we have been talking about the different aspects of building of quantum computers and in this
regard let us go back and look at some of the cases that we have looked at and so let
us see what we need our qubits as we have discussed before and which are typically two
level quantum systems which can undergo super positions which means they have to be isolated
from outside world otherwise their super position will not stay so that is the fragility of
this problem they had to be confined characterizable and scalable so the main constrain on the
qubit lies on the fact that it has to be at two level quantum system which can undergo
super position but since it can undergo super positions it becomes fragile which means there
it is to be isolated from the outside world so such qubits which are confinable that can
be characterized and can be scalable are good qubits for building quantum computers in terms
of preparation we would like to have the computer being ready in the standard start state we
should be able to have a readout of the process and finally we should have logic gates that
are controllable with the interactions with outside world and we would like to have qubit
gates that can be of either single or multi qubit type now thats in not a necessary requirement
because there can be qubits which could only work on
say the single or a few qubit operations and yet in terms of gates and yet get to useful
computation generally for a general purpose computer however may be this requirement is
also useful in terms of logic gates most of the time in implementations we have started
discussing from atomic states in terms of qubits and so a natural question often may
arise is to why atomic qubits mostly because of the fact that they have the unparalleled
persistence of quantum super position that is one of the best situation for atomic qubits
mainly in terms of iron traps and isolated atoms they can act like atomic clocks which
have absolute accuracy and precision so the technology exists in terms of using atoms
in this form so also possible to have control over the quantum states both internal and
external in the case of atomic qubits for example bose einstein condensate fermi degeneracy
which is controllable mott insulator transition quantum squeezing quantum state engineering
and so on and so forth so there are several control points in case of atomic qubits the
atomic ions have been demonstrated for building blocks of scalable quantum computer and that
is one of the cases where ion traps have remained very useful in terms of quantum computing
and we have also shown that very recently even commercial ventures are starting on the
ion trap principle
ion traps are basically trapped ions which are placed in controllable conditions by the
trap itself if we generated through electromagnetic interactions which is possible through the
magnetic and electric fields that are provided to such trapped ions either through the laser
or through the field providing gradients that are possible through the electrodes and as
far as detection is concerned light can be used to have some interaction with the trapped
ions which can be then looked at through a photo detector in terms of trapped ion quantum
computing a collection or a string of tat a collection or a string of trapped atomic
ions are used as qubits which could be the internal atomic levels of the system or it
could be the relative condition of these ions so for example in this particular case we
have all the trapped ions having the same nature so ground and excited they have the
same condition now the preservance of this condition is the quantum memory of the system
the time it takes for this system to change from its original state would be its decoherence
which is in relation of each of them being in ground state if some of them flip then
that is the decoherence time and therefore its important that the decoherence time be
larger than the application of the gate as the gate itself is doing trying to do some
operation of this kind
for many cases it is known that these are long times in terms of decoherence t two for
instance is ten minutes in in a situation like this where the relative states are all
the same so this is a very good system in that sense and as we know has been used in
clocks with accuracy and stability of a very large number so once we apply the field which
is the one which would be used for gate processing others the system can be made to go from the
ground to the excise state from the zero it straight to the first excise state and the
other option is to use them in terms of data bus or which is the common mode motion condition
which can be achieved through transitory activities once again here the decoherence has to be
greater than the gate operation mode and so here for instance this particular set would
be your ground state where as the other one where the ions are being squeezed to come
closer would be your excised state and this have a time scale of ten to the power minus
two to ten to the minus three seconds which is not as great as the other case of changing
the nature of the ground or the excise state is the relative closeness of different ions
which are being played with in this case so this is a transitory operation in that sense
both of them are useful for doing quantum computing with ion traps
so here is a basic operation principle which have been earlier shown to you in one of the
earlier lectures a quantum logic gate between two different ions for instance has been shown
and i take this opportunity to revisit that part because thats a very interesting point
in this particular case the qubits are being prepared using single qubit gates so in this
case the qubits would be prepared by using single qubit gates by the use of
a laser where the laser would be used to map the qubit i state to motion with laser so
for example this is the case where this state was put to motion and so their relative conditions
change between the first case to the case where
the laser selective to the ith state was applied so once more first a laser is provided to
prepare the qubit in the single qubit gate condition next the qubit ith state is set
to motion with the laser the j state remains the same and now that has happened we now
have this condition and then the two qubit gate between the motion and i and j is being
possible to be generated so we can put the information from motion back into i and i
by using the laser so that was the set of operation where the basic principle case is
often used in terms of ion traps where the utility of having several ions being together
can be said to use both in terms of their energy states as well as their relative position
and their addressability with the lasers with relative to each other thats the advantage
which is used now the difficulty in terms of scaling up as the number of ions keep on
increasing is that the iron strings get heavier and the gates gets lower and the more motional
modes essentially also lead to greater noise and therefore it becomes harder and harder
to do it one of the advantages is to apply optical multiplexing between different states
by using optical fibers and detectors and lasers being operated simultaneously in this
form and this is one of the ideas which have been utilized where the cavity modes of different
states have been excited so that they can be also additionally used and laser raman
stimulated emission and all these other characteristics by use of laser have also been applied for
making this go further
details of this have been discussed in the earlier weeks lectures where we dealt with
ion trap quantum computing the major part of the effort in that direction in terms of
using single atoms per say for doing quantum computing are related in this fashion we know
that there are different parts where the principle works and can be scaled some of them the do
a better job in terms of scaling versus the others so in terms of ion traps and atoms
in optical lattices as well as cavity q e d it is essentially the individual atoms and
photons which are in action in terms of doing that quantum computing so its either the cavity
modes of the q e d which is as represented in this form or the atoms in optical lattices
has been shown here or the ion traps as we just showed with their relative positioning
or their energies which have being conditioned in terms of individual atoms and photons in
this particular idea of using this individual atoms and photons for quantum computing so
this works there are difficulties but they can be made to work and the advantage here
is the sensitivity as well as the coherences is very less and so it can help in terms of
executing the operations the other principles that we have used throughout this course have
been in terms of using superconducting materials or superconductors per say and there we have
discussed about cooper pair boxes which are basically charged qubits as well as r f squids
which change their property
based on the applied radio frequency fields and they are and they act as flux qubits so
they have also shown promise and have been used in fact certain types of applications
of the superconducting qubits have been shown to be of much use in the d wave computer also
they use some parts of this technology to build their
commercial quantum computer semiconductors or quantum dots are the other
kinds of qubit structures that we have also discussed in this course in terms of using
for quantum computers and they have their advantages although the lifetimes and others
associated issues we have discussed can be difficulty as well as addressability sometimes
can become very difficult the other condensed matter aspects or applications which have
come to quantum computing are the electrons floating on liquid helium or single phosphorous
atoms in silicon this is one of the areas where defect atoms have been utilized for
quantum computing
and their properties have been manipulated and shown to be useful in terms of quantum
computing so there are various aspects related to single atoms and photons which have been
put to use when we use these kinds of approaches towards quantum computing one of the biggest
issues in almost all of them has been the idea of noise and the concept of decoherence
where the relative phase of the system is going to interact with environment so that
the system can no longer keep its information intact so in other words the question which
we always ask is what happens to a qubit when it interacts with an environment in terms
of a quantum computer as long as its isolated it has the quantum property and his information
however if this information is lost due to decoherence as the environment essentially
removes its quantum nature and sort of brings it back to an interaction condition where
it loses the particular characteristic
so this is a very important issue and this has had always been addressed in various different
cases in different ways now there are two types of decoherence which is typically talked
about one is the t one process which is longitudinal relaxation energy is lost to environment through
the potential interaction the other one is the t two process or the transverse relaxation
where the system becomes entangled with the environment and instead of having the entire
information in the particular quantum state of interest it is distributed over the entire
system and so in essence the information is no longer easily perceivable so in order to
look at this its important to see how decoherence effects its one thing to just say that its
a loss of information but its also important to know what are the exact consequences so
here are the effects of environment on quantum memory the one which is more known as the
longitudinal or the t one effect has a straightforward exponential decay in its behavior whereas
the t two or the transverse relaxation procedure has an oscillatory kind
of a behavior and overall the fidelity of the stored information essentially decays
with time however in the transverse relaxation case the decay is oscillatory in nature and
there is a coupling and thats why it is considered to be an entangled with the system and the
decay is in oscillatory fashion
so the effect of environment on quantum algorithms can be seen in terms of this kind of a modeling
where in case of an ideal oracle to measures the results as the number of qubits increases
the decoherence increases and this is an example case for the grovers algorithm where the success
rates for the number of qubits keeps up going down in this particular format as we show
here as the oracle gets more and more noisy it becomes difficult to look at it in some
sense the errors accumulate lowering the success rate of the algorithm and that is one of the
reasons why environment has a large effect on quantum computing so a lot of effort goes
in suppressing decoherence one of the approaches is to remove or reduce the effect of the environment
or the coupling potential between the quantum and the environment and this can be done by
reducing the coupling or potential that is can build a better computer the system is
to be isolated for the environment and that is whereas one of the greatest strengths which
the d wave quantum computing has shown in isolating their system so well from the environment
and making sure that it works much better way as compared to the others
you can also increase the applied field so that the splitting our cross the levels increase
and so the decoherence is also lesser and in terms of magnetic field applied spins and
other cases this is how it can made to work other option is also often use is to use decoherence
of free subspace and finally we can use pulse sequences to remove decoherence and this is
one of the cases that we will discuss later on in in a case where we have shown how pulse
sequences can be used to remove decoherence from such systems there are lots of applications
of making sure that the decoherence is not going to affect the quantum computing and
as far as quantum computing is concerned the factorization as we have talked about is a
major factor and that can be utilized from building quantum encryption as the current
approach of r s a encryption may fail because factoring at exponential speeds can compromise
the way computing or the encryption works for the classical sense quantum simulation
is also another very important area where quantum computing once the decoherence properties
and other things are removed can be very useful there can be spin off technology as we have
discussed earlier in terms of spintronics quantum cryptography and others which have
been put through for developments they can also be spin off theory for example of the
theory of development of density matrices and n represent ability of theories and so
a lot of applications in terms of the quantum computer becomes applicable once the decoherence
aspects of the problem can be looked at so with this background we will be looking at
some more aspects of computing quantum computing which wherein we address the decoherence principles
so that they can become more practicable as we have done in this course but some of them
will be highlighted in the upcoming lecture thank you