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