will be given in an independent publication.
Due to the composite nature of the particles, the scalar products
of N-coboson states do not reduce to a set of Kronecker symbols, as
for elementary bosons, but contain subtle exchange terms between two or
more cobosons. These terms originate from Pauli exclusion between the
fermionic components of the particles. While our many-body
theory for composite bosons leads to write these scalar products as
complicated sums of products of “Pauli scatterings” between
two cobosons, they in fact correspond to fermion exchanges
between any number P of quantum particles, with
2 ≤P≤N. These P-body exchanges are nicely represented by the
so-called “Shiva diagrams”, which are topologically different from
Feynman diagrams, due to the intrinsic many-body nature of the Pauli
exclusion from which they originate. These Shiva diagrams in fact
constitute the novel part of our composite-exciton many-body theory
which was up to now missing to get its full
diagrammatic representation. Using them, we can now “see” through
diagrams the physics of any quantity in which enters N interacting
excitons — or more generally N composite bosons —, with fermion
exchanges included in an
exact — and transparent — way. 相似文献
17.
We discuss a type of measurement in which a macroscopically large angular momentum (spin) is “created” nonlocally by the measurement
of just a few atoms from a double Fock state. This procedure apparently leads to a blatant nonconservation of a macroscopic
variable—the local angular momentum. We argue that while this gedankenexperiment provides a striking illustration of several counter-intuitive features of quantum mechanics, it does not imply a non-local
violation of the conservation of angular momentum. 相似文献
18.
It is proposed that the state space of quantum objects with a complicated discrete spectrum be used as a basis for multiqubit
recording and processing of information in a quantum computer. As an example, nuclear spin 3/2 is considered. The possibilities
of writing and reading two quantum bits of information, preparation of the initial state, and the implementation of the operations
“rotation” and “controlled negation,” which are sufficient for constructing complex algorithms, are demonstrated.
Pis’ma Zh. éksp. Teor. Fiz. 70, No. 1, 59–63 (10 July 1999) 相似文献
19.
Fabio Gavarini 《Czechoslovak Journal of Physics》2001,51(12):1330-1335
The “quantum duality principle” states that a quantisation of a Lie bialgebra provides also a quantisation of the dual formal
Poisson group and, conversely, a quantisation of a formal Poisson group yields a quantisation of the dual Lie bialgebra as
well. We extend this to a much more general result: namely, for any principal ideal domainR and for each primepεR we establish an “inner” Galois’ correspondence on the categoryHA of torsionless Hopf algebras overR, using two functors (fromHA to itself) such that the image of the first and the second is the full subcategory of those Hopf algebras which are commutative
and cocommutative, modulop, respectively (i.e., they are“quantum function algebras” (=QFA) and“quantum universal enveloping algebras” (=QUEA), atp, respectively). In particular we provide a machine to get two quantum groups — a QFA and a QUEA — out of any Hopf algebraH over a fieldk: apply the functors tok[ν] ⊗k H forp=ν.
A relevant example occurring in quantum electro-dynamics is studied in some detail.
Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June
2001 相似文献
20.
Paul J. Werbos 《International Journal of Theoretical Physics》2008,47(11):2862-2874
The classic “Bell’s Theorem” of Clauser, Holt, Shimony and Horne tells us that we must give up at least one of: (1) objective
reality (aka “hidden variables”); (2) locality; or (3) time-forwards macroscopic statistics (aka “causality”). The orthodox
Copenhagen version of physics gives up the first. The many-worlds theory of Everett and Wheeler gives up the second. The backwards-time
theory of physics (BTP) gives up the third. Contrary to conventional wisdom, empirical evidence strongly favors Everett-Wheeler
over orthodox Copenhagen. BTP allows two major variations—a many-worlds version and a neoclassical version based on Partial
Differential Equations (PDE), in the spirit of Einstein. Section 2 of this paper discusses the origins of quantum measurement
according to BTP, focusing on the issue of how we represent condensed matter objects like polarizers in a model “Bell’s Theorem”
experiment. The backwards time telegraph (BTT) is not ruled out in BTP, but is highly speculative for now, as will be discussed.
The views herein are not anyone’s official views, but this does constitute work produced on government time. 相似文献