So it's a reply sure to weapon
Professor Ken Brown with us today.
Got his bachelor's degree in chemistry
at University of Puget Sound and
then his Ph D.
also in chemistry at U.C. Berkeley to
the post back at MIT before coming
to Georgia Tech starting here in two
thousand and seven where he's currently
an associate professor in chemistry and
biochemistry although not for
long as can be moving starting next
semester to go to the patent route to
conjugate at Duke University joining
the huge influx of Georgia Tech
faculty to that that part of the world so
we certainly wish you were very.
Candid when a number of words
come out of the more recent ones.
Being appointed as a kindly
fellow in two thousand and
thirteen his research
he's one of those rare.
Researchers whose whose work spans both
experimental and theoretical work and
I think we'll hear some of that today
Bradley in the areas of traps and
quantum computing so
I'm going to turn it over to Ken.
Thanks David thanks for
the opportunity to talk and
tell us a little bit about
quantum computing and Miami.
With all talks to try to transfer
information so if you have questions about
anything at any time stop me happy to
talk about it talk about it offline.
So.
When you think about.
Computational resources spent
in the US A good place for
a lot of scientific competition is done
is the Department of Energy This is kind
of a plot from two thousand and
eleven showing how the computational
resources of the Department of Energy
are spent and you'll notice these big.
Which are calculations that only make
sense if you include quantum mechanical.
Arms and most importantly these two
guys here materials in chemistry
I really about calculating the quantum
mechanical way functions of electrons
that's all that's going on so
what's the problem with electrons so
in one nine hundred twenty nine Drac
knew that we knew everything there is
to know about electrons there are simple
particle they have a simple spin charge
easy interaction with corms law but
he also noted that even though these laws
are simple they lead to questions which
are much too complicated to be soluble.
And he then goes on to think about
ways to do approximations and in fact
a lot of our technological development as
a society has been as computers get larger
I believe to solve complicated chemical
material problems gets better which allows
us to make better computers which then
kind of feeds naturally of itself but it's
Want to take a second to talk a little
bit about like why is this problem hard.
So the basic idea of a quantum chemistry
problem is you have a bunch of nuclei
which are fixed in space and
then you ask wish I put these electrons.
So it doesn't seem too bad the electron
should of course float around the nuclei
and all we have to do is
minimize the shooter equation
find the ground state we function for
some given him will Tony and which gives
us this minimal ground state energy.
Now.
There are simple rules
really simple rules right so
electrons move electrons repel each
other electrons are attracted to nuclei.
Then there's a kind of a weird rule which
is that electrons have to have different
addresses the public schools in principle
and so in some sense the problem is how
do we choose these addresses like what
what would select trans go where.
And so.
One way to make the problem solvable is
to start with addresses we understand so
we kind of know how electrons arrange
themselves and it happens so what we do is
we just pick atomic orbitals as possible
addresses for the electrons to set.
And then what we want to do is we want
to basically asked the Hamiltonian
can really be thought of as equation which
governs how electrons change addresses so
there are two parts the first part
which contains the kinetic energy and
the attraction to nuclei it
basically says an electron
will change its address from say K.
to Jane.
That's it kind of just a hopping
of the electrons around.
The second term which is about
electrons repelling each other
says the two electrons and
two addresses because you know
I don't know you kind of think of them as
bad neighbors right there if they live
next to each other they prefer to live
further away from each other and so
of one of the neighbors tries to move
closer you might indeed move down next
house so these are these electrons
repelling each other and that's it
that's the whole problem and that's why
Drac said basically the problem solved.
Now what is the solution to
the problem is pretty challenging so
there's some good news and
so the good news is
that the problem size if you think about
it in terms of the number of addresses or
spin or bottles is pretty small
it's just and the four and squared.
The bad news is the possible number of
configurations is basically the number of
addresses choose the number of electrons
which is exponential in the number
of addresses which is usually linearly
proportional to the number of electrons.
And so this is a huge configuration space
and this is where the quantum mechanics.
Rears its ugly head and says that the
ground state is actually some c reposition
over over potentially all possible
ways to configure these electrons.
That means I have an exponential number of
these coefficients I need to keep track of
if I wanted to directly map
the the state of the molecule
Now the good news mixed news so to speak
is that many molecules actually are will
describe by only a few configurations and
that's why when people use things
like density functional theory or Hartree
Fokker like simple Catholic cluster
methods you can get really good answers
for some problems the bad news is some.
Things such is often catalyst in say
high temperature superconductors they.
Need many of these configurations and as
a result we have a hard time we have a OK
time if experimentalist brings us a good
catalyst we have an OK time using these
theory to try to explain how it works we
have a very hard time predicting catalyst
like I can't go to my computer in like
crank through a bunch of catalysts and
have and have a high certainty that
the catalyst will work in a lab
all right and so
the way I think about this is basically.
Classical computer requires
an exponential number of electrons
to store all of those coefficients
to represent only an electrons.
A molecule on the other hand somehow uses
an electron it's represent an electrons
which is clearly just as intelligent but
it's kind of an interesting
point of the gap between nature and
the way we do these competitions.
So Richard Feynman had this
disruptive idea in the eighty's.
Which is why not build the computer
out of quantum mechanical pieces
that would break this is symmetry.
Now in the eighty's.
Classical computers were not so good so
it's hard to imagine building a quantum
computer but it was a provocative idea and
no one cared no one cared maybe two or
three people cared everyone else was
like you know physicists get all they
have crazy ideas we just forget about it.
But then in the mid ninety's Peter
sure who is a mathematician it
Bell Laboratories.
He showed that if you wanted to so
you had a large number N.
which is the product of two primes and
you want to give in and
find one of these primes and then you
get the other one basically for free.
And it turns out the methods we have to do
that are not that different from what you
learned in grade school it does divide
by three is divided by five no.
But it turns out of if you had a quantum
computer you could actually factor this
number quickly there's a polynomial
algorithm exponentially faster
than the best known classical approach.
And this is important because this
one way function so if I have P.
and I can get Q.
right but I have and
it's very hard for me to find P.
and Q.
is one of the ways that
we keep the Internet's.
If they're encryption OK And so
as soon as this happened everybody cared
mostly spies right because they want to
break codes may be thieves who
want to steal your bank account.
And we but
what I like about it is that unlike fine
mins idea which is which is
a which is a grand idea of I have
a quantum computing device which allows
me to simulate other quantum systems
Peter shore is ideas mathematically very
direct It's like you have these steps
you put these steps together and
what's nice is if you take those steps and
you apply them first a system of electrons
and then two electrons within a molecule
you find that you get a linear
scaling in the number of quantum
bits that you need to the spatial basis
functions which are these addresses and
so even with a modestly sized quantum
computer of a few thousand quantum bits
you can start doing pretty much exact
calculations on molecules which will never
be able to be exactly calculated using
classical computers and so the way I think
about that is again classical The computer
is the exponential number of electrons
to represent and electrons
molecules use and to represent N.
and a quantum computer basically
uses a linear number of electrons
try presenting the analytics.
Right.
So now how do you build these things so
I just like to remind people that.
You know we did not always
have possible computers
that we have some choice of bits
it's like in one hundred B.C.
we use gears we actually use gears for
the next basically two thousand years.
Then in the one nine hundred forty S.
We shifted over to this
vacuum tube type technology.
In this period where there were
functioning large vacuum tube
computers which you could
argue won World War two.
The first transistor was also made and
this first transistor which you can see
example of it Bell Labs you know is
about the size of a Coke can and
now we get to you know closer to today
this is just a picture of my laptop so.
So quantum bits we have the same
choices so we have you can represent
it the physical system into any physical
system that will hold quantum information
and these are not all possible
examples these are just some examples.
A lot of the early work in quantum
computing was done using an M R
because due to the utility of an M R for
understanding chemicals it
already had sufficient control electronics
that you could directly map these quantum
albums onto this device but it has
some quite probable criminals ation.
And I would say at the moment the two kind
of leading contenders are superconductors
and atomic ions but if you saw the cement
from Microsoft yesterday about quantum
computing there's hope for
these future Meyer on a kind of pieces but
there is great work in photons
neutral atoms and quantum dots.
So what do we need so
we need something to care.
The information some kind of quantum bit.
We need to be able to manipulate
that it to single cubic Gates.
We need to able to do conditional
operations these to keep the gates.
Allow us to do logic.
We need to be able to measure the outcome
of our experiment and then we
need some way to connect many many cubits
and I would say at the moment these.
Parts here for superconductors and I and
are well understood and
the focus technologically is thinking
about this problem how do we start to
put together many of these pieces.
So the problem is any quantum
system that we can talk to you.
Other things can talk to you and
typically it's something boring
like the air conditioning in your
lab sometimes it can be you can
see the magnetic field of the MARTA moving
as your quantum bit it's really good.
And in the end of the day there are always
these quantum effects of vacuum
fluctuations which will always create
some errors errors errors are unavoidable
and when I think about my quantum
information work I really think
about it in the context of always trying
to improve reliability and so these
are just different ways you can imagine
improving reliability of the software and
firmware level thinking about algorithms
in architectures that are better some kind
of open loop feedback closed loop back and
then better hardware like can we make
hardware that's there when I am a clear
kinetically protected from noise.
And can we make hardware which is
compatible with this closed loop control.
So today I'm going to really briefly
just talk about surface like should I
entraps and then I'm going to explain.
How quantum error correction works.
And then talk about a recent experiment we
we did in collaboration with the research
Maryland on quantum error detection.
All right so here's this list of
criteria so the cubits are going to be
the internal internal states of Iowans
this is a picture of single atomic I and
strapped to my lab here at Georgia Tech
Kelso my aunt's one cubit gates are done
by laser microwaves to keep the gates
are done by lasers Mike waves are cool and
reported the measurement is through
the fluorescents of the eye and
you can see they're quite bright in
currently scale ability this kind of two
main ideas the one idea is
you basically have a C.C.D.
chip of truths which you that you have it
a chip with many electrodes and
you shuttle the ions around like a charged
couple device sort of thing the other
one is you have a small quantum register
which is then in tangle with other quantum
registered via photon interconnect OK.
So laser cooled ions the basic
important thing is that you can
scatter many many many photons and so
even though the apparatus is at room
temperature the ions themselves can be.
At a Millikan even down to
like five micro Calvin.
You just need a ANY we choose ions
that are simple to understand
because we don't know how to solve every
And so we we pick ions that have a single
electron in the valence shell and then off
that transition we can measure this for
us since we've done some work
in my lab pushing towards
being able to do this with molecular
ions that's a totally different topic.
The iron trap.
Which has been used all kinds of mass
spectroscopy analysis many of you probably
use an eye on trial for some aspect what
it does is the ions are held by D.C.
confining potentials acting.
Axially and then radially is held by this
flipping and flopping oscillating field
and so the eye and can't move fast enough
it can't find its way out of this trap.
So in.
Motivated by this idea
of this scalable C.C.D.
type architecture for
ions John Cheever really in this boulder.
Realized you could cut you could
imagine cutting the select trode and
faulting the trap onto a plane and
when you do that you now can build
these traps in two dimensions and
actually make any layout that you would
like so here is just a movie of that from.
The folks.
There is the forward trap these ions are
sitting there you cut that top electrode
plane you flatten it out and the ions
continue to float above the surface.
Here's a movie.
That I took with Rob Clark sitting
there back in two thousand and
five I think of these
are just dust particles so
the other beautiful thing about a surface
Alectryon trap is you can I interrupt work
for anything that I have to work for atoms
so we just trap these polystyrene beads
you see they float through here
we can control which way they go.
And in the key thing is they
float above the surface.
But the surface is totally the trap itself
is defined by the electrodes in the plane.
So the last ten years or so so.
If you're doing the.
Charged couple device architecture or
if you're doing photon interconnects
in both cases here you definitely
need these kind of serious traps for
the photon interconnects you kind of
need it because you want to get your
band with Photon
connections high enough so
you need a place to store Iowans and
shift them around.
As part of this work so it's been
great in the last ten years is that
there's been tremendous progress and
how these junctions have been made.
This is a nice picture of
a similar cross junction from
here at G T R I where ions can be
shifted a crossed we print them now
their risk printed using kind of typical C
mass technology of metals and insulators.
Here's an example of
that from my student true
who use the clean room facilities here.
I guess before this
building to make a small
spherical mirror in these traps by
etching here into the silicon layer and
then just building the trap on top and
what I loved about this
is the rest of the process didn't really
change the only part of the process that
needed tweaked up was figuring out how to
get a very good smooth surface here and
then here you can see how it works right
there is a silicon chip and then metals.
Insulator metal layers this is a very
there are many more layers of metal
insulation now but in two thousand
Levon this was the state of the air and
what's great is we can take the single
atomic ion and we could shuttle it over
this Mir And then here you can see
the reflection this is one atom and
the reflection of one atom and it's an
important step towards building a device
which has enough scalable points that
you can do measurement everywhere
what's great is I mean there are many
different places making these kind
of chips Here's a chip that we got
from Sandia National Laboratories and
this is an image in our laboratory of a
single atom moving up the arm of this chip
and we've been able to show that
we can move ions through these
junctions without causing too much
heating which is really critical for
then laying out this whole process.
So what I like to say is humans humans are
pretty good at making things and three D.
really good at making things and tutti So
in two dimensions we can take
these traps and start to add in.
All kinds of different features we
can add injunctions we can add in
places that improve a measurement and then
I'm going to talk about it we can also add
in control of Tronics two to directly
apply the single into cubic it's we need
what's great is really a global community
of people working on the surface traps.
We for the last ten years of
actually had a standard so people
can make traps anywhere and send the trap
in the standard package to anywhere else.
It's been quite good.
All right so now I'm going to start
to shift gears to Eric direction.
And.
The SO Remember the goal is.
The goal is we want to try to solve
a chemistry problem I can't solve today
right I don't want to solve a chemistry
problem that I can solve today so
one chemistry problem we can't solve is
we don't understand exactly how bacteria
which fixate nitrogen to ammonia
we don't exactly understand how.
Their enzymes work so
we know that there's this complex here.
Of iron in the lived in the sulfides
where the action takes place but
we don't know what action we don't
know exactly what happens there and
we can't really simulate this so
the group at Microsoft the quantum
architecture but Microsoft.
In collaboration with E.T.H..
Tried to see how many gates would
it take on a quantum computer
to actually just simulate
this piece here and
they calculate this number of ten
to the fifteen Gates roughly.
Which is a lot of gates but when you think
about how many gates are in your classical
computation it's not crazy and
the problem is the best current error
rate for doing Gates in quantum
devices is tied to the minus three on
average averaged over all gets it.
So that means we can basically
only do with thousand gates so
how are we going to get from a thousand
gates to ten to fifteen kids.
So well first what can you do with
a thousand kids so there is actually
very recently this nice Nature paper
from the superconducting group at I.B.M.
wherry with a thousand gates you can
get there closer to one hundred gates
you can get a really good
measurement of the grounds if I did.
In.
Lithium hydride things already
start to go kind of goofy So
these black points are the experiments and
this green fuzz here
is the theory of how they expect their
experiments to work because they know
their experiments have noise right so
we know like I'd like the community
knows there is noise and knows where it
is but it kind of also shows you that
we need to really suppress this noise
to get very accurate answers so
this is a very beautiful experiment is
the first time people have done a quantum
chemistry calculation with three atoms on
a quantum computer small quantum computer.
But it also shows I think that the real
necessity of getting these areas down.
So we have kind of two
ways to do things and so
one is we can imagine let's just get
the controls really good like let's
just make these get the lasers perfect
the microwave is perfect Let's then add
control theory on top and
my group actually done a lot of that So
this is a kind of a review article about
some of the work we've done a single Cuba
control very recently my student
James loan there should be a one here
yes seventeen o eight looked at a new way
to do to keep the control which is indeed
work in the laboratory but
we're still limited by technical noise and
if we could get rid of the technical noise
so if we get below the technical noise.
Yet we expect for ions kind of
an error ten to the minus six.
Which is still rate we need nine orders of
magnitude to get to something with ten to
fifteen gates so what we really
need is some way to reduce the.
Air which I think of kind of algorithm
production of entropy through quantum or.
So I think of the control
situation is sort of a quick segue
to the Three Little Pigs story if you're
not familiar we can talk about it later so
ideally we'd like a cube it would
be like a brick house right and
then the bad wolf comes in bounces off
the house take a saved everybody's happy.
Now the problem is we only
have these straw Cupid's
and the wolf comes in each the pig.
It's not so good for us so
still straw is much cheaper than bricks.
So so this is not what happens when
kids story but you can imagine
the strong house pig was like well
just build a bunch of strong houses.
And as long as I move from
house to house pretty regularly
when the work comes in you'll probably
snag a house that I'm not at.
If I can repair these houses right faster
than the wolf is destroying them and still
save money versus making brick houses
it's a much better way to do things.
So.
So quantum error correction error
correction generically works like that.
So in classical era correction
the simplest example is majority voting.
And so you can imagine if I wanted to
send a message of one bit I just send it
three times and I always say this is like
talking to my grandmother on the phone
right Blake coming over anyway so
the problem is.
There's two problems so the first thing
is if I measure the value of these bits
quantum mechanically it'll collapse me to
some classical state which will be bad.
This copying this this basically is
an example also of copying right so
we need to make a backup of your computer
as effectively the simplest error
correcting code you just copy the data so
in quantum mechanics we can't copy and
we can't stop to measure the data because
then we would lose the advantage.
Yet we basically would lose
the advantage of the quantum machine.
So instead what we do is
we ask a different question
which is we measure the subspace.
So here if you think of this is again
three day Bers you could ask these
neighbors like do you agree with
your neighbor Yeah yeah Greg and
when they agree with their neighbors
you know there's no air but
you actually don't know what the data
is you don't know if it's zero
you don't know if it's the one
you just know they agree now here
this neighbor in the middle disagrees
with the neighbors on both sides and
so you can tell that neighbor they should
change their mind without getting any
sense of what the neighbor things
that part still hidden to you.
And that allows you to keep the quantum
superposition you need for the speed up.
Without but
still being able to measure the errors so
the way you meant instead
of measuring the data and
comparing the data you just you set
up a way to measure the errors.
Now quantum mechanically there are two
types of errors that you can have
a bit flip in a facelift.
And that basically means we
need to classical codes and
we can further concatenate these
codes to suppress the air so
that brings us to a key concept
which is the threshold and so
this is an example of concatenated
codes a calculation we did here but
the point is here is the physical error
rate this red line and then below
some threshold and this threshold
will depend on all kinds of things.
You can use you can find a family of
codes they can suppress that air.
As low as you like it to go right Sue
The plan is we make the physical errors
good as we can and then we use the fact
there's a family of codes of different
distance to lower that aired down to
the ten to the minus fifteen we need.
And I guess I should point out that
actually to break people's bank accounts
you only need about ten
to the twelve gates.
So you can just focus on that if you want.
All right so in the early ninety's.
People took classical era correcting
codes they made quite America codes.
And then the problem
was when they tried to
figure out how good the gates
had to be to meet this threshold
they had to be good to say a part per
million to about one hundred perfectly.
And it was.
I'm an optimist so
that seems possible to me but
it's like it's kind of at the edge
right if this was like a part
per trillion that maybe we'd say OK forget
it like we these codes are going to help.
Now people thought well you know there
are other ways to protect information
not just through codes like so
if you think about a magnetic hard
drive or like a cassette tape.
It's it's controlled by actually
the physical interaction of a magnet.
And so people said well can
we make a quantum harddrive
if we make a system whose physical
interaction preserves that information.
And the bad news the good
news was yes the bad
news was that required basically
the system to be four dimensional if it
wasn't four dimensional there would be
some error that would act like a string.
Which would ruin
your memory in the same way that if
you have only a one dimensional magnet
it's also not there manically still
right you need higher dimensions.
But what's incredible is this idea.
Could be coupled with some ideas
about quantum Eric rection I mean
it was a start is a quantum.
Move to this idea back
to your question idea
where resin different Harrington showed in
two thousand and six that you basically
say use your quantum computer
to simulate a two D.
version of this hard drive but
with feedback where why.
Ching in fixing things and
what they found is that you could
then do quantum computation
to arbitrary precision if the underlying
gates were only good to one percent.
And that I think is when companies etc
started to really pay attention because
I don't really need my cubits to be that
good my kids are already better than this
so this actually earlier this month
I organized a workshop on quite
America action quantum Fourth
International Conference on quantum era
corruption at the University of
Maryland Corgan I was with Jake Taylor.
And we are sponsored by the University
of Maryland and NIST to the.
These joint centers visit to sponsored by
Georgia Tech through this nice Center for
Research and all the beating heart disease
sponsored by the government labs or
television sciences sponsored by
Microsoft right Northrop Grumman and
then these two companies are getting and
I and Q.
which are startup quantum
computing companies.
Right now there is a ton of jobs for
people who know about quantum computers
how to build them quite American action.
And I think if you yet
I wait if you're interested in
changing directions think
about changing the structure.
Yet But what I want to point out
actually just to come back to
is that this we all think that we
need this quantum era correction
to make these computers
actually do something useful.
All right so back to hardware so
ions if you have say seven ions
you can imagine implementing one of the
smallest quantum error correcting codes
one of the codes that was devised
in the early ninety's and
this is the least the basic
operations of including the state
were done in two thousand and
fourteen in minor blood scrip in spoke.
But what's neat about a chain of violence
is that even though the ions are in
a linear chain the connection
between the eye and
because it's through
the normal modes of motion.
It's basically a fully connected graph so
if I want to change quantum error
correcting code I just basically change
the firmware but not the hardware
up to up to some sort of size.
And so now.
So this this is been a big
current Big direction of what
we've been doing in the group.
I'm only going to talk about
this quantum err detection
code an experiment we did with
University of Maryland but
we recently had this nice
paper showing how if you take
into account physical errors you can make
better codes but most of you likely and
then we have a paper which should be
out soon on the archive talking about
how to implement the surface code which is
the code which has this one percent error.
Threshold the smallest instance which
doesn't have that good of pseudo threshold
using I introduce which is kind of our.
I would say three year plan.
All right so.
If you think about.
So if you think back about this.
The three big code if I think about.
Vastly question about agreement between
neighbors I don't care if they're plus or
minus right I just care that they
agree and that this is easy to.
So Izzy asked one guy are you plus or
minus into
Z S basically say are you both
Plus are you both minus and
if you're not there's a switch so
these check operators look for
the parity of bits of these four bits and
this check operator looks for the phase
parity of those four bits which is hard to
explain but it's the quantum kind of
the quantum analog of that bit flip and so
then there are these four logical
operators corresponding to measuring
in the classical computer basis or
measuring in the.
In this rotated kind of quantum basis and
this for Keep it up for a cubit
checks are the basis of many ways to
build quantum of character acting codes.
So let's say I want to prepare
the logical zero state
what I can do is I can start with all
of my bits just in a zero state and
then I apply the sequence of operations.
But there can be errors and
these errors will also be propagated
through these two cubic things
leading to possible Q.B. errors so.
So here if we forget about the errors
the state that I get here is either
all of the states are in zero or
all the states are in one and
this is sometimes referred to as a short
and her cats to it's like the cat is alive
or the cat is dead and
if I measure any bit of information
I completely collapse to everybody's
dead or everybody's alive.
Now this stupid error what it will do
is it will flip these last two bits and
if I think of my logical cubit space what
I see is the second logical cube it is
flipped but the first logical
cube it has been preserved
so it turns out that for
this code if there are errors
in the gates if there are errors in
the gates right it's not a channel.
Yet if there are errors in the gates then
I can only preserve one
of these coupons and so
what I do is I build my check operators in
a way where that single cubits preserved.
And all of the errors accumulate
kind of on the other cute
So yes that single Cuban air here
can lead to a two Cuban air here
which is equivalent to a logical
error on that second will keep it.
And so this organization of these.
Said the organization of how these
circuits look is is actually related to
work my student you to me to did
when she was an intern at Microsoft.
And there's been a similar work on
the stabilizers from the I.B.M.
superconducting group and what I'm going
to talk to you now with our experiments
is on the archive and should be published
in Science advances you know this month.
So what's the hardware look like at
the University of Maryland who you
collaborating with where you have these
you have a big laser that comes through
there's a multichannel A.O.M. which
allows you to then interact with indeed
digital ions and
there's a multichannel P.M.T.
which then allows you to measure
the states of these guys.
Here they have kind of one percent
fidelity on the measurement.
When you measure over all
of these different states
what you find is that
you don't quite get it.
You don't just get the product of
these single Keep measurements and
the reason is there's classical
crosstalk in that photon counter and
so if the if the one channel goes off
there's a higher probability that one
of its neighboring channels can go off.
Sue what's nice is that secondary
error that would occur.
Happens in a way where distance to code
can still suppress that
underlying detection or.
So we do this we prepare the state
zero logical zero and this is all of
the states written like right the binary
state is now transformed to just a number.
We should only get basically population
and zero in thirty we see there's some air
the fidelity is quite good and
if we look at these two cubits So
the one cubit which we've built in
this way which is fault tolerant.
We see that ninety eight
percent of the time.
It's correct.
Almost on a side time.
But the point three percent
of the time it goes bad
We're as the cubit which is we've made a
kind of sacrificial you see that it fills
much higher right is filled closer to
the two percent right and this is really.
So we also do this by by
doing adding a check and
you see basically the same plots that
the cube it the sacrificial cube it
fails at two percent which is kind
of the error rate of the gates and
the good cube it fills at a rate
of point five percent or so.
Now it's only an error detection code so
that means we don't have
enough information to correct
we only have enough information to
throw out the runs we know we're bad.
Right we don't.
Write we still keep runs that are bad but
we threw out the ones where we've been
heralded to know that they in
fact have gone incorrectly and
that means there is some loss in kind
of data rate because we end up throwing
the ones that are bad but the ones that
get through we know in fact are good.
So here is the physical error
rate of the physical cubits.
This yellow curve is the area
eight of the cubit which is
fault tolerant which we've set up so that
no single gate error will destroy it and
here is the error curve for
the sort of more sacrificial cubit and.
Hey this plot is really good news and
because some sense it's
boring it more or less matches like our
theoretical guess of what should happen.
But in terms of building an era corrected
circuit that's incredibly good news
because the thing that the quantum error
correction theorist are most worried about
is that there is some unknown correlated
errors that we aren't accounting for and
at least in the small system there
are no surprise unknown errors which
means there is no there still remains
no in principle reason why we can't
make these logical keep it's large enough
to make the error sufficiently small.
Let me just check the time.
I've done it's OK so
I just briefly there's some cost.
So if I have.
So.
For every error correcting code.
There is some limit on the number
of steps that I can take and
some don't this is basically number of
gates a number of gates is the number
of cubits times the number of competition
steps and as I increase my error
correcting code I can get to the point
where the algorithm that I want to do.
Will succeed right so
if I have no error correction not much
works as I increase the air correction
I get to the point where succes.
So one of.
My first papers here at
Georgia Tech was the question of
What if the what if the N.S.A. is already
built a factoring quantum computer.
And they get tired of factoring everything
and they give it to you to do science
like what kind of science can you do and
so this curve here corresponds to
one level of error correction two levels
of Eric direction three levels of error
correction for those that are correction
and these Dagen allows here
tell you how much air correction you
need to succeed at what you're doing.
And the first thing is it depends
a lot on how you do the algorithm so
this is the right the way to do sure
is algorithm that takes more cubits and
less steps of course you could use
less cubits and more steps but
it turns out the amount of error
correction you need becomes really tough
so what we did is we just looked
at a simple magnet model and
what's nice is that the you
can see the linear.
That the cost only goes
literally like you hope but
the amount of time step seem quite
long when you do the air correction.
And so we spend a lot of time
with other people to feel
particularly Fred chunkier Chicago and
Margaret Manu see at Princeton.
Thinking about.
How can we actually calculate what's
the real cost of doing these things and
in that process not only our team but
many many teams around the world at
Microsoft elsewhere realize
the all of these numbers are just.
You know we haven't had the years
of optimizing that we've had for
classical algorithms so
better compilation shifted all of this to
the yeah all this the left by a factor of
a thousand with no change in the number of
keep it's and better sub routines and
end up costing a little more cubits but
basically ship there's another
factor of one hundred and
we don't think that we're
near that limit yet and so
I actually think there's a lot of
opportunity in for a long time to feel had
people working on quantum algorithms
people working on devices and there was so
much space in between that there is
very little information flow and
many missing instructions and we're
moving into an area now where there is
good reason to work on things like
technologically where correction and
better ways to do these optimizations and
as I mentioned before there is like
a growing industrial effort Microsoft
working on my on a cube it's Google and
I.B.M. working on super doctors and we've
got to reconsider the actors into working
on a super good actors and so
I could actors and Kubrick and ions.
I think.
I hope that I've convinced you that it's
kind of an exciting time to do quantum
computing that they were reaching
the point where quantum era correction
is really right on the horizon and
once that errors of these quantum
bits drop sufficiently low I think it will
revolutionize the way that we calculate
the properties of materials and
chemistry and with that I'd like to
just thank the sponsors National Science
Foundation and our research office.
I arpa.
The humble foundation for a fellowship.
This is the group and we do other stuff we
work a lot on called Molecular ions and
we have some new project on sorting
cells using surface electrode ion traps.
And I said thanks for attention thanks.
But.
Well an.
So tell you the one optimist thing and
then I'll switch to the other side so
the one optimist thing is that right
now we don't have a device and so
when people calculate how many gates
you need and how many cubits you need.
We actually the whatever the.
The feel of the character of
the field is be pessimistic so
you like people try to prove rigorous
balance they say there's a rigorous bound
between these two operators right and
if you think about how we actually do
calculations of molecules on
a classical computer we all know D.F.T.
will fail sometime we all know we all use
D.F.T. all the time and then when it fails
we don't get upset but it's like OK I
guess I move to the next program and
so the optimist in me things once we have
working hardware all those numbers will
come down right so
in that Microsoft paper for
nitrogen is you need on the order
of two thousand logical cubits
which means good and you need about ten of
the fifteen gates so you need basically
two thousand logical cubits that fail
at a rate of ten to the minus fifteen.
Now if an ion traps we could
hit ten to the minus six
physical cubits then I would only need.
I basically need three hundred fifty.
Three hundred fifty physical cubits to
logical cubit which would be a great deal.
The Microsoft is working on these my
on a cubit which don't exist yet but
they think if they did exist they would
have an error of ten to the minus eight
and so they'd be able to do this
transformation at about a factor of.
Yet you know basically seven they need
seven logical keepers of what he was.
However if we're stuck in areas that
are close to only ten of the minus three.
Then we're going to need
thousands of logical cubit that
thousands of physical keep it.
And that's.
That's the question right so.
We're still.
Yeah.
I would say there when there were one
to two years away from one hundred
like machines that can really use
one hundred physical keep it.
I really think the challenge in the field
from my perspective is really skill
ability like how do I then take this
hundred cubits put them into blocks and
make a thousand cubits.
And whether that turns out
to be you know that's.
You know coming from like a scientist
background we always think of that as like
someone else will scale
stuff up later it's fine but
of course that's a really hard problem.
It will take some.
Sort.
Of that that's really.
What it is.
For the space station.
What is the off yeah so so
we used to Iran's calcium and
you to be mine so in callously my on on is
the electron in the sorbitol Basically
the ground state of calcium and
off is where you show the electron into
this deal orbital Sisson optical keep it.
For you terbium on and off.
Is basically the nucleus of
your terbium and so we off so
it's a hyper fine state but off it is
the lower state and on is the upper right.
So.
Yeah in the same for each area so so
for atomic ions we always detect by for
us since But what we use is the on and
off states different.
Yeah yeah.
And so the nice thing I mean the nice
thing about C.U. terbium ions
is hyper find States don't decay in
a time scale which is relevant to us.
The hyper finances you terbium
also have a clock state which
means they're relatively insensitive to
magnetic field fluctuations so with with.
Yes Actually with not that
much work you can get a.
Kind of Q State like the oscillations you
can do relative to the decay of it of of.
You have a million without much work and
you can do better by adding magnetic
shielding and all this comes.
From what.