this week we are continuing with the understanding of implementation of aspects and we had into
the third major implementation aspect that we are looking at we introduced you to
the ion trap scheme which has been one of the very important and successful approaches
of quantum computing and so in terms of the approaches that we have discussed before
this the major aspects were in terms of n m r then we came and talked about optical
schemes and then we also mentioned that optical schemes had been utilized in conjunction with
many other approaches so we went up to a certain level and then left it and then we entered
one of the major advantages or applications of quantum computing that implementation
has been which is the ion trap case and in this particular ion trap case the advantages
has been that it represents the simplest form of cubit representation which is the atom
itself to start with or its corollary which is the ion that we are looking at so we discuss
how typically this has been utilized in many different ways in this lecture now on
we basically look into the various different aspects of ion trap which have been utilized
and how it stands in at present times in terms of its implementation and as well as its
advantages into the future so with this let us look at into our ion
trap issue so we basically know that the trapped ions are generated inside a setup
where we have these r f being applied with oscillatory fields so that the trapping condition
is achieved and we are able to put multiple ions in relation to each other so that their
independs states which basically represents the internal property of the system as
well as the proximity so basically there were two different aspects that we looked at one
is the principle of the individual internal state of the ion that we are talking about
and secondly is the relative position of a bunch up ions that we are looking at so that
is how we have been discussing this issue of the ion trap and how it has been taken
advantage of so in some sense its say the state of the ion that we are looking at thats
internal state whether its in the ground state or excited state then the second one is the
polarisation where you often that is also some times which are used polarisation of
the ion state and the third one which is often used is the position or the relative motion
of that so translational so it is sort of related to the momentum so or energy in
that sense also so basically many a times these two are coupled in order to get advantage
of multiple quantum bits been encoded at the same ion ionic conditions so this is how
the gates and the ions in the ion trap have been utilized and roughly speaking we showed
how the addressability of these ions can be achieved by using lasers which can then
be modulated to be off and on and that additional to the condition of the ion which is being
placed with respect to its property as well as its relative position can all be put together
into use when we look at the implementation of quantum information or other aspects of
quantum into the ion trap condition so with that diagram now we also discussed
some of the major candidates for these ion states and they are mostly candidates like
calciums strontium barium mercury each of them simply ion also we have one electron
available in the outer mode state which could be then utilized as available entity which
could also be used and so these are states which have long lived and so thats why we
have the advantage of keeping them for a very long period of time we also looked at it
that under conditions where we keep it at we can actually isolate it to a very good
extend then the life times can be extremely long and so that has an advantage many
of these operations so one of the principles which adva/advantage] advantage have an advantage
in this and trap case the longly electronic states that we are looking at also there are
many of them which have auto find ground state levels which are very very long lived and
thats another place were the addressability of these states have been achieved by using
say r f or megahertz or gigahertz pulses which can radiation which can then address these
states and these states are say stable to for example in this case or some of
these ions that we show in the range of over ten thousand years in times of the stability
of the state that you are going to create with respect to the starting states so
thats the long lividness of these states are extremely advantageous when we are looking
at the implementation aspects in terms of quantum processing as we are been discussing
so one of the examples which were utilized and used was the c not gate for example on
berylliums ion in the ion trap and this was one of the example where after the control
not what happened before the control not gate apply application what happened and we are
coming to this in a minute so this sort of like shows that these traps have been utilized
so the other property which we we were discussing at the very beginning is the mode
of the ion oscillation so there can be the lower energy phonon mode which is due to the
relative positioning of these ions with respect to each other when they are further
apart then its the lower energy phonon mode when they are closer to each other then it
becomes a higher energy phonon mode and so thats how you can get the these these other
couple states which can then which can become a two qubit condition instead of the single
qubit which is due to the internal energy state of the ion per say so the interaction
which is between the ions which is the phononic interaction for instance in this
case due to their motion and oscillation is one kind of mode and that can be addressed
in addition to the internal state of the system so so for example here is the energy level
of a single ion spin phonon so here we are talking about spin as well as the phonon coupling
conditions and the phonon (Refer Time: 08 :00) the spin of the ion is thereby connected
to the phonon state because of the oscillation which are due to relative motion verses the
spin condition of individual ions which can be kept at one kind with the others and
that can be addressed and that can be utilized and this is a case were the couplings which
are there as result of this can be utilized to do a f control face let in this kind of
way two qubit operation so many different operation of these kinds
are possible and this is very simple in terms of operation because this mimics the classic
case of the theory that we were discussing at the very beginning of this course where
we were its in some sense is the text book criteria definition of many of these gates
implications on single cubits and two cubits which we were initially introduced in this
particular aspects of using ion traps help gets it so close to that and therefore
ion traps were one of the natural early sources and advantageous it have been happening
with this case and most of the time the read out is done by shining the light of an appropriate
frequency where the ion fluoresce so many cases the read out is essentially done by
shining a light over an appropriate frequency that reads out the property of the system
by making the ion to fluoresce according to whether the electron is in the lower state
or in lowest energy state or not the c not gate applications for instance required about
fifty microseconds to perform and the coherence time as we were discussing can be
twenty times as long and so these kinds of a systems are very effective in terms of
an application of the gates because the times scale are not much of a problem
so here is an example case of the implementation of the deustsch josza algorithm using trapped
ions and which shows the suitability of ion traps in quantum information processing relatively
simple algorithm and it uses in this particular case using only one trapped ion the two problems
which are looked at is essentially the more common d j algorithm or the deutsch josza
problem where the individual concerned is going to use constant of balance function
and the other individual is supposed to determine which kind the individual has used and so
basically its the job of the reader to be able to find out what the function is being
used by the person concerned the other problem is to use the quantas problems where deustsch
problem where quantas is whether it is fair or a forged coin is been utilized has to be
determined by the user so there are therefore four different types
of coins that we are looking at it here essentially we have these are we have these
as define earlier in terms of d j algorithm and deustsch algorithm that we are essentially
looking for constant functions verses balance functions and there are two cases for each
of these which makes this different types of coins we are talking about and what
we have is in one case we are using the third line is essentially finding out the addition
module two of the two which we are looking at we are applying the application of these
individual functions and then we are looking at the result accordingly so the implementation
aspects therefore is essentially solving this particular diagram in which we have the
input so these are a and w which we are inputting and accordingly we are looking at
their different aspects as we go around and before we finally make the measure and there
are these unitary transform case that is being applied which does the addition module and
that is what is been used so the hadamard gates are the ones which are
originally being utilized to get to the initial condition which is then which then is
going to have the unitary being applied to it to create the addition module which would
be of these different kind as we look at it and so we basically can do both this algorithms
in with the help of just a single ion in this case because we can have the different
modes of the ion coupled to each other and get this done so here is a example which
has been taken in case of the calcium ion inside the linear trap where the states
of the motional degrees of freedom are being relabelled as the states of the set
so this motional degree is essentially the the condition of the ion within the
trap so roughly this is the one which is like this simple harmonic oscillator condition
of this ion trap are trapped ion whereas the so that is the one which is to be set up in
terms of the degrees of freedom and the doppler side band cooling is way where which creates
the which prepares the ground state typically whenever a laser inter acts with this kinds
of a trapped ion and the depending on whether the leading edge is doing the job or the trailing
edge does the job which is what is meant by the dopplers side band but the leading
edge creates heating whereas the trailing edge essentially does the cooling and thats
how the ion is is cooled so the idea is to make this motion minimally minimal
as it get cooled and this is due to the interaction where the momentum of the particle
of the ion is getting decelerated because of this interaction with the applied this
of it so the two cubits which are involved in
this case as i mentioned is the two level atom in itself which is the well in
this particular cases the [at/atoms] atoms slash ion is we are looking at calcium ion
with one electron in the exited outer mode shell so is the in in some sense is two level
system with the lowest possible excitation they lowest energy outside the core shell
is just going to have electron which is then corresponds to the ground state and then the
next level up is the excite state so in spectroscopic terms symbols we have the s state and the
d state which we are looking at this particular case for the calcium ion and it is then getting
coupled to the harmonic motion of the trap as we just discussed which is the one where
we have these two states being coupled so the electronic quantum state of the ion as
well as the phonon number of the axial vibrational mode are the ones which gets coupled because
of these particular principle and they can they are the ones which are being put
together as our cubit system which can be swapped these states which we generate as
result of this coupled states can be swapped by their help of a pulse sequence as i was
discussing and there this is the reason of the use of a laser or r f it depends
on which particular condition we are talking about mostly its the laser which is used for
the traceability which is what is going to address these joint energy levels and make
them make these states be swapped as a result of the interaction with the laser parts
the manipulation of the trapped ion therefore results in reasons so we have these resonant
pulses which perform the single qubic rotations whereas the detuned pulses perform the
two qubic rotations the the thus the so we have this detuned pulses which we do the
two qubic rotations because the detuned pulses will essentially have the doppler effect of
sort of cooling the system or heating up the system so that create a situation of having
the two qubits where as the resonant pulses are going to either take it from one particular
s level to the other particular sorry one particular spin condition to the other particular
coupled spin conditions the this manipulation is therefore achievable by by sequence of
pulses which is what is utilized for getting the states the main sources of barrier in
these kinds of experiments have been the that the phases introduced by light shifts
of the lasers may not be appropriate and the system may leave leave the computational subspace
because if the trapping fails for some reason or the other then for a particular
ion let say then it would leave the computational subspace so these are the two cases but in
most cases these are pretty controllable so once in a while these are the error
sources that can come so typically this is how the time evolution kind of shows up
in one of the typical experiments which where it was first depicted years ago and that was
shown that these different qubits that have been prepared by these conditions for
these particular case of the calcium ion can be spin in the vibrational mode which
have been excited and looked at as a part of this so basically the d five by two
states is being looked at by this particular technique
now when as we discuss in the last case its only a single qubits system i mean single
ion system which has been subjected in effect which has been subjected to a coupling of
two different parameters or two quantum conditions under the [state/statements] statements under
the conditions that we are doing experiments if we want to have lot more ions being
put together in this kind of symatic scaling up has a many different issues to worry about
and as the number of ions go up the ions string gets heavier the gates get slower because
now we are i am talking about phonon interactions of the large mass and so the interactions
become slower and therefore the effectiveness of the gates which are going to do these
changes will become slower and there are much more motional modes to be to be taken
care of which means that there is a greater noise condition and so thats basically saying
that we have difficulty in cooling the system because we have lot more states which are
already getting rise to as a result of the size of the system
so optical multiplexing always helps in these cases so for example here is an example
were if the system put in such an arrive at these independent trapped system can be individually
addressed by using fibre optically coupled lasers so then they will have better capability
in terms of addressing them so that is one option option the other aspect which has
been also looked at is to use the cavity mode of the system so this is more to do with
the cavity coupling of the system with the ions that we are now talking about and these
can be connected by using cavity modes and the qubits now we haven't really studied
much about the cavity q d aspects also thats another way of looking at quantum computing
so once we again revisit the cavity q d kind of problem we will perhaps have a space
where we can see how the cav[ity] coupled condition of the ion trap with the cavity
modes can also be effective in terms of producing or enhancing or scaling up the problem so
everywhere what we are essentially coming to understand is that is not just one particular
way of looking at the problem that we are interested in whatever more ways we can couple
the system and have more different approaches that we have used if we can couple them then
they are going to gives us better answers and therefore we have often utilized the
principle of the already existing optical approaches let say in addition to the ion
trap and similarly we have been using the other approaches of teleportation adaption
which are often available very affectability in the optical approaches into these different
modes so here is a some work which have been done
very effect[tively] heavily by these groups in fact the both einstein group which
receive the noble prize in does a lot of work in this particular trapped atomic and ionic
qubit system they in fact were one of the first to demonstrate many of the events that
we have also discussed here there is there is a university of group and university of
merryland and so there are many groups around the world which are looking at it and this
particular work were ytterbium ions seven of them were coupled together and utilized
is is a very important aspect of trapped trapped condition and so here is a experimental setup
condition which was utilized while this particular [exp/ experimental] experimental approach
was done so these are the seven qubits and they are separated by about two micro metres
from themselves so this in this case for example this ytterbium qubit can be
this photons can be collected in about hundred micro seconds every time they are in one
particular state or the other is hyperfine ground state for example of these particular
state particular ion can have an excited electronic state which which can then flurries
back and so this is a bright state coupling so we have these two different spin conditions
which are then being satisfied so the spin conditions are provided by the hyperfine ground
states which y i excitation to the electronic excite state it can be can be made to go
one way verses the other so thats one approach of showing how the ytterbium qubit works
the other thing is that when once the once the higher [hype/ hyperfine] hyperfine
state is is populated then then that is not coupled to any of the excite state
so that is sort of known as the dark state because in the previous case where we looked
at the bright state there was a coupling so the light could essentially the excitation
would essentially bring back the light and the that coupling could be seen whereas
is in this particular dark state there are no photons to be collected as a result of
that so most of the probability is the fact that there is a no d coupling or like de
coherence or like there is no state which is going to result because this is not a coupled
state so excitation whenever only if this particular spins state is populated then its
the bright state where as the excited the other rotational state is populated then
its the dark state so this corresponds to the dark state and this corresponds to the
bright state so so these hyperfine ground states are the ones
which are sort of utilized for getting into these states which have been put together
in terms of the mapping which are shown here so so for example a combination of these
a states from one particular spin hyperfine spin condition which is of lower energy is
being utilized with and utilized with respect to the [elec/electronic] electronic excite
states to produce a coupling between these two different states and these can be mapped
by using this kind of approaches as has been shown in this particular diagram
and if you want to learn more about it you may want to look up the original paper by
pregan solar in ninety ninety five where they have discussed this entire process in detail
for this particular class we are not going to go into these kinds of details because
that take a lot more effort then what we are actually trying to show in terms of implementation
aspect here we would like to actually just suffice to point out that the laser beam is
essentially looking at by a motional condition of the trapped ion in the in the system
which is then being excited by the laser at different positions and by looking at these
lasers interactions we are able to do the interactions which are going to make them
the internal states of the ions entangled in one way or the other
so this is basically the principle as to how the experiments work once we except the
fact that the the states are going to be coupled by using the laser which is going
to bring them come closer so the so here for example the coupling between these states
which i just showed with the laser again which i will again show you is is possible due to
these states getting coupled and thats the exact thing which is been shown in this cartoon
where initial a laser essentially put some of the this study here and then there is other
coupling which is done by the other state and finally the third one puts it on together
such that the internal states of these ions gets entangled these is an similar to the
to the initial initial i j states of of the ions that i had shown in the
last lecture where to at the very beginning i was discussing as to how the ions of
of a particular set can be coupled in these kinds of scenario so this is actually a practical
application of that initial opening few slides where i had shown how to address
different ion sets and then have them coupled so ion traps have gone from being just
very complicated objects being under vacuum and other kind of difficult conditions to
to states which can be addressed in terms of chips which one put under appropriate
conditions and they can be again addressed and brought back to the similar conditions
so here are some ion trap chips we have been shown these are the studies from different
groups where they have essentially put together how how they have done the this entire
process in solid states conditions where these channels and these were conditions were
these injection points are the ones where the these trapped ions are been placed and
they are traverse and they are addressed and that is typically how these different systems
are and as you can see that they are very small and miniaturised hundred micron gaps
in one direction in this whole device is about in this case for example in sandier is about
two point two millimetres in lucent also you can see these are these are all the
technologies that they have developed over the years and they are very well addressed
can be utilized in many different cases currently the ion trap quantum computer that we are
looking at are up to about ten ions that we are managed to see in our particular presentation
here in this class we have shown experimental set ups with about seven ions in place
however for actual useful applications say for example factorization of a two hundred
digit number there would be requirement of about three thousand five hundred qubit
and if you would like to implement that with error correction there should be about hundred
thousand qubit so it it requires a lot more scaling up then
where the current condition is for the ion trap case although it has been excellent
start up point for demonstrating some of the very classic of the text book style concept
principles for quantum computing it needs to be scaled up and so there have been
lot of applications as a or at attempt so one of the cases in terms of scaling up for
example these are solutions that we found in many of the literature cases it has been
related to coupling for example to optical schemes which has been attempted by maths
plunk gaussian where they use the calcium as we discussed in this particular case
the case of the maths plunk institute quantum optics or gussian they used as calcium ion
as one of the ion trapped condition and they were able to address the calcium ions but
using the optical light sources and that was one where the resolution was limited by how
far or how far away these ions could be put together and so the resolution there is about
lambda over ten which is quite a good resolution the unisberg for example with the same ion
and has been addressing this by using laser detuning and so that they have been utilizing
the cooling principle and that particular one has resulted in over lambda over hundred
resolution so the the resolution is much better when it has been utilized in terms
of the doppler shift condition because thats the one which is using the advantage of cooling
the system so and it is essentially is looking at differential coupling to the motional side
bands of these kinds of motion so in terms of scaling up we mentioned before
it it would be perhaps be interesting to see a c c d couple coupled device for
instance where the charged coupled device kind of a condition were these segmented electrodes
which are necessary for manipulating and motion of these ions are are being put together
in such a ways so that they sort of look like a coupled condition and in these kinds
of charged couple conditions which is the which is the work of this particular groups
where they claim that they could essentially use the idea of a c c d to making in to
a quantum c c c c d by using the segmented electrodes to bring the ion trapped trapped
ions into these condition where they would be creating the accumulator and they would
be keeping the rest of the ions waiting for action as memory once you have encoded
them and kept them the this particular works for ion traps because as we have discussed
ions traps have very long coherence times that they can be kept as and their interactions
and their times scales that we have been discussing of the d case are very very long and so this
particular approach of design condition where we are setting up states like this
and their being cooled or interacted by using lasers or r f or other ways of addressing
them are been done in this accumulator or these other places where they can be made
to work with and so this is a design condition which can be provided which has been provided
by this groups and if you are interested you can look more into these papers to realize
or understand a little bit more on this area the other interesting way of scaling up
the problem has also been using physical multiplexing aspects where the the ions have been transported
between traps so that they can have a larger number of traps which can be put together
and trapped ions which can be put together and they can then be subjected to subjected
to the different r f or laser conditions to achieve the kind of information processing
that would be liking to do that or put in information and manipulating them in terms
of data registers so that is another approach which has been used where there are two different
cases one is to by using into formatic approach and the other is by separating the
ions by using r f electrodes so in either case generally the n result is the fact that
you are applying lasers to kind of c how they are going to interact and they can be made
to work if the separation is made too large for example here separating electrodes has
been made too wide then it will not be possible to get the results effectively and so
these are the kinds of work which have gone into these kinds of experiments to show what
is the good condition what is the bad condition so in in case of informatrix cases it has
been shown with say like about ninety six point six percent of success to how this course
or like transport verses spin ago is one of the conditions which are used for seeing
that the d codence is minimized and that is with ninety six percent contrast ratio
means that the coherence is maintained in terms of the transform and so it is important
to realize that these are the processes that have been utilized over these years to see
if this concept of multiplexing the ion traps and their conditions can be improved
so this is sort of look like how it looks like when you are looking at these physical
multiplexing objects they can be utilized in gold traps silicon traps and solid states
devices alumina silicon and alloy and this is how they have been made to go forward
they have been also efforts in making single electron quantum dots which can act like these
these devices where the traps into a trapped condition and this is the work which has been
done by a group in duke university in order to say that they can actually generate
single electron quantum dot conditions and that can also work almost as a these kinds
of ion traps trapped and conditions but this is again one of the other cases where
different object is being mimicked to be applying to these kinds of applications of
quantum information processing and coupling of the different concept so but it is it
is important to point out the different aspects of applications have been put together
to make the progress more work has happened in terms of utilizing
the say host atom in different kind of lattice and where the the host atom is essentially
acts like an ion which is sought of trapped under these conditions so these are like solid
states conditions where these are achieved the qubit is then stored in say for example
in this case the phosphorus spin nuclear spin inside the silicon lattice so this is sort
of like the condense face version of the of the ion trapped where we were still individually
addressing these ions or the atoms that we are talking about but in a different format
and they can then be addressed by using different electrodes which are then be put
together (Refer Slide: 39:00) to be placed in different ways so voltages and registers
so these are different ways of addressing these particular variance of a the very original
idea of using ion traps but its not exactly the same way that we have been starting on
the idea of ion trap so there have also been concepts which arise from this very basic
principle of ion traps to go into super connecting currents were the quantise flux qubits
states of super conducting states have been utilized and once again its again a deviation
from this in principle but again its utilizing the atomic modes and atomic conditions and
therefore it is somehow related to how these quantum information processing started
of a ion traps all of these have been summarised in one of these reviews which came out some
years back in nature where they were discussing about how the qubits at that point of time
have been looked at its catching the bus catching the quantum bus kind of an idea where they
were able to transport and talk about charged qubit states quantised charged qubits state
based on these principles and since they all have ionic behaviour so so they sought
out are connected to the original concept of the ion traps however let me also point
out that this is not exactly the way how the original ion trap principles evolved as
i have essentially showed in the beginning of the in the rest of the presentations
here another useful solid stating implementation
of this area has been the principle of utilizing doped impurities in glass for instance
this is the this is been looking at a glass which is a which has been doped with impurities
which are florescent and these florescence of these arise of single impurities in diamond
in the glasses structure has been utilized for this kind of cases where the nitrogen
plus vacancy impurity in diamond is the one which has been put forward as another idea
of utilizing most of these invoke the principle of ion traps and or address it to sort of
out explain the way how they are going forward about it but generally speaking and the original
idea of ion trap is the one which essentially uses a very high very different conditions
and sought of the principle of cold atoms and things like that which brings us to the
principle of the original ion traps so if we look at it this context various
aspects related to ion traps in quantum computing this is what we have in principle where the
where the idea of the individual atoms and photons doing the job is where we have
concentrated and discussed over the last few weeks where we have shown that the ion traps
the attempts and optical fields we have not quite discussed the cavity q d part but
we have eluded to here and there where its it essentially shows that this can
be worked on and they can be also looked at in in the present context in terms of these
lattice structures either because the ions are getting trapped or presented in
this kind of a fashion where each of them are addressable in this form or in the
solid state form where they have been put together in one place of the other and they
have been entrusted in this particular ways and there have been other difficult principles
which we have not yet addressed but we showed some indications where these principles
have been extended to and we are with the claim is that they separately they seem to
scale better then these working condition cases we also looked at another working
case which is the n m r case in this case and n m r and photons by themselves so
we will put them under the working conditions whereas these others scaling condition ones
are the ones which are being proposed and looked at more in recent years because they
are seemed to stem towards a direction where they would perhaps scale better and so in
the next few weeks that we have left we will perhaps go a little bit more into these
newer concepts of the work that has been going on in terms of implementation of quantum
computing we might actually spend little bit time later just to give you one of the other
historic principles which has shown that quantum of computing work in terms of cavity q d but
generally we will spending more time on principles where scalability issue seem to
have been of some sort which we are going to address in the future courses future part
of the discussions before i close in this in this particular
week i would like to point out that although presently the picture of quantum
computer and information processing and the way how things have been are looking not quite
as what we aspect and it also looks to be a something of the extreme future this
is a cutting from news paper which came out in exactly when the first computer in any
eniac turned fifty at so february twelve ninety ninety six was the day in was when this
news paper came out because a fifty years before on the same day the eniac was
was first put to action and although the the electronics people said that there were too
many vacume tubes and it would never run the mathematics people said there were no problems
complex enough that the computers were needed that was the thing at that time where the
eniac team had to work work on to get it to work and this one fully of operational
was filled by if thirty by fifty foot room in terms of the scale as to how this look
like and the current day power of this particular machine is worst than a present calculator
that you have in your hand and yet this was the beginning of the concept of the computer
that as we know today and so if in fifty years computers have gone through a huge revolution
as to what we know today there is a lot of hope still that these different implementation
principles although they have far from being what we expect or want them to be would in
the future someday become one of the major horsepower of computing perhaps which as we
are discussing is quantum computing with that thank you very much and see you next week