Name: Estimation of statistical significance of quantum supremacy (QuantumCasts)
Uploaded: 2020-04-15T16:15:57.000Z
Duration: 14 min 22 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

and I'm going to talk about the statistical significance

So a quick reminder on statistical significance,

you start with a null hypothesis, H0 or H

null, which means that there's nothing interesting.

And you have a statistic called F, and also

a probability distribution function of F given H0.

Then you go ahead and measure F in your data.

Let's say you come up with a value of F hat,

and the tail probability gives you the p-value.

And if p-value is smaller than a pretty fine significance level

alpha, then we say it is statistically significant.

And for major scientific claims, we usually

for Gaussian, which corresponds to this value.

are we talking about rejecting for a [INAUDIBLE] purpose?

OK so before going to that, I have a new hypothesis

So hopefully, you can help me reject it at the end.

So the null hypothesis for the quantum supremacy--

the value F here is the fidelity of the Sycamore processor

So the first one is that F is consistent with zero.

That means the processor has lost quantum coherence.

And the second one is that F is not zero,

but it's low enough so the classical simulation is easy.

OK, so we want to recheck both of these, no quantum

What we do is, of course, we follow this p-value thing.

And here, apparently, if you could reject the second one,

and we set this threshold to be 0.1%, which

comes from a complex analysis of classical simulations.

So at which value the simulation should be already hard enough?

That means we are significantly above it.

All right, so the tail dr is that with 53 qubits,

20 cycles of circuit, and 3 million samples

per circuit with 10 different random circuits

would come up with an F hat of this value, which

corresponds to a p-value of about 6.4 sigma in Gaussian.

OK, so that, of course, is above 5 sigma, so that's good.

And of course, there is a systematic uncertainty

So we estimated the uncertainty to be 4 times 10

And the p-value with that distribution here of F hat

is estimated to be 2 times 10 to the minus 10,

which corresponds to about 6.2 sigma in Gaussian.

So again, both null hypotheses are rejected.

how we came up with those numbers and this function,

So there are a few factors in coming up with--

First is the distribution function of the H0.

And the third is the distribution around F hat.

First of all, the data set I used for analysis can be

downloaded here, bit.ly/quantum supremacy dataset.

is based on the quantum circuit sampling.

So this is an illustration of a random circuit.

which is a linear combination of, of course,

2 to the n different computational basis states.

So you sample those bitstrings from this n state many times,

and the probability of sampling a particular bitstring

And for random circuit, those probabilities actually

follow a distribution. a so-called Porter-Thomas

And here I'm using a variable called scaled probability,

which is the dimension of [INAUDIBLE] space times

Then the distribution becomes a very simple

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Estimation of statistical significance of quantum supremacy (QuantumCasts)

scale

experiment

random

combination