PHYSICS and COMPUTERS
a long time not much importance has been given to the physical
modalities around which a calculation device could be realized. Only
recently, extrapolating the relentless progress of the practical
technology of modern computers, it has been perceived that the
physical principles upon which a calculating machine is built have a
operational impact on its ability to transform an insoluble problem
to a soluble problem. Richard Feynman, reflecting on this second
possibility, conceived of a machine working on the base of the
principles of new quantum physics and so of opening a promising new
chapter in computer science.
In 1981, the Institute
Massachusetts of Technology (MIT) hosted the first convention on the
relationship that exists between physics and computation. Feynman,
introduced one idea in a Paper entitled "Simulating Physics
with Computers". Feynman did not see anything particularly
exciting in the approximate computer simulations of reality made
until that date. In his paper, Feynman was, instead, interested in
the possibility of obtaining an exact simulation of Nature in a
grasped that computation was not only a mathematical discipline, but
also a physical one.
simulation of a phenomenon on a classic computer requires an
predictable deterministic world. There are no uncertainties in the
behavior of circuits constituted from billions of trillions of atoms
and electrons. "But can a traditional computer of that time can
emulate the quantum world?" asked Feynman.
argument, over a period of forty years' research, has produced a
remarkable output of theoretical work; it turns out that
developments leading to designs for possible hardware can be
expected in the near future.
it will be enough to say that the entire body of "Classical
Information Theory" from C. Shannon onwards, is up for
traditional definition of the unit of information - the bit - is an
unavoidably classical concept, based upon a classical operating
bistable circuit ( "On-Off" switch), which must be revised
when you base switching operations on quantum phenomena, such as the
spin of an electron or the polarization of a photon.
Qubit - the new unit of information based on quantum phenomena -
must now be set alongside the Bit, based on classical phenomena. The
concept of informative entropy must opportunely be revised. In
effect, the concept of accessible information, or the effective
information which can successfully be retrieved from a quantum
system for making a measurement, must be reviewed as well; this is
most important in estimating the theoretical possibility of
designing physical systems with which to carry out operations beyond
the reach of the classic techniques of computation.
quantum effects applied to the calculating machine.
is important to observe that the interest in the quantum calculation
lies not in repetitive procedures and calculations, which can be
executed on conventional computers operating in classic mode, but in
the fact that, by means of this new technology, operations that are
impossible with the traditional technique can become possible or, at
least, operations which are grossly inefficient on classic operating
systems can become very much more efficient with QC (Quantum
remains however to observe that the problems which can best be
solved with QC are rather specialised, whose solutions can be quite
are some examples problems which are insoluble with deterministic
methods, but which become possible in quantum terms, : the problem
of the generation of really random numbers and the problem of the
factorization of great numbers, which are of supreme interest for
cryptography. But already quantum i algorithms have been developed
for the problem of efficient database searching (database search
problem), for the calculation of the Hamiltonian cycles, for the
solution of the problem of the clerk traveller and of that one of
the i discreet logarithms. Finally, all the simulations of quantum
phenomena, which are important for the exploration of the world of
subatomic particles, become possible with the QC, as brilliantly
foreseen by the physicist Feynman.
evidence from experiments has shown that microscopic phenomena obey
different laws from those of classic physics, which humanity has
long believed capable of explaining all of physical reality. In
fact, on the one hand, the macroscopic classic phenomena derive from
the principle of causality in a strongly determinist sense, while on
the other hand, for the quantum microscopic phenomena, the principle
of causality of classical physics breaks down.
and paradoxes of quantum physics.
on the basis of the observations carried out in the microscopic
reality which presented apparently insoluble difficulties in classic
terms, proposed that the determinist principle must be jettisoned in
favour of the principle of statistical causality. ( Laws of
PRINCIPLE of UNCERTAINTY
Uncertainty Principle has, in fact, consequences of immense scope,
which upset the consolidated certainties of the most obvious daily
experience. To the idea that the electrons, the ultimate constituent
of matter, are material balls or particles of the smallest
dimensions we must add the realisation that, even if they are
particles, they behave very differently from our commonsense view,
to say the least.
well as the Uncertainty Principle in quantum physics, there is
another principle, known as Principle of Indistinguishability, which
states that all microscopic particles of the same type are
indistinguishable from each other: that is all elementary particles
are identical, and cannot be distinguished from each other either
with techniques of coloration, or in any other way.
the Uncertainty Principle we must another singular fact of
microscopic reality - the Principle of Complementarity. According to
this principle, there are some complementary properties at the
microscopic level which are mutually exclusive, in the sense that
the detection of one, by means of experiment, excludes the detection
of the other. To give an example, a quantum particle can, from time
to time, in different experimental systems, be demonstrated in one
form (corpuscle) or in the other (wave), but both aspects can never
perceived at the same time. This dual nature of Quantum
"particles" is sometimes referred to as the Wave/Particle
PRINCIPLE OF SUPERIMPOSITION
the basis of another principle (the Principle of Superimposition)
for the microscopic objects, it is possible that different states of
a determined entity, can calmly coexist in a state of
non-definition, as a linear combination of several of the states in
which it can be found.
looking through the glass of a window, has not sometimes seen not
only the external landscape but also his/her own image, more or less
clearly? Perhaps if you were watching from other side of the glass,
you would see the same landscape partially reflected. This
phenomenon usually goes unnoticed, but is in truth an
extraordinarily accessible example of the quantum world for
is known to be constituted of photons. These photons cross the glass
in order to show the landscape; but it is not determined. The
quantum world of elementary particles, like photons, is not a world
of certainties but of probabilities. The photon that hits the glass
can cross it, but it can also be reflected: the photon has one sure
probability to pass less or through the glass. The phenomenon is
more blurred, and defies the Aristotelian logic to which we are
used: in which the photon either passes through the glass, or not.
The sense of one of the conceptual pillars of the quantum mechanics
is this: the superimposition principle. If a quantum entity can
assume two values or exist in two states it is in one
superimposition of the two, with a non- zero probability of being in
one and the other.
a superimposition, it cannot be said that an entity is found really
in one state or another that but that is not known which one; the
superimposition contains, instead, all the possible cases, but is
not equivalent to some of them.
every particle a wave can then be associated, and every wave is one
manifestation of one particle. First, Max Born realized the nature
of this relation: the wave associated to a particle is a wave of
"probability", in the sense that it indicates which will
be the possible evolution for that particle. The state of a particle
is not more that classic (position in the space and the time and
speed). The state of a particle is given from the superimposition of
all its possible future states, each one "weighed" with
classes of problems can be tackled by a quantum computer?
this point two questions naturally arise:
can be assumed that the quantum computer is not a typical computer
designed to be annoying on the Internet, or to sending e-mail. What
end it can serve, then?
it has been observed that, according to the fundamental dogma of
computation, in the realm of calculation a machine conceptually more
powerful than the Turing machine does not exist.
the point of view of computing power, an algorithm can be derived
from the number of operations, and from the amount of memory
required for an input of x dimensions.
characterization of the algorithm determines the complexity of the
same algorithm. Among the problems considered complex are surely
those that grow as the power of a number. The function y =x2 grows
very quickly. For high values of x it is necessary to execute more
and more laborious multiplications. If the power grows further, as
an example y =x4 or y =x5 the difficulty increases still. Similar
problems, defined polynomials, are today within the capacity of
classic computers. But problems exist that grow very more quickly
than those polynomials. The problems of exponential type increase
more quickly in complexity than those of polynomials: ex grows very
more quickly than x3, x5,x 7,per increasing values of x.
distinction used more today is between problems that can be resolved
in apolynomial way (P), and are considered tractable, and those that
instead cannot be resolved in a polynomial way which are generally
considered intractable; these one can subdivide into various
classes. Among these latter there is the so-called class NP.
Simplifying, the problems of type NP cannot, in a generalized
manner, be resolved from determinist algorithms of polynomial type
and are, therefore, intractable. The initials "NP", in
fact, stand for non-deterministic polynomial time.
Determinist" means that, in any specific step of the algorithm,
it cannot be established unequivocally established the next step
should be. As in the game of chess: given one move of adversary,
there is not at the moment an algorithm that can, a priori,
determine in a reasonable time what the next move should be.
problems, defined as NP-complete, are set in such a way that, if a
problem in polynomial time is resolved, then all the group is
resoluble. Among these problems the famous problem of the store
clerk traveller who must visit a certain number of cities, without
retracing his route, in the minimal possible distance.
summary, the algorithms can be classified as:
polynomials: (for example, multiplication)
non-determinsitic polynomial: (for example, factorization)
complete: subclasses of those NP in which all the group are
tractable (as an example, the problem of the store clerk
the classes of NP type are not the most complex, they contain
however some intermediate problems which are,, at the moment, of
greater interest. Among these, for instance, the problem of the
factorization of a number is intimately connected with the
possibility of decrypting a cryptography system, like the system
RSA129 that uses keys constituted from 128 ciphers. It has been
estimated that, in 1994, the factorization of a number of 128
ciphers required 5000 MIPS-YEARS (MIPS: million instructions per
second), And it is just in the area of similar problems that the
quantum computer enters the game. It has recently been discovered,
as an example, than just the factorization in first factors of great
numbers can be performed with an ideal quantum computer, using
superimposition and entanglement, can solve, say, the algorithm of
Shor (devised by Peter Shor in 1994). The algorithm of Shor is
mathematically simple enough and demands modest quantum hardware, at
least for small numbers.
problem for which the employment of quantum properties seems to open
promising horizons relates to the solution of the so-called problem
of the courier in the cryptographic systems. This problem is
relative to the fact that any protected cryptographic transmission
includes the unavoidable employment of a courier for the transport
of the key. The courier is the weak point of the whole system
(he/she can "betray", or, can be seized and forced to
betray the key).
do I think it can be helpful to suggest that the two partners in
transmission can meet once to exchange the keys for all possible
connections, because, for obvious security reasons, it is advisable
to change the key at every connection. Therefore, for the two
partners, if they want to communicate while each remains in his/her
own base of work, there is no choice but to entrust one's message to
systems have remarkable similarities to a safe box, in which two
security aspects can be described:
physical security, represented by the robustness of the system
against thefts carried out with physical means (instruments of
varied kind, thermal nozzle etc.).The physical security
corresponds to the problem of the courier in a cryptographic
system of transmission.
logical security, represented by the complexity of the opening
key. The logical security corresponds to the problem of
constructing algorithms which are sufficiently complex as to not
be easily penetrated.
is possible to demonstrate that intrinsically protected
cryptographic messages can be obtained where, at every session, keys
realized with random sequences of data are used, which a hostile
cryptanalyst cannot work on. A cryptographic technique using a
quantum procedure in order to realize exchange of keys produces
absolute water tightness.
of physical reliability
physical reliability of devices for QC is strongly conditioned by
the famous phenomenon of "quantum de-coherence", which is
an unavoidable effect of interchange between a quantum system in
which it is dipped.
exciting effect of the superimposition of states with the consequent
possibility of that it has been called quantum parallelism, faces a
serious difficulty from the phenomenon of de-coherence. However,
much progress in this direction has been made out and there is the
now the possibility that the problem of de-coherence can be solved.
maximum limit of scaling seems at this time to be about 50 qubits.
And above all one does not know if a quantum program can be executed
for the time necessary without incurring the phenomenon of the
de-coherence. One of the more complex problems to resolve is how to
prevent the interference of several calculations from being
reflected in the macroscopic world. In fact, if a group of atoms or
molecules is subordinate to a phenomenon of interference and
interacts at the same time with the macroscopic environment, one is
quite likely to find interference with measurements that relate only
to atoms of the original group that therefore prevents any useful
FUTURE PERSPECTIVES and SCENARIOS
is not possible at the present moment to formulate forecasts on the
effective technical ability to construct a quantum computer able,
for example, to decode in factors a first number at least 10
ciphers. There are at least three types of problems that are
necessary to resolve.
the first place, the maintenance of the state of quantum
superimposition of several elements, and therefore an effective
isolation of the quantum circuits from the macroscopic world that
encircles them. In the second place, the management of the errors
which however appear in a such delicate circuital complex. Finally,
the constructive wisdom necessary in order to realize the
calculational functions that, through superimposition, entanglement
and interference, concur to create answers from the questions and to
correlate the former to the latter.
quantum computer would allow us, finally, to understand better not
only the reality of the subatomic world but also the real meaning of
computation, perhaps, and its role in the world.
advent of "pocket" quantum computers does not seem
imminent and not even interesting. The QC is not placed as
competitive technology with the current computer (greater economy,
more reduced dimensions ecc.), but rather in terms of allowing the
solution of problems which the current technique are clearly
first steps will surely be undertaken in the direction of machines
specialized in the solution of particularly arduous problems, with
important impacts on the theorist-practical plan, that are not
soluble, or hardly soluble, with the traditional classic techniques.
the other hand, the founder of the mythical Digital (computer
company ) the fifty years ago foresaw a market of hundred computers,
at most, in all the world; therefore forecasting of the
technological future is a hopeless enterprise.
road to cover is enormously complex and it is not even sure that is
really runneable. But even if in the end the quantum computer turns
out to be as large as a building and demands hundred of specialists
for programming and management, and cost hundredss of millions of
euros, or still more, it could reveal a formidable instrument of
a strategic or economic point of view it could be harnessed to
decipher any cryptographic key or to investigate any archives in a
does it mean to assert that the state of a particle is a set of
possible states? The photon that affects the glass passes or? An
electron is here or there? In the quantum world the electron is here
and there, but with various probabilities of being here and there.
After a measure it can only be said if it is here.
if it is attempted to measure a physical quantity of a system, the
wave function of the system collapses and a precise value for a
quantity is obtained that before was simply one of the many
is just the observation that leads to the "choice" of that
particular value between all those possible ones. What causes the
collapse of a wave function? The answer to this question is very
complex but it can be answered, to a close approximation, that it is
the interference between the quantum world and the macroscopic
surprises from the discoveries of quantum physics are great that
Heisenberg was led to observe that, in order to understand quantum
physics, it is necessary to leave behind the certainties of classic
physics, to which every being human is unavoidably attached, and
that classic physics are no more than the description in rigorous
mathematic terms of the daily experience of the physical world,
necessarily based on macroscopic objects.
PARADOX (EINSTEIN-PODOLSKY-ROSEN) (entanglement)
from the consideration that spin (the quantum entity that does not
have equivalent in classic physics) is a conservative physical
quantity, a quantum system is seen as constituted from two protons,
strictly coupled and with null total spin. This situation
corresponds to having the spin of two protons, measured along an
assigned direction, oriented in opposite senses, that is, if a
proton has spin +1/2 along a direction, the other will necessarily
have spin -1/2 along the same direction.
now one imagines that the two protons move indefinitely apart from
one other until reaching an enormous separation (even very many
light years, if it is the case!) it must be admitted, for the
mentioned conservation, than the relation of antiparallelism of the
spin remains conserved.
where the spin measure of one of two particles is carried out along
an assigned direction, forcing it into a determined state,
necessarily also the far particle will be forced immediately in a
determined state of its angular moment so as to conserve, along the
same direction, the relation of antiparallelism of departure. In
order to indicate this interdependence between particles in the
Anglo-Saxon world the expression "Entanglement" has come
instantaneous action at a distance has been for along time
considered paradoxical, until J.Bell demonstrated that the strange
effect, even if apparently paradoxical, effectively is verified in
paradox on examination was thought to threaten the conclusions of
theoretical physics: it was argued that possibility of having an
effect at a distance in a null time violates the so-called principle
of locality. Indeed, the cited paradox dose not infringe the
locality principle, in that the result of the first measurement is
as random as that of the second measurement (on the proton far
away), is not compatible with the described experience of
transmitting information between the two ends and, therefore, of
producing an effect at a meaningful distance.
PRINCIPLE OF SUPERIMPOSITION and the QUANTUM PARALLELISM
quantum system evolves, according to an equation discovered by the
physicist Schrödinger, until a measure is performed, then the
system collapses into one of its possible states. The equation has
the property that the linear combination of its solutions is still
one of its solutions, consequently if the system starts in a
superimposition of states, it will evolve into a block of all the
superimposition of states.
consider the qubit: the qubit is considered homologous to the bit,
that is the contained information in a quantum system of two states,
like the spin of an electron. Where the electron is not in a defined
state, but in superimposition of states 0(Spin "on") and
1(Spin "down"), in case checks to the state 0(Spin
"on") the binary value "0" and to the state 1
(Spin "down")the binary value "1", the
conclusion will be that the system electron is in a state
representing the superimposition of" 0" and "1"-
unimaginable in a classic world!
superimposition, entanglement and interference are the three pillars
to the base of the operation of the quantum computer.
to the quantum mechanics the spin can be in a state of
superimposition, that is in any combination of the two directions,
as an example 30% clockwise and counter-clockwise 70%. The entire
system is, therefore, an incredibly complex aggregate of
superimpositions of all the possible combinations of spin for every
particle. The evolution of a similar system, described from a
complex probabilistic wave function, even today is an intractable
problem, in any supercomputer. Image having an atom that has a
single electron in the last occupied orbit.
electron can be moved, that is "excited", in a more
external orbit by illuminating it with a light of a determined
frequency and duration. The electron makes therefore a quantum jump
to a more elevated energy. If such state is sufficiently stable it
will be used, with a lower state of energy, in order to represent
respective numbers 0 and 1.
"an excited" atom receives a hit from a further impulse of
light, similar to the previous one, the electron returns to the
state of lower energy emitting a photon.
what happens if the duration of the first impulse of hard light is
half of the time necessary in order commute the state of the
electron? The answer is amazing for the logic to which we are
accustomed: the electron will simultaneously be found in both the
orbits. The electron will be then in a "superimposition"
of the two states, fundamental and excited.
qubit is a "superimposition" of 0 and 1 and can be defined
from the mathematical notation to |0> +b |1>, meaning with
that, if measured, it could be 0 with probability a and 1 with
probability b, being a and b complex numbers. For simplicity,
without wanting to complicate matters, the mathematical nature of
the states represents to you
from the symbol |>, however one should remember that such symbol
represents a vector, for its oriented nature. The state |1>
+|0> is various from the state |0 >+|1>.
how can the values stored in a qubit be modified? In other words,
which type of operators can be used in order to modify the content
of one or more qubit? The question is more general still.
the quantum world it has possible to invert the content of a qubit.
The impulse of light of opportune duration is equivalent to all the
effects to an operator NOT. But illuminating the atom for half time
it obtains a superimposition of states. A complete impulse is
equivalent, therefore, to operator NOT. But what is equivalent to
one of half duration ? To the operating square root of NOT.
the operator NOT other applicable types of operators exist in
quantum mechanics,. Here is where finally the principle of
Entanglement enters the game. If two qubits are both in the
superimposition of 0 and 1 they are defined as Entangled if the
result of the measurement of one of them is always correlated with
the result of the value of the other qubit.
together with Superimposition, it is the key of the entire operation
of the quantum computer. Without Entanglement, in fact, how could
results be correlated with the input values? In order to illustrate
this fundamental concept more clearly, a simple metaphor can be
used. Imagine having a set of questions; for example, the
multiplication of various couples of many great numbers, and
distributing such multiplications between several persons. Every
person will transcribe the result on a piece of paper and will place
it in a box. The box in this example represents the output registry
of a qubit. To extract from the box a result on each occasion is
equivalent "to collapsing" the registry of a qubit to a
precise value after a measurement. But to which question does the
correspond, that is which multiplication, if there is only a piece
of paper with the result? In the quantum computer it is precisely
the mechanism of Entanglement which associates each results with its
the same time the principle of Interference acts so that if a piece
of paper with a result is extracted at the same time all the others
are destroyed. With the three fundamental mechanisms of
Superimposition, of Entanglement and Interference it is possible to
construct an entire circuital quantum logic, at least on a
conceptual level, with which the extraordinary calculating ability
of a quantum computer can be highlighted.
now a registry constituted from two electrons is constructed, whose
stable spins are four, correspondents to the four binary states
(00,01,10,11), where the state of the registry is not a defined
state, but in superimposition of states, the system "electron
couple " (= the registry at two electrons) will be found in a
state that represents the superimposition of the couple of states
00,01,10,11. Therefore, in a registry with two cells, all the four
states can cohabit in state of superimposition. In the registry the
symbols 00,01,10,11, are written and overlapped and can be extracted
with an appropriate measurement.
important conclusion follows: in order to record the four values in
the classic theory it would be necessary to have four registries
with two cells,; instead, in the quantum theory, the four values are
included in a single registry with two cells! And proceeding in the
construction, a registry with 1 cell can contain 2 1 values, a
registry with 2 cells can contain 2 2 values, a registry with3 cells
can contain 2 3 values... a registry with n cells will be able to
contain 2 n values.
second conclusion follows: if the quantum system
"registry" is left to evolve, it will cause all the states
in superimposition to evolve simultaneously, realizing a type of
operation in parallel, termed quantum parallelism. If the evolution
equation is chosen in such way to lead to the solution of a defined
problem, it will be sufficient to let the system evolve towards the
desired solution, to which it will proceed by itself, simultaneously
estimating all the supplied data in superimposition. This technique
can turn out to be enormously favourable in cases where the computer
must be used in order to estimate a large series of data.
the probability of finding the correct number will be very low
because in the registry the not-solutions will be in state of
superimposition with the solution, rendering the intended operation
order to solve the problem it will be necessary to find how the
not-solutions can interfere so that they cancel themselves.
Naturally quantum registries of appropriate sizes must be available
and that constitutes a still unsolved technological problem with no
the procedure has been verified for the decomposition of a small
number (15 = 5 x 3), having demonstrated that the operation is
enormous advantage of the proposed procedure in quantum parallelism
is that it allows one to carry out, at a "single stroke",
the enormous number of products requested for the desired
Information is physical
technology of the micro fabrication and the development of the
materials for microelectronics have reached and will continue to
grow to a progressive level of impressive, exponential
miniaturization of the electronic components of computers.
effects cannot not be a factor if accurate operation of microchips
is required, when these are used in devices for manipulating
also be possible to compute with molecular devices, thanks to
miniaturization in due course, but these will not be quantum
computers. In fact, quantum computation, is very different. Beyond
energy there is another property of physics, at first glance so much
more rarified that it would be said to belong rather to the realm of
metaphysics, that has universal validity, which can be expressed in
totally different ways, independent from its physical support:
Information. Like the observable objects of physics, Information
must be contained in forms that can be o fgreat variety; spoken
words are tuned from the variations of air pressure, written words
from the disposition of molecules of ink on paper, thoughts even
correspond to particular configurations of the neurons, and above
all, as with the observable data of physics, raw Information comes
from solid transformations.
behaves in some ways like a physical entity, in that it can be
conserved, be transformed, be measured and dissipated.
we all know, the computer is an excellent source of information.
facility with which the information can be manipulated automatically
is derives simply from its universality, from the fact that it can
be expressed in various ways without losing its essential nature and
that, as in physics, more complex transformations can be realized
with many simple operations.
is no Information without a physical bearer, but Information is
essentially independent from how it is expressed physically and can
be freely transferred from one form to another: so Information is a
natural candidate for a fundamental role in physics, exactly like
energy and momentum.
the great role of fundamntal physics has been to discover the
fundamental constituents of matter and the laws that describe and
govern their interactions and their dynamics. Now IT begins to
emerge as an important and equally fundamental program to discover
in which ways the nature allows or forbids Information to be
expressed, stored, manipulated and transmitted.
ambitious program to reconsider the fundamental principles of
physics from the point of view of the theory of Information is still
in its infancy; however it promises to bear important fruits: the
concepts and the methods of Information and quantum computation are
the first among these.
the time of Turing, essentially no substantial change has taken
place in the idea of what a Computer is and how it works; until now,
quantum mechanics has not opened the possibility of a change of
effect, the Aristotelian logic of the Turing machine is badly
adapted to the human rationality (are True and False sufficient
concepts?). Perhaps another possible logic exists.
mechanics is a mathematical structure set up in order to describe
Nature that, at least in principle, compares any physical system
from the corresponding classical picture with an outline made from
of a great variety of paradigms : variable dynamics are associated
with a series of states in which the vectors can have infinite
complex members, the wave functions. Only after difficult
reinterpretation of observed concepts and of the meaning of such
weird properties of operators, can the classic ones be put into an
analogous variable relation.
interesting to notice how the more important properties of the
quantum theory are not in the details of the equations of motion and
of dynamics that they generate but just in the fact that the
quantization of a classical physical system with N degrees of
freedom generates a quantum system whose space of the states has a
volume that exponentially grows with N; so the quantum theory leads
to an enormously large,complex, combination co of possible dynamic
structures. The idea that Information can be stored in microscopic
states is for the physicists an unprecedented challenge, in opening
vast perspectives in the use of that same matter, in its fundamental
structure, in order to make calculations.
possibility of the realization of this program is very arduous as
well as fascinating. The interference effects that allow quantum
algorithms to work render such algorithms also very fragile. Quantum
computation aims to realize exponentially more efficient
computational schema than the classical equivalent precisely thanks
to the characteristic property of quantum physics.
class of problems that can efficiently be resolved by quantum
computers are called BQP "bounded error, quantum, polynomial
time". Quantum computers substantially execute randomized
algorithms only a. One says that a quantum computer resolves a
problem if for every request the answer will be correct with high
probability. If the solution is found in "short time" the
problem belongs to the BQP class. Although the quantum computers are
often faster than classic computers, they cannot resolve all the
problems. One Turing machine instead can simulate a quantum
requirement that a quantum computer must satisfy:
scalable in order to increase the number of qubits
can be initialized to an arbitrary value
gates must be faster than the de-coherence time
Turing-complete gate set
can easy be read
difficulties are numerous in constructing a quantum computer and
those existing, "ad hoc" for specific problems resolve
banal problems only.
candidates technologies in order to make quantum computers:
Superconductor-based quantum computers (including
SQUID-based quantum computers)
Trapped ion quantum computers
"Nuclear magnetic resonance on molecules in
"quantum dot on surface"-based
"Cavity quantum electrodynamics" (CQED)-based
ESR quantum computer
solid state NMR Kane quantum computer
quantum computers do not exist but emulators exist. It is possible
you want to correspond with the author, please wrtite to Luisa
text editing by Michael Martin-Smith]
[024. LS. TDF. 2005 - 10. 11. 2005]