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  • KEVIN SATZINGER: Thank you.

  • My name is Kevin Satzinger, and I'm here

  • today to share with you our latest

  • results on Quantum Supremacy: Benchmarking the Sycamore

  • Processor.

  • The promise of quantum computing is

  • that it can solve certain useful problems that

  • are simply beyond the reach of classical computing.

  • And most of those applications are here

  • in the useful error corrected machine,

  • which is still years of research in the future.

  • But we also hope that in the near term, in this blue region,

  • we will be able to find useful applications.

  • But, of course, before a quantum computer

  • can do something useful that is intractable for classical

  • computing, it must first do anything

  • at all that is intractable for a classical computer.

  • And so a real question that has been on our minds

  • in this whole industry for the last decade is,

  • can we cross this line?

  • And this is something that our group has been focusing on

  • for the past several years.

  • It's something that was given a name by John Preskill in 2012.

  • He called it quantum supremacy, to perform tasks

  • with controlled quantum systems going

  • beyond what can be accomplished with ordinary digital

  • computers.

  • He went on to ask, is controlling large-scale quantum

  • systems merely really, really hard

  • or is it ridiculously hard?

  • Well, I am pleased to say that it is merely really,

  • really hard.

  • And we demonstrated this with the paper

  • that we published last fall where we showed crossing

  • this line for the first time.

  • And looking at this slide, I see there's

  • a lot of words on there.

  • So maybe a picture would be a better way to reflect this.

  • And I want to emphasize that this is a huge team effort.

  • And I'm very thankful to each and every person, each

  • and every member of this team who contributed to this work.

  • And I'm honored to be here today representing them.

  • You can find our paper on Nature.

  • It's open access.

  • And also at this archive link, we

  • have updated versions of our supplementary information.

  • At the centerpiece of this paper was a new processor

  • called Sycamore.

  • And it's positioned here right at this boundary

  • between classically simulatable and

  • beyond classically simulatable.

  • And that's what I'm going to be presenting about today.

  • First, the march from graduate school in the upper

  • left toward industrial technology that

  • can take on a supercomputer.

  • And then how that plays into this research

  • direction towards useful error corrected machine.

  • For there is this talk, I'll be following this outline.

  • So we'll look first at the Sycamore processor.

  • Second, how to calibrate and benchmark Sycamore.

  • And finally, quantum supremacy itself.

  • So let's get started with Sycamore.

  • And before we get to Sycamore, I want

  • to flash back a few years to what the state of the art

  • was in 2015.

  • This is a chip from the Santa Barbara group.

  • It's about a centimeter in size.

  • And it has nine transmon qubits in a linear array.

  • And what I'd like you to observe is

  • that the control wiring takes up about half

  • of the area of this chip.

  • And when you look at this device,

  • it is not at all obvious how we could scale it up

  • to a two-dimensional array with 50-plus qubits.

  • It's not a matter of copy/paste.

  • We need to really re-engineer the system in order

  • to make it scalable.

  • And one of the key technologies that

  • made it possible to make such a two-dimensional array

  • was moving to a scalable flip-chip design, where we

  • have two chips instead of one.

  • So one chip, this top chip, will be solely responsible

  • for a two-dimensional array of qubits.

  • And the other chip will take care of all the readout and all

  • the control wiring.

  • And by dividing the responsibilities like this,

  • we'll be able to have a more scalable design.

  • One of the key technologies that makes this possible

  • is these indium bumps, which provide a superconducting

  • interconnect and a mechanical connection between the two

  • chips.

  • This is a photograph showing a small processor

  • prototype that demonstrated this flip-chip technology.

  • So there are four chips in this photograph.

  • At the bottom is a qubit chip that has a small 2 by 3

  • array of superconducting qubits in the center.

  • And the rest of the chip is just covered in those indium bumps.

  • In the center is a separate chip that's

  • responsible for readout and control

  • and interfacing with the outside world.

  • And what we do is we take the qubit chip

  • and flip it over on top of the control chip,

  • align them, and press them together.

  • And that completed assembly is what's

  • at the top of the photograph, where we have two chips stacked

  • together and ready to use.

  • Now, this is how you can make a quantum processor.

  • But one of the lessons that I want

  • to share with you is that there's a lot of hardware

  • infrastructure that goes into making one of these experiments

  • actually work.

  • So let me share with you a couple of highlights.

  • One is packaging.

  • This is basically anything that goes

  • between the quantum processor and our dilution refrigerator.

  • And in our case, we have the processor

  • embedded in a circuit board with superconducting metal.

  • And the circuit board interfaces with about 150

  • coaxial connectors around the perimeter.

  • We also encase the processor an electromagnetic

  • shielding to protect it from the outside world.

  • We then take this package and bolt it

  • to the bottom of a dilution refrigerator, which

  • will cool it down to about 10 millikelvin

  • and also is responsible for delivering signals

  • through a couple hundred coaxial cables

  • that go from room temperature down into the device.

  • Another key piece of hardware infrastructure

  • to get these experiments to work is our electronics.

  • These are room temperature electronics

  • that generate the control signals for our processors.

  • And we use custom scalable electronics.

  • Here's an example of one of our boards.

  • In the center, is a field programmable gate

  • array that's responsible for driving eight

  • digital-to-analog converters circled

  • around it, which then drive these eight channels.

  • These can output arbitrary waveforms from 0

  • to 400 megahertz.

  • And we can also up-convert those with mixer

  • to microwave frequencies like around 6 gigahertz.

  • This is just one card.

  • We can have many of these cards in a crate, like depicted here.

  • And then several of these crates in racks working together

  • in concert to control one of our processors.

  • Now I'd like to turn to Sycamore itself.

  • One of the key advances of Sycamore

  • is that it's a new tunable coupling architecture.

  • This is a new feature where we're

  • able to turn the qubit interactions on

  • and off at will.

  • So the qubits can be independent of each other most of the time.

  • But then when we want them to interact and get entanglement,

  • we can turn on the coupling for a brief period of time.

  • This, it turns out, was immensely

  • helpful to making the full system work

  • and was really a key breakthrough

  • in order to get this processor to perform.

  • We did this with a scalable two-dimensional architecture,

  • where we introduce an extra coupler

  • transmon between each pair of qubits where qubit itself

  • is also a transmon.

  • And this is depicted in this device schematic

  • here, where we have 54 qubits and 88 couplers,

  • one between each pair of qubits.

  • I want to share with you a little bit of data showing

  • how these couplers really work.

  • So let's look at a simple experiment

  • where we have two qubits next to each other

  • at the same frequency.

  • What we're going to do is excite one qubit

  • and then have the two qubits interact for a period of time,

  • the vertical axis, subject to a certain coupler

  • bias, the horizontal axis.

  • And let's look at the center first.

  • So, in the center here, the coupler

  • is at its maximum frequency.

  • And so there is a few megahertz of coupling between the two

  • qubits.

  • And what happens is this photon leisurely swaps back and forth

  • between the two qubits.

  • That's what these oscillations are.

  • But as we march to the right, as the couplers' frequency comes

  • down, there is this divergence where

  • there is no more swapping.

  • This is where the coupling is turned off

  • and the two qubits can act independently.

  • This is a very valuable place.

  • This is where we operate ordinarily.

  • But sometimes you want the qubits to interact.

  • And to do that, we'll post the coupler a little bit further

  • to the right so that we have very strong coupling

  • for a brief period of time between the two qubits.

  • I'll end this section with this nice photograph of our Sycamore

  • processor.

  • And a nice symmetry that I could highlight

  • is that the center chip here with the qubits

  • is about a centimeter in size, which

  • is the same size of the chip we looked

  • at the beginning of this section.

  • So now let's move on to calibration and benchmarking.

  • Suppose that I handed you all of these electronics-- the fridge

  • and cables, the packaging and the processor.

  • It is not a trivial matter to turn all of that stuff

  • into a quantum computer.

  • And calibration is the process of learning

  • how to execute quantum logic with our hardware

  • so that we can go from all of our stuff

  • to a system that can run an arbitrary quantum

  • algorithm in the same way that you could play music

  • on a finely tuned piano.

  • But this is not a trivial task.

  • There are around 100 parameters for each qubit.

  • We need to choose a frequency for every qubit and coupler.

  • And there are strong interactions

  • between those frequencies and biases.

  • And then we need to tune up all of the gates

  • and readout for each qubit and pair of qubits.

  • Now, if you have just a few qubits,

  • you can park a graduate student in front

  • of a computer for a couple of days,

  • and they'll be able to work it out.

  • But if you have 5o-plus qubits, you

  • need a much more scalable solution.

  • And in order to solve this problem,

  • we encode our calibration routines into a graph.

  • And this allows us to solve the problem using standard graph

  • traversal algorithms.

  • Pictured here is an example calibration sequence

  • for two qubits.

  • And this network is really a graph

  • distilling decades of research from groups

  • all around the world learning how

  • to make these processors work.

  • In this graph, each node represents

  • a physics experiment, where we acquired data, and then

  • the analysis that we use in order

  • to figure out what the data says and decide what to do next.

  • This is an example for two qubits,

  • but there are literally thousands of these nodes

  • when we want to calibrate Sycamore.

  • So it's crucial that we use algorithms

  • to work through this graph, to calibrate the device,

  • and then maintain the calibrations.

  • To give a flavor of how this works,

  • we start on the left learning some device parameters.

  • And as we work to the right, we iterate back and forth

  • between single-qubit gates and readout

  • until eventually we get around to two-qubit gates

  • at the very end.

  • A key step in setting up our device

  • is choosing a frequency for each of the qubits.

  • And we're going to kind of follow a two-step program here.

  • First, we're going to measure the qubit lifetime

  • as a function of frequency.

  • This is an example of data set for one qubit from Sycamore.

  • And then we're going to use that data and all the information

  • we know about our device and how it performs in order

  • to choose optimal frequencies for each qubit.

  • This is a pretty rich subject, but let me just give you

  • a flavor for how this precedes.

  • For example, each qubit is least sensitive to control noise

  • at its maximum frequency.

  • So we might want to park all of the qubits

  • at their maximum frequencies, although there

  • is some variation in those frequencies across the device.

  • But then if we consider pulse distortions,

  • for a two-qubit gates, it's actually nicer

  • if the qubits are close to their neighbors

  • so they don't have to move very far in frequency

  • in order to interact.

  • So this will kind of smooth out this shape

  • here so that the qubits will be close to their neighbors.

  • But you don't want to be too close because there

  • can be stray interactions, parasitic couplings

  • between qubits and their neighbors and next nearest

  • neighbors.

  • And this might suggest kind of a checkerboard type pattern

  • like we see here.

  • And finally, we include the information

  • from this qubit lifetime versus frequency data

  • to find an optimum where we expect each qubit to have

  • good performance.

  • And solving this problem is not a trivial matter.

  • It's very difficult for a human to solve it.

  • But we have developed good heuristic algorithms

  • that find us good solutions to this problem.

  • Now, once we've set up all of our qubits

  • at their desired frequencies, we need to actually carry out

  • the calibrations.

  • And I'm just going to share with you

  • a couple of nice snapshots of what that calibration

  • data looks like throughout the process.

  • And an early crucial qubit experiment

  • is Rabi oscillations, where we oscillate back and forth

  • between the qubit zero state and one state.

  • And this is very nice because it allows

  • us to choose the initial amplitude for a pi

  • pulse for our qubits.

  • This is an example for one qubit.

  • And here we plotted the data for all 53 qubits

  • that we're measuring on this device.

  • And we can see, although there is some diversity in these data

  • sets, our algorithms can readily pick out

  • this first oscillation that gives us one of our earliest

  • calibrations.

  • Another critical calibration is readout.

  • So an example experiment here is readout clouds,

  • where we prepare each qubit in the zero state

  • and then measure the readout signal.

  • That's the blue cloud.

  • And then we do the same preparing the qubit in the one

  • state using our pi pulse, and that's the red cloud.

  • And we want separation between these two clouds

  • in order to achieve single shot readout of the qubit state.

  • This is an example for one qubit and across the full device.

  • I'll mention-- I'm not going to go deeper into readout,

  • but this is quite a sophisticated subject.

  • And managing to achieve good readout on all the qubits

  • simultaneously is very challenging.

  • And even just benchmarking the readout

  • for 50 qubits at the same time is not a trivial task, either.

  • The final calibration data I'll share with you

  • is for calibrating two-qubit gates.

  • And I'll talk a little more about two-qubit gates

  • in a moment.

  • But basically, we want an iSwap between the two qubits,

  • where we have a resonant exchange of the qubits'

  • photons.

  • So what we do is for each pair, we

  • tune the coupler amplitude so that we have the correct amount

  • of coupling between the two qubits, about 20 megahertz

  • in this case, so that they'll completely

  • swap a single photon.

  • And that's that first maximum there.

  • And here we've plotted 86 of these plots.

  • It's one for each pair of qubits across the device.

  • Now, I said I wanted to talk a little bit more

  • about two-qubit gates on Sycamore.

  • Our basic idea is to use fast resonant gates,

  • where we pulse the coupling on for around 10 to 20 nanoseconds

  • so that the two qubits can interact.

  • And for two-transmon qubits, the natural interactions

  • that will take place are an iSwap interaction

  • and a conditional phase.

  • And we can map the gates onto this two-dimensional space

  • here with those two axes.

  • And you can see some of your favorite familiar gates,

  • like iSwap square root iSwap and CZ on this plot.

  • Now, for quantum supremacy, we did something a little unusual.

  • We did what we would call an iSwap-like gate

  • on all of our pairs.

  • This is the data that I was just showing you.

  • And we actually determine the unitary specifically

  • for each pair of qubits.

  • But fear not, although this is a little unorthodox,

  • you can take two of those iSwap-like gates

  • and compile them into a CNOT, which

  • is classic textbook gate, along with single qubit rotations.

  • I'll mention as well, as a part of his PhD thesis,

  • Brooks Foxen actually filled in this whole space

  • for a pair of qubits and was able to execute an arbitrary

  • gate in this space.

  • And you can read about that at his paper here.

  • Now, suppose we've tuned up all of our two-qubit gates

  • and we want to benchmark them to figure out

  • how well we're performing.

  • There are many different techniques to do this,

  • but I'm going to focus on one of those, which is cross-entropy

  • benchmarking, because it closely relates

  • to what we do in the quantum supremacy experiment.

  • The first step is to choose a bunch of sequences

  • that we're going to measure.

  • And these are sequences of our two-qubit gate interleaved

  • with randomly selected single-qubit gates.

  • Like depicted here.

  • We'll then take each of these sequences

  • and run them on our quantum processor

  • maybe a few thousand times each in order

  • to compute these experimental probabilities associated

  • with each of these sequences.

  • Now, on the other hand, we can also use a classical computer

  • in order to basically run the same circuit

  • and come up with the theoretical expected probabilities.

  • And those depend on the unitary that we're trying to run.

  • But say we have an idea of what unitary

  • we mean to run with our two-cubic gate.

  • So we have two probability distributions.

  • One that we measured with our experiment.

  • And one that is computed.

  • And we can compare these two probability distributions

  • to estimate the fidelity, which is

  • like how well are we executing the expected quantum gate.

  • And this is where cross-entropy actually

  • comes in because that's the metric we

  • use to compare the two probability distributions.

  • There's something special here.

  • We can have a feedback loop between these two sections

  • in order to find the unitary model that

  • maximizes this fidelity.

  • And when we do that, we're finding the two-qubit unitary

  • that most precisely expresses what exactly

  • we're doing in our two-cubic gate.

  • So we're basically learning what is the two-qubit gate

  • that we're actually doing.

  • This is very useful because it helps

  • us identify coherent errors.

  • For example, suppose you were trying to do a CZ gate

  • and it turns out that the optimal unitary actually has

  • a little bit of swapping in it.

  • This is telling you where your errors are coming from so

  • that you can learn from that and make your calibrations better.

  • In the case of quantum supremacy,

  • we use this tool to identify what

  • is the unitary that each qubit pair is actually running,

  • and we're going to use that information when

  • we do that experiment.

  • There's another important detail here,

  • which is simultaneous operations.

  • And so, in addition to benchmarking each qubit one

  • at a time or each pair one at a time,

  • we get a benchmark all of the qubits operating

  • at the same time and all of the pairs operating simultaneously,

  • as well.

  • This kind of simultaneous operation

  • is essential to near-term applications

  • because, because of noise, we have limited algorithm depth.

  • It's also a necessity for our long-term plans

  • for quantum error correction.

  • And the key question here is, does the processor

  • work when we're doing operations simultaneously?

  • There is one other detail that I want to highlight here.

  • You can't actually run all of the pairs

  • simultaneously because each qubit participates

  • in more than one pair.

  • So we divvy them up into different layers

  • that we can benchmark simultaneously.

  • So let's look at some benchmarking

  • results from Sycamore.

  • And I'll start with the single-qubit gates.

  • And we're plotting the distributions

  • of errors across the device for 53 qubits on the left.

  • So if we do the single-qubits one at a time,

  • their gates have an error of about 0.15%,

  • which is pretty good.

  • And if we do them all simultaneously,

  • it only modestly increases to 0.16%.

  • This is great because it suggests that there are not

  • stray interactions between the two qubits

  • or crosstalk that would cause these gates to mess up.

  • As we turn to the two-qubit gates, in the isolated case,

  • we see an error of 0.36%, which is really outstanding.

  • And in the simultaneous case, this modestly

  • increases to about 0.6%, which we're really

  • still quite proud of.

  • And this increase in error could be attributed, for example,

  • to stray interactions between pairs

  • of qubits that are becoming slightly

  • entangled with each other.

  • We also have readout, which I won't delve into too deeply

  • here, where we have a few percent error per qubit.

  • I'll make a note for this simultaneous two-qubit gate

  • benchmarks, the unitaries of the two-qubit gates

  • actually change slightly when we run them all at once.

  • And we can measure that and take it

  • into account in our experiments.

  • Instead of plotting the distributions,

  • we can also plot these single- and two-qubit gate errors

  • on the device layout itself.

  • And we were really excited when we got this to work

  • and got to see this for the first time.

  • These are the errors associated with the simultaneous

  • operations for each qubit.

  • And also each coupler is colored in with the simultaneous error

  • for each two-qubit gate.

  • Now, this was basically looking at pairs one at a time,

  • not having entanglement across the whole device.

  • But an important thing that we want to do

  • is to evaluate the performance of the full processor doing

  • a realistic algorithm.

  • And once you have 50-plus qubits,

  • this technique of cross-entropy benchmarking we were using,

  • where we were comparing probability distributions,

  • is no longer tractable.

  • And that's because of the simple fact that two to the 53

  • is about 10 to the 16 different amplitude

  • or probabilities that we would be trying to deal with.

  • And it is simply not possible to resolve

  • all of those probabilities.

  • So instead, we're going to reframe

  • the question of cross-entropy benchmarking to,

  • can we sample from the expected distribution?

  • So we'll get samples, bit strings,

  • and we'll compare them to the probabilities

  • that we're expecting based on what we thought we were doing.

  • In this case, we'll make some observations,

  • like maybe a million or so bit strings for a circuit,

  • and then we can take the bit strings that we actually

  • observed and compute the expected probability,

  • the theoretical probability that's

  • associated with each one.

  • And this allows us to estimate the fidelity using

  • linear cross-entropy.

  • That's what this equation is here.

  • This is the only equation in our paper, I think.

  • And this fidelity stated plainly is basically

  • how often we sample high-probability bit strings.

  • With that, let's move on to the final part

  • of my presentation, which is quantum supremacy itself.

  • So what we need, if we're trying to pit our quantum processor

  • against a classical supercomputer,

  • is a well-defined computational task.

  • And the task that we chose is to sample

  • the output of a pseudo-random quantum circuit.

  • And the point here is that for a sufficiently large circuit,

  • the classical computing cost of performing this task

  • becomes prohibitively large.

  • And to give you an idea of what these circuits look like,

  • this is very similar to what we were doing before,

  • but now we're getting entanglement

  • across the whole device.

  • So we have layers of randomly selected single-qubit gates

  • and then layers of two-qubit gates.

  • There is a bit of a problem here that you

  • might be picking up on based on something

  • that I said a couple of minutes ago.

  • I said that we're going to observe a bunch of bit strings

  • and then compute the ideal or expected

  • theoretical probability associated with each one.

  • So on the one hand, we want to beat classical computers.

  • But on the other hand, this test seems

  • to need them to check our fidelity

  • to see if our quantum computer is doing the right thing.

  • And we can look at that schematically

  • with this cartoon, where we plot fidelity

  • as a function of the computational difficulty

  • for our quantum processor.

  • You can think of that like the number of qubits, for example.

  • And as we add in more qubits, this fidelity

  • goes down because there are more opportunities

  • for errors to happen.

  • But we can still check our results

  • and see what the fidelity is using this technique.

  • But at some point, we reach this boundary

  • where we're no longer able to check our work.

  • So this is a problem, but we have a solution to it.

  • And that is to control the difficulty of the circuits

  • that we're executing.

  • The most natural and obvious way to do this

  • is by changing the size of the circuit.

  • So a smaller circuit will be much easier to run classically.

  • But there are some more subtle techniques

  • that allow us to run large circuits

  • and still check our work.

  • One of them is to remove a few gates.

  • Instead of running every single gate in the circuit,

  • we take a cut down the middle of the device

  • and remove just a handful of gates

  • from the very beginning of the computation.

  • This decreases the entanglement between the two halves

  • of the device and makes it much easier to simulate or compute

  • with a classical computer.

  • But it's still essentially the same for a quantum processor

  • because we've just removed of gates from the beginning.

  • Another even more subtle way to change this difficulty

  • is by changing the order in which we execute the gates.

  • It turns out if instead of doing this hard sequence,

  • we do this very subtly different sequence of gates,

  • there is a slight simplification in the way

  • that the entanglement propagates across the device that

  • can be exploited in order to perform

  • the classical computation more efficiently.

  • So the idea is to use these circuits

  • at the top as a proxy for our hardest circuits,

  • which have all of the gates running in the difficult order.

  • And what we'll be able to do is evaluate our performance

  • with these circuits and then infer

  • what our performance is on these, which

  • are very similar from the point of view

  • of the processor, the quantum processor.

  • Now let's look at what this data should look like.

  • So before we run the experiment, let's

  • make a model for what we expect to happen.

  • And we'll make a very simple model

  • here where we say our fidelity at the end

  • is going to be the product of the fidelity of each

  • and every gate that we're going to execute

  • times the fidelity of the readout at the end.

  • So this is using the numbers that we

  • were looking at in the previous section on benchmarking

  • in order to estimate how well we expect the device to do.

  • On the left of this plot, we have a dozen qubits.

  • We're going around 14 cycles.

  • So there are a couple hundred operations that we're doing.

  • And the fidelity of the full circuit on the full system

  • is about 40% is what we expect.

  • And that's actually really good for hundreds of operations.

  • As we move to the right, we add more and more qubits.

  • So there are more opportunities for errors.

  • And this fidelity will decrease.

  • For example, at 50 qubits, it's at about 1%,

  • which is still large enough that we can measure it reliably.

  • So this is our model.

  • This is what we expect to happen with a very simple model.

  • Now let's look at some results from experimental data.

  • And there are two data sets that I'm plotting here.

  • One uses the simplified circuits,

  • where we've removed a few gates from the very beginning

  • of the circuit.

  • And another uses the full circuit, where

  • all the gates are present.

  • But in this data, we're using the easy ordering of the gates

  • so that there's kind of a backdoor

  • so that the classical computer can still run this computation.

  • What we see is a remarkable agreement between all three

  • of these.

  • First of all, our prediction, our very simple model,

  • matches the data extremely well.

  • And this is great because it means

  • that our very simple error model is able to reflect the system

  • performance going from a dozen qubits up to more

  • than 50 qubits.

  • Another crucial lesson here is that the simplified circuits

  • and full circuits are also consistent with each other.

  • And this makes sense because for the quantum processor,

  • they're only slightly different.

  • There's just a few gates missing for the simplified circuits

  • out of perhaps 1,000 or more.

  • But it's great to see experimentally that these

  • agree with each other.

  • One last note here, although these are the easy circuits,

  • once we get to 53 qubits, it still

  • becomes pretty computationally intensive

  • for the classical computer to check our work.

  • For example, that last red data point

  • took about five hours to verify with a million cores

  • on a supercomputer.

  • But let's pull out all the stops now and use our hard circuits.

  • And this is what that data looks like.

  • You'll notice that there's something missing here.

  • We no longer have the full circuits represented

  • because although we took that data, we cannot process it.

  • So we have our model prediction, whereas we increase

  • the number of cycles, how many operations we do,

  • the fidelity decreases.

  • And we have the data points from our simplified circuits.

  • Each of those data points represents 10 circuits,

  • a total of 10 million samples, and took our quantum processor

  • about 200 seconds in order to execute.

  • And I can summarize the last data point.

  • It has 53 qubits, 20 cycles, over 1,000 single-qubit gates,

  • and 400 two-qubit gates.

  • We predict from our model a fidelity

  • of 0.2%, which is remarkably consistent with what we observe

  • for our simplified circuit.

  • I'll mention as well that this data is all freely available

  • online at this URL.

  • The last chapter in this story is the classical competition.

  • And an important lesson here is that all

  • known classical algorithms to perform this task

  • require memory or runtime that is

  • exponential in the number of qubits.

  • In fact, they all require exponential runtime.

  • And in order to test this and see how well we're performing

  • compared to classical supercomputers,

  • we actually ran benchmarks on several supercomputers

  • like these pictured here.

  • There are a couple of algorithms that I want to highlight

  • that we considered.

  • One is the Schrodinger algorithm.

  • This is what you might come up with if you understand quantum

  • mechanics and want to run a simulation of a quantum

  • circuit.

  • Basically, you put the full wave function

  • into the memory of your computer and then do some linear algebra

  • to do its unitary evolution.

  • And this is pretty rough because it

  • has a memory requirement that is exponential in the number

  • of qubits.

  • In this case, it would require about 65 petabytes

  • in order to run this computation on 53 qubits, which

  • exceeds the memory of any computer in the world.

  • I'll also mention that the runtime

  • is exponential in the number of qubits,

  • although it is linear in the number of cycles.

  • Another algorithm that we explored

  • is the Schrodinger-Feynman algorithm.

  • And this is a really nice algorithm

  • because it allows us to trade off

  • between the memory requirement space and the runtime.

  • And instead of having the full system in memory,

  • we just have subsystems in memory at any given time.

  • And basically what we do is we see how much memory we

  • have access to and use as much of it

  • as we can in order to make the runtime as short as we can.

  • And in the case of solving this particular computational

  • problem, we're using around a petabyte

  • of memory, which is a huge amount but something that's

  • totally achievable for a supercomputer.

  • But this trades off with the runtime.

  • We estimate that to solve the same problem

  • that our Sycamore processor did in 200 seconds

  • would take thousands of years.

  • And this runtime is also exponential now

  • in the number of cycles that we perform.

  • And let me emphasize here that these numbers, these estimates

  • are based on real benchmarks that we performed

  • using our quantum circuits, doing subsets of them

  • on the Summit supercomputer.

  • So let me conclude now.

  • We looked first at the Sycamore processor

  • and the crucial hardware infrastructure that makes

  • these experiments possible.

  • We then reviewed how to calibrate and benchmark

  • this processor and compared it to the world's fastest

  • supercomputers to demonstrate quantum supremacy.

  • I want to thank one more time this huge team

  • that worked so hard in order to make these results possible.

  • And I'm really honored to be a member of this team

  • and to share these results with you today.

  • Thank you.

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