Experimental Studies on a Single Microtubule (Google Workshop on Quantum Biology)

>>
I'd like to welcome Anirban Bandyopadhyay from the National Institute for Material Science
in Tsukuba, Japan. Thank you very much. >> BANDYOPADHYAY: Thank you very much. First
of all, I would like to thank Hartmut Neven for organizing this and also Stewart for taking
this, all the hard work, and making this a possibility. And I will talk about remarkable
electronic properties of a microtubule. So here is the outline of my talk, so I will
talk about Fröhlich condensation and the microtubule, most of which has already been
said by Professor Porconi. And then I will talk about coherent transport in microtubule
and temperature independent conductivity of microtubule; then detection of topological
qubit in microtubule; then ferroelectric property of microtubule, this prediction was done by
Jack Tuszynski, and then dynamic instability; and finally, I will conclude. So microtubule
basically is a polymer made by proteins and it has three concentric layer of cylinders,
so one on top of another. And the inner core is water channel and on top of it, we have
tubulin dimers rolling around. And then on extreme outer surface is our nucleus. So if
we just think of microtubule as a physicist who wants to think of energy terms, so you're
alternating signal frequency, for the same true of microtubule, what will happen? So
we have to basically divide the microtubule into three functional parts. The outer layer
is ionic part, so basically kilohertz range signal makes a resonance with the outer surface.
Then we have the dipolar protein part which is--which responds merely in the megahertz
frequency range. And the water signal, the water channel inside, it's the hydrogen-oxygen
bonds that vibrate so we expect a resonance in the gigahertz frequency range. So this
makes microtubule unique. Unique in the sense that if we send, say, its particular band
of signal ranging from kilohertz to gigahertz range, when it enters into the microtubule;
first, it will find the ionic chains; then it will be absorbed. Some of them will be
left. Then to hit to a kilohertz signal, it will not be able to see the proteins or the
waters. The megahertz signal will see the proteins and the gigahertz signal will see
the waters, so it will be filtered out. And the interesting thing of a microtubule is
that all, everything, all of it is crystals. So it has three distinct symmetries one top
of another. So those who are interested in information processing, though you know that
symmetry has very close relation with the information content and information path.
So that means whenever there is a symmetry condition, you are going to have some information
exchange and other processes. So these are some of the points which I will ignore in
the--in today's talk. I will concentrate only on the protein parts. So
okay, let me go forward. So the question that we asked for our research two years back was
to understand how molecule is born spontaneously in the cell and how it survive and then disappear.
So we have 50 trillion cells in our body, and if microtubule is responsible for the
information processing, that means somehow microtubule is processing information and
is able to coherently link up the entire body that we have. So how is it being possible?
I mean, if continuous change of length of microtubule, does it have anything to do with
the information processing? And if it has, how exactly can we define the information
in it and how exactly we can prove it, how exactly we can tell that, "Okay, look if,
you give me, say, 10 micrometer long microtubule, okay, this is the information content, these
are the informations, these are the things it is doing." So we want to define it in the
exact terms. So, if we know about Fröhlich's theorem in 1968, some of which has already
been told by Professor Proconi, but I would like to tell once again. The debate was about
how first life came into being on Earth. I mean, was it just a chemical reaction or some
energy was available and constrained dipoles took that suitable energy and formed a structure
or architecture automatically? So the theory that was prevalent was something like, along
with the chemical energy there was also electromagnetic energy involved in it which took energy from
the environment, right energy, right electromagnetic energies from some source, and it formed us
from molecular architecture that was the first form of life. So this proposal went on and
this proposal says something like that we need a heat bath and we need a constrained
dipole electric--field constrained dipoles and we need electromagnetic energy. So we--and
there is--there was no experimental--direct experimental evidence of this Fröhlich condensation
process until now. And there are some papers in 2009 by J. R. Reimers who has discussed
well in details how to realize this Fröhlich condensation in practice, how to do the experiment.
So we did this experiment in reality and we have successfully realized the Fröhlich condensation
process. None of my videos are running. Can we do something about it?
>> Do you have some separate stuff there? Open it in separate files, you could just
execute... >> There you are.
>> BANDYOPADHYAY: Okay. Okay, so this is the heat bath and we have electrodes. These are
positive and negative arrays, red and blue-colored. And we supply the AC signal into it and microtubule
grows spontaneously within three to four seconds only, not 30, 40 or 60 minutes. So you have
four seconds and we have plotted average length with frequency and you will find that if we
go on increasing the frequency from, say, 10 hertz to 50 megahertz, we will find that
the maximum, the highest long--length of microtubule that we get is around 23.5 micrometer. That
is grown within two to three seconds, not 60 minutes. Only two to three seconds. Just,
you apply the AC frequency, connect the wires, done. And you will see the large microtubules,
the giant dipoles predicted by Fröhlich is formed at the bottom of the surface. So this
is the experimental result and some of the FM pictures. And I have not done any filtration
on these images but when I will publish in the papers, they will be made beautiful. So
just raw images, just you see now. And here you can see the--at particular frequency,
the giant dipoles are formed. So the smallest length that we'd be able to see--or even two
seconds if you apply, say, a 500 kilohertz signal, then you can get only 200 nanometers
long within two seconds. And if you apply, let's say, four megahertz signal or five megahertz
signal, you get 23 or 24 micrometer long chains all along the surface within two seconds.
So you can--you can see the selection. Once we realized the Fröhlich condensate--now
we should--we should keep it in mind that it could also be a classical process because
Reimers have challenged Fröhlich other--in different ways. But before I move on, I must
say that Professor Proconi who is sitting here, he was the first person who said that
this kind of condensation could occur also in megahertz range. Because Fröhlich condensation--Fröhlich
himself said it should be in the gigahertz frequency region but he calculated and said
that it's megahertz. So, our experimental results directly relates his proposal. Now,
where to go from Fröhlich condensate? So shall we try to find out the quantum qubit
or try to find out classical bit of information how things are happening? I mean, it is--is
it a Bose-Einstein condensate or where--which direction should we go? So we decided to leave
the--that--the issue of detecting matter wave for this moment and we decided to go towards
bit and topological qubit. Because topological qubit, those who are interested in quantum
computing, those who know that topological qubit is a version of quantum qubit in which
you are more interested in the space rather than simultaneous multiple steps coexisting
together. So instead of this concept, if you just switch a little bit towards space along
with it, then the entire concept changes and it becomes much easier to detect, much easier
to handle and to--and it becomes more practically feasible. That's why for the last 12 to 13
years, topological qubit has been--has been in the forefront and we have tried to see
this. Also, there were some experimental evidences which prompted us to move towards this direction.
So coherent transport in microtubule, we wanted to detect whether the transport along the
microtubule is coherent or not, and this is a very straightforward and easy experiment
to detect. So--and this is a nice image. We have--we can do filtering and you can see
that it is beautifully done. And instead of two probe measurement, so there is a microtubule
chain and the two gold electrodes are there. So two probe measurement are always faulty,
because if you have two probes and you are sending the signal to understand what is the
electronic property of a device or of a material, and on--and using the same two probe you are
reading out of the system, then you are always taking into account the noise of the system,
the context potentials, and all related phenomenon that is associated with the material. So,
always it is preferred that we should go for the four probe system. In the four probe system,
what we do is we save the current from the outer two terminals and read the voltage from
the inner two terminals. Or the signal that we want to change, we send by far apart from
the farthest points, and from the nearest point, we want to read what is going on inside.
So these are defined structures we have created and it is--and we didn't use any chem--external
chemicals and other materials. It was everything--was very pure and we used dry lithography technique
so that there is no flow of ions along the microtubule. And the first experimental evidence
is this. So we made that AC resistance at different frequencies. As you can see that
we go on increasing frequency and near around eight point--around eight, near around nine
in this region, on the resistance of the device of the microtubule falls and it goes around
3 to 48 or 50--50 kilo ohm with a very--a small AC voltage bias. So for the coherent
or ballistic transport, we need around to 25 kilo ohm, or 40 or 50 kilo ohm is sufficient.
So we did another experiment. We measured the current voltage, by two probe and also
the four probe measurement and we found that you can see nearly one volt is applied on
one MPR current we are getting. So nearly one ohm resistance and this is the direct
evidence for that. So it is the evidence too for the coherence transport along the microtubule
at 300 Kelvin. That means it's the room temperature so it is not blasted off. And one point I
would like to, you know, draw your attention, if you look at the central part, you will
find that it's something like heat resistance are embedded so we--we will, later part of
my talk, we will figure out what it is. Now the third evidence is, if some system is coherent,
that means if you change the link, if it is 1 meter or 100 meter or 1 kilometer, there
should be no change in the resistance. That is the fundamental definition of a coherent
system. So we took--here you can see that four length devices we have measured, 800
nanometer to two micrometer, and there is no change in resistance and we go to approximately
10 to the minus four, minus five MPR current, you go to the ballistic region. If you go
a higher current, resistance will go down. Another evidence, the fourth evidence for
coherent transport is that we measure the power loss. If we send a power stream one
side of the microtubule and then we check the other side, then we find that it is nearly
0.5% or something like that. At particular frequency you can--it is around 9.03 or something.
That means, in this region, definitely the microtubule is becoming coherent so there
is no power loss while information transport. Temperature independent conductivity. So before
we get into this temperature independent conductivity, we got--we found that microtubule is independent
of--microtubule conductivity is independent of temperature. That means if you start from
5 Kelvin, you go up to 300 Kelvin, you find conductivity remains constant, absolutely
no change. So first, when we got this, we didn't believe ourselves. We thought that
there is something wrong. We repeated our measurements several times then we handed
over our material to our superconducting material center, Professor Hirata, and he also measured
and he found the same thing, there is no change in conductivity. We thought that we are the
first person who have discovered such a material, but when we went for the literature, we found
it was--first, one Indian saw this in M. Chowdhury in 1981 in some materials in high pressure
condition and then in 1988, there was another observer, and there were at least five reports
before us where conductivity did not temp--change with temperature in the extreme conditions.
But in our case, it is the normal condition, normal room temperature and ambient atmospheric
conditions. In 2004, I found that the coherence theory for when and how coherence can appear
in a room temperature system. It was explained by Kunio Takayanaki and he published this
paper in Science. And he took golden nanowire, which is helical, and he measured and found
that it is coherent. And also, there was a report in 1997 on carbon nanotube, which was
in room temperature coherent but carbon nanotube experiment is a little bit debated because
what did they do? They took mercury liquid and then they put the carbon nanotube from
top and then they measured it. But when later people tried to reproduce their result on
a--keeping the carbon nanotube on the surface and putting two electrodes lithographically
the way we did, then they found that carbon nanotube is not room temperature ballistic.
So that makes microtubule--that our experiment, the second candidate after Dr. Kunio Takayanagi's
gold nanowire which is showing room temperature conductivity. Now the theory says that if
you have a periodic potential-like system, then in the Hamiltonian, you--what happens
is fluxes get quantized and starting conditions if it is there, then you are naturally going
to see coherent transport. And there are several papers since 2004 to 2010 you can find where
you can find coherent transport. So what happens is something like this. So we calculated the
energy level diagram. Please try to see the bending of the orbitals, bending of the energy
levels. This right here. Go back. Because this is important because when we will apply
external thermal fluctuation, then we will see what happens to those. So what happens
basically is this, all point contexts are formed. So it is not like metal, not like
semi-conductor, not like insulator. So, multiple point contact gaps are formed between the
valence band and the conduction bend. And these--and energy, when we supply external
energy, it sews the electrons at the edge of the connection bands and then lifts it
up in the--in a particular frequency or in a particular energy, and that's why the coherent
transport occurs. So if we see varied temperature, we see conductivity like this. So it is not
absolutely constant. It changes quantized manner with temperature and it fluctuates
in a quantized way. So we could encode any resistance by powering it to a particular
conducting state. Why we could include particular conducting state of our choice? That, I will
explain when we will discuss about the ferroelectric property. So, we can include a particular
conducting state and we can vary the temperature, and that conducting state, that conductivity
retains along the sweep. So Professor Kagita in 1997, he first explained theoretically
with some experimental materials how and for what reason this kind of temperature independent
conductivity could be realized in practice. So, if we zoom out, we will find that their
encoded energy level, which are shown with an arrow, this has a pair of levels also just
beside it. So both side, upper and lower value, you have--and their conducting states where
it basically jumps. So it is not a random jump. It is always quantized. So these are
different experimental results. And when we encode very low resistance, say, we can encode
a couple ohms in microtubule, here we encoded 40 kiloohm, so then we find that this resistance
variation goes very lowered, two to three kiloohm. If we encode, say, 10 ohm, it will
be nearly one ohm. That means you'll get almost a straight line. So we tried to find out an
explanation, and then we, what we did in the Hamiltonian, we added another thermal fluctuation
term. And then we found that our energy band diagram changes a little and it forms two
other kind of versions where the point-to-point contact is like the circular point contact
instead of a single point. And the fluctuation occurs from black to red, red to blue, blue
to black continuously and it maintains that particular conducting state. So, microtubule
is neither metal, insulator, or semiconductor. Its density of states is in between metal
and semiconductor and it switches back and forth. And conducting--conduction needs accumulation
by standard calculation, we found that it is 0.23 dG; dG is the 2e squared by H at the
quantum conductance. Then we go for detecting the topological qubit in MT. Initially, what
we did is we tried to find out the ferroelectric conduction modes that is--that was all ready
proposed. But later we thought that, let's try--start from scratch. Let's try to do some
picture. Let's try to play with the--with what could be possible or what could be not--could
not be and then later stage of our research, we will try to find out how much ferroelectric
conduction modes are feasible. So what are the differences between bit, qubit, and the
topological qubit? Bit--in--suppose we have a molecule and then we change the conducting
state of the molecule by reducing it or by changing confirmation of the molecule, then
classically, we can observe it, we can measure its conductivity so it is called bit. When
qubit, then that means the--two or three are multiple states. It can coexist. And at a
particular time, we cannot say that we are surely this. And a topological qubit is also
similar like that but topoligical qubit is associated with their particular space. If
you want to destroy a topological qubit, you have to destroy the space. If you disturb
the space, if you change it by any means, you cannot destroy it. So, topological qubit
was first proposed by Kitaev maybe in 1997 and the topological qubit until now has been
realized only in the superconducting systems in the millikelvin temperatures. And the basic
reason has been that you need quantum liquid and flux of quantum liquid to flow and--if
you want to detect it. Because quantum mechanical states, if you want to detect it, they are
very solitary in nature. If you want to detect it, it will change into something else. But
in topological qubit, there is a good possibility of detection because suppose one space changed
to another space, some energy will be released, and then you can detect it. That's why there
is no direct evidence of detecting qubits very feasible manner. But there are many papers
of detection of topological qubits. In the last 10 years, you can find that topological
qubit has been detected several times. And so, in case of topological qubit, you can
measure the phase slip directly. That means if you have any space, if you have topological
qubit, you send your signal from one side, you measure from other side, you will find
very defined quantized phase change in the signal. If you change the length of the space,
you will find in some length, the distance decreases; in some length, jumps, so all the
benefit should be there. So very nice ways and simple experiments are there as in which
you can verify that topological qubits are there. So here are some simple things.
>> Well, can you clarify what you mean by a topological qubit?
>> BANDYOPADHYAY: Huh? >> Can you clarify what you mean by a topological
qubit? >> BANDYOPADHYAY: Yes. A topological qubit--shall
I explain with the microtubule? >> Yes.
>> BANDYOPADHYAY: The meaning of topological qubit, because I already said a lot, because
now if you will see the picture then I think it will be easier to go on. Also, I'm sorry,
I don't have very simple cartoons, but you can find in Google many simple cartoons what
is topological qubit and how it is done. So, basically, it is associated with the space
to some certain patterns, and it has quantum state, quantum state is similar to the qubit,
but it is a very typical space. And if you change the shape of the space, the fundamental
property of the pattern does not change. So that is the basic difference with the qubit
with the topological qubit. But there are many, many different specifications right
there. So microtubule is a 2D hexagonal close packing structure and eight nanometer is a
dimer. Now we try to form the topological qubit patterns. And if we repeat the first
layer on the 14th, 1, 2, 3, 4, 5, 6, 7, 8, up to 13, 14th, we find that they are the
same so hexagonal packing breaks there, so this is called of type lattice B. And if we
want to start from one side of the blue and reach to the next state, we'll find that six-cell
gap, we get periodicity, that means 48 nanometer pairs, so more than this we cannot create.
Similarly, if we change the hexagonal close packing a little bit, we can get to lattice
A where there is no break in the hexagonal close packing. And then, 26 cells is required
for it to come back to the same point, one periodicity, that is 208 nanometers. So that
means if there is a topological qubit, so you need a minimum 200 nanometer revolutions
gap. So we--what we did is we did not consider any mathematics or something, we just took--if
we have a gap 2, that means one line starts, we count one, two. We draw the second one
and then the third one. In this way, we went on creating different lines, so it would be
spherical lines continuously, so we call each lines as one topological qubit, this goes
one unit. Now, if you see, you'll find that in gap 2, it is a direct overlap of two lines.
So if you have 100 lines on a particular space you cannot differentiate how many lines are
there, so that means we'd take only one restriction that is if they touch, they disappear. So
we just neglect that possibility. So in this way, we have found that if you send 8, at
the gap of 8, which is a Fibonacci number, then you will find that when you come back
and start, you will find it decomposes into 8, 5. If you send 7 gap, you will get to 7,
6. In this way decomposition occurs. And if we try to put multiple qubits, we will find
only four sets of combinations; 8, 5, 10, 13; 7, 9, 11, 13; 5, 7, 10, 13 and 5, 7, 9,
13. And the decomposition lists are also given here. So if you just, on a piece of paper,
you play with the pen, you can find this kind of relations. Okay, so this is about horizontally
if we send signals into a microtubule. What if it takes information from the environment,
E1, E2, E3, then we can find that if we start with topological qubit eight, then it decompose
into--if another signal enters, decompose into 5, 3. Another signal enters 5, 3, 2.
Another signal enters 3, 2. Another signal enters, qubit then will disappear because
we said touch, disappear. So in these operations, in the future, people can work on. But if
we go to lattice B, I got very interesting things. That is, gap 2 survives, gap 3 survives,
gap 4 decompose and it goes to 2, and you can send signals straight. If we--if the gap
is X, that is straight, then helicity c is infinite. If you put it in the Hamiltonian,
you will find that you get a typical situation where MPCG, or the Multiple Point Contact
Gaps, that we showed at the beginning of my talk, that appears spontaneously. That means,
if this kind of microtubule is there then it is coherent. You don't need to have any
external energy supply, it is always ready to do that. And this, lattice B, is very prompt
towards information transport. Lattice C and lattice B are complementary to each other.
So lattice B, you know, gives us 2, 3Q, 2, 3, 4, and X and it gives us 5 to 13 something.
Together, they cover entire series. One is good for computing, that is simply we are
finding it decomposes into its states, other don't want to decompose. So, what can we detect
about the topological qubit for different lengths? So for four different lengths of
MT, we should be able to get four different sets. So let's go for the experiment. Now,
we cannot do--the biggest problem when we wanted to do this experiment, we wanted to
measure quantum hall--fractional quantum hall effect which is the easiest and the direct
mean to detect the topological quantum qubit but microtubule does not respond to Rxy, that
is the particle, because we have in the megahertz frequency range only one molecular layer thick
so we cannot create the magnetic flux gradient which is essential for the Rxy. So we have--we
are left with only Rxx. But we found that when magnetic flux gradient is created, basically
Rxx, the horizontal resistance, also changes. Our principle is that we cannot absolute time,
we cannot detect a quantum state. But we can change the--we can change the transformation
from one topological qubit to another. That means, if we can convert topological qubit
A to topological qubit B, energy will be released or absorbed. So what did we do? We sent an
AC signal in the middle part, the shaded region. So AC signal, we know very well that does
not change the resistance of a device, the DC resistance of a device, because DC resistance
of a device depend on the topological order. AC signal cannot change unless--until there
exists some topological order and that undergoes a quantum transition. So, this is a simple
experimental set-up. So we have a function generator with two capacitor because DC's
part doesn't come into it, and a resistance measurement device. So we measure only the
DC resistance of the system. We change the function near the frequency and see what we
find. We find four, always, four different regions where you see the large DC resistance
change. This figure almost looks like, if you have gone through the literatures of fractional
quantum hall effect results, the result--this result, if you leave frequency to B and DC
resistance, this looks nearly similar. That means we are seeing the absorbance and we
find that seven distinct peaks appear and disappear repeatedly on different lengths.
So we measured--we repeated this measure on different devices. Then, if there is a qubit,
there should be a quantum phase slip. That means, one side we will send a signal, on
the next side there should be a phase difference. So, you find the phase difference and they
are also quantized, 45, 90, 135, 180, and 0, these repeats statistically. Then we try
to find out the condition, Q, ABCPCDE, that peaks that we have, and 8, 5, 10, 13. We,
again, we used the condition, topological qubits don't touch, and we find that exactly,
unless until you have this topological qubit you cannot get these peaks. You can verify.
So quick summary of the energy levels that we have got. So 9.03 megahertz, you get a--you
get resonance in the microtubule. It becomes coherent and no phase change, nor it is even
phase coherent. 20.56 megahertz; again, phase coherent; 16.35, 18.15 megahertz, in this
megahertz you get 135 degree phase difference and--or 180 degree phase difference and they
are coupled to each other. And the 23.00, 24.00, 23.27, 24.06, and 24.91 megahertz also
add to that absorbance peaks, which varies. What we did is we measured, we, you know,
changed the length of the microtubule from 200 nanometers up to say 10 or 20 micrometers.
And we found for every length which are the qubit peaks appear which are--which disappear.
So we tried to find out--we found that it is strongly dependent on the length and follows
a very particular algorithm continuously along the length. That means if you now give me
a particular length, let's say 22 micrometer, what should be the qubit properties? I can
tell exactly that this, and this, and this, and this energy band will get the absorption,
and this energy band we will get the absorption with this angled phase change and that angle
phase change so I can exactly tell you. Okay, two interesting thoughts. One is that one
period for this particular operation that we say that phase locking is a two micrometers
and 12 different ways it could be done. So, 24 to 30 micrometer long microtubules are
necessary to get all the states. And there is negative delta R minus delta R, plus and
minus delta R. That means in microtubule, particular signals you can send from this
direction and particular signal at the same time you can send from this direction; both
direction you cannot. So we tried to create in both directions but we didn't get. And
last experiment that we did to detect whether there exists quantum topological qubit or
not is quantum interferrometry. The experiment--it suggests theoretically that if you have from
both two ends, if you generate topological qubits into the system, and if you can make
it feel gradient in such a way that you trap it, then what happen, the middle region will
automatically create pulse with a certain time. So the--here is the two end qubits that
we created with two signals and the top radars we got continuous oscillations from that so
there must be existing some sort of topological order inside the system. What kind of TQs
are these? There in literature you will find there are at least 15 different kind of topological
qubits. We do not want to definitely define right now because we have got the experimental
radars and seven different kinds of signatures we have got of why this is topological qubit.
But still, since it is room temperature, we want to be very, very sure what is the real
nature of this kind of topological qubits. Finally, ferroelectric property of microtubule.
In the month of April, I came to Center for Consciousness conference and I saw the bottom
result. We'd--we had lots of noise at that time. We removed the noise and we have got
perfectly square. So there's--this is noise-less. Any kind of--if you get perfectly square behavior,
that means to store energy you don't need to spend energy to retain a particular bit.
And if you change the temperature, the information is not lost. It retains. As you can see, 250
K and 300 K at different bias we can create. So multiple states, you can write and you
can retain. Both kind of measurement could be done simultaneously. And as I have all
ready said, that if there is a length change continuously, that was first sentence of my
doc files, our objective, that if there is a dynamic instability, that a microtubule
is continuously changing, why it is changing and what are the nature of a particular length
of microtubule, we can tell exactly what qubits are. So, we want to build now the languages
in which we want to communicate with the cellular organisms. So this is the conclusion. Microtubule
processes classical bit and quantum topological bits together. Its conductivity is independent
of temperature. But whether it should be classified in metals, semiconductor, or insulator, we
don't know. But we think that it should not be classified in any of this. Lattice C and
lattice B are complementary to each other as far as topological qubits are concerned.
And together, they build a fantastic system of information processing by changing length,
MT tunes, nature of its topological qubits, MT stores and processes bit without releasing
or consuming heat, it's perfectly solitary. So finally, I would like to acknowledge Hartmut
and to Stuart for their contributions, AOARD [INDISTINCT] is here. I cannot--I would like
to acknowledge him for his kind grants, and JSPS, Center for Consciousness Studies for
some of the grants. And Professor Daisuke Fujita and Dr. Satyagit Sahu, and Dr. Subrata
Ghosh, and Professor Kazuhiro Hirata. Satyajit and Subrata are my post-docs, they have done
majority of the experiments and Professor Hirata reproduced our results because it's--it
was hard to believe at the beginning. And Professor Fujita also generously helped in
AFM measurements because he is very expert and he suggested that we should move to 4th
probe systems all to prove data useless. And also finally, I would like to thank all of
you for listening for this long time. Thank you very much.
>> Thank you. Thank you very much. Thank you. Are there any questions? Maybe we can take
one question. Yes? >> One question. You said that the conductivity
is not metal, not semiconductor, and so on. What type of the conductivity is this?
>> BANDYOPADHYAY: I don't know. But it is... >> Is that not electron conductivity? Or what
type? Because if you transport electricity, you must transport charge and therefore that
is something that should be explained. Because I assume that there is a certain amount of
electrons in the--I may say, conductivity band of microtubules.
>> BANDYOPADHYAY: Yes. I have shown the conductivity band. I have shown the picture, the point
contact. So it is--there is no--and in case of metal, there is no gap. In case of semiconductor,
you have a gap, a small gap. And in case of insulator, you have a large-band gap, right?
So it is very well-known. But in this kind of material, you have a point contact gap
in between the valence band and the conduction band so you can say it is another kind of
material, new kind of material, that does not fall into this category, so you can find
a new name. >> Thank you.
>> Thank you. Any more questions? Yes? >> Hi. So I guess I have a couple of questions.
First, I'm trying to understand why you call these topological qubits bits [INDISTINCT]
how do you read that information from them? >> BANDYOPADHYAY: Okay.
>> Yes. >> BANDYOPADHYAY: First, I call this topological
qubit for three reasons. Topological quantum bit. We have got the bit, we detected it.
We have got the topological order of change by measuring DC resistance change with the
AC particular frequency. >> I'm sorry, what are you detecting?
>> BANDYOPADHYAY: "What are you detecting" means?
>> Like, what does your--like, you're showing like a loop around the microtubule. What's
that loop mean? >> BANDYOPADHYAY: No, no, no, no, no, no,
no, no. You saw the experiment of--when DC resistance change using the AC signal frequency
that we supplied to the device? Did you check that? So if we apply a very particular energy
you will find sudden fall in the DC resistance. So, DC resistance of a system, you know, DC
resistance of a system determines the topology, the confirmation, and the structure. When
there is a sudden change in that that is quantized. That's why I call it topological qubit.
>> So... >> BANDYOPADHYAY: So at a particular frequency,
at six and seven different frequencies, always, whatever be the length of the microtubule,
you will find it will be enhanced, or I mean, dominated or sub-dominated. But in those frequencies,
if we apply a signal at a very small part of the system, AC signal, purely AC signal,
you will find the DC resistance is getting changed. So that is how we did it. Of course,
there are many other detection process by which we said. So there are standard five
different experiments, five or six different experiments, which has been established theoretically
to detect topological qubits which you can find in the literatures.
>> So could you store--could you store a quantum state? I mean, could you store a superposition?
>> BANDYOPADHYAY: No. The--when we tried to do this kind of experiment basically what
we do is we send a particular kind of current, particular magnitude of current which reaches
the material to the coherent state. For an example, suppose we are working with, say,
we know if we send DC current of 1 microampere we know that the resistance will fall below,
say, 20 kilo-ohm or 1 kilo-ohm. We know that. That means it is going to the coherent state.
So externally, we first send that current. When you send that current, we take it to
the coherent state and we store the topological qubits. Then, we try to transform one set
of qubit to another set of qubit. One qubit, we cannot write. One topological qubit, we
cannot write. But a particular set is possible to write. But what set we will write depends
on the length of the system. >> Let's...
>> BANDYOPADHYAY: We cannot control... >> Okay, let's--can we take this discussion
off-line because I'd actually like to join in it too, because I don't think this is a
topological qubit to be honest. >> BANDYOPADHYAY: Yes.
>> But next speaker is Stuart Hammeroff, and we'll reconvene in about five minutes. Thank
you.