YouTube Transcript:
Quantum sensing of noise based on Machine Learning (Shreyasi Mukherjee)

Skip watching entire videos - get the full transcript, search for keywords, and copy with one click.

Video Transcript

Video Summary

Summary

Core Theme

This thesis explores the use of machine learning, particularly supervised learning, combined with quantum control techniques to characterize and classify environmental noise in multi-level quantum systems. The research aims to develop robust strategies for understanding noise correlations and statistical properties, which is crucial for advancing quantum technologies.

Mind Map

Click to expand

Click to explore the full interactive mind map • Zoom, pan, and navigate

is going to perform a final examination.

So I leave the floor to the commission

let's say.

>> Okay. Okay. Thank you. So welcome of course.

course.

>> Thank you.

>> And u so we give you 25 minutes to make

a speech and after that we will have 15

minutes discussion section. >> Okay.

>> Okay.

>> So I will take the time.

>> Okay. Okay.

>> So when it is 5 minutes left I will

speak. Okay.

>> Okay. Um

>> so please start.

>> Okay. Um hi everyone. So I am Soshi

Mukharji. Um and first of all I thank

the committee and all for being present

here and uh I thank to my supervisor

professor Luigi Dan Nali. Um I thank you

for everything especially for being so

patient with me. And um I also thank to

my uh co-supervisors u professor Mao

Patnostro from University of Palmo and

Dr. Fabio Cherina from Leonardo SPA for

their cooperations

and u a special thanks uh goes to our

group leader professor Fali who has

always been very supportive and

encouraging. And at the end I um I am

also grateful to my family and the and

my colleagues here who made the state

who made my stay in Italy memorable.

So um okay today I'm going to talk about

my thesis titled as quantum sensing of

noise based on machine learning. So um

we know that uh exploiting coherence

properties of quantum systems such as

superposition, entanglement is essential

for achieving quantum advantage.

But the presence of the environmental

noise can disrupt these properties as it

causes decoherence and thereby reduces

the fidelity of uh quantum operations.

Um we do have some noise mitigation

strategies for example dynamical

decoupling or passive error avoidance

etc. But all these methods rely highly

on the knowledge of the noise itself or

on the characteristics of the noise. So

if we want reliable quantum technology

then noise characterization is

essential. Um even though single cubit

noise characterization have has been

well established um um which led to

quantum operations uh beyond uh error

correction threshold which have been

shown in many different works but still

it's a challenging task in multicubit

system because here the special and

temporal correlated noise can really uh

have some uh detrimental effects. In

fact, specially correlated noise um can

affect badly uh quantum error

correction, which is one of the pillars

of quantum computing.

Um and in the last decade, machine

learning has emerged as a great

diagnostic tool. And in this thesis

work, our goal is to enable a robust

noise classification or characterization

strategy based on on their temporal,

spatial and energy correlations in

multi-level quantum systems by combining

quantum control and machine learning

especially supervised learning.

Um so I I will mainly talk about uh

three main main works that uh we have

done during my PhD period. The first one

is classification of noise correlations

in a three-level system. The second is um

sorry the second is two cubit quantum

sensor for detection of noise

correlations. The third one is detection

of noise gausianity in quantum systems

and at the end I will show you the

conclusions and uh discuss some future perspectives.

perspectives.

So let's move to the first one uh which

is classification of noise correlations

in a three-level system with machine

learning. Here we considered a

three-level system with basis 0 1 and

two. The system is driven by two time

dependent pulses omega p the pump pulse

that couples the states 0 and one uh and

the stock's pulse omega s which couples

the states uh one and two. So we have a

lambda system.

It is also subjected to diagonal noise.

Um and the parameters here are delta P

and delta which are the single and two

photon D tunings respectively. And X1

and X2 are two stochastic processes that

represents the noise.

So basically the role of the noise here

is to induce fluctuations in the energy

levels and based on the characteristics

of these two stoastic processes we will

define different noise classes that will

eventually be distinguished by the

machine learning tool.

So um to control the dynamics of the

system here we exploit um stimulated

ramen diabetic passage tab or in quantum

dot system it is called sitta protocol

which is an diabetic protocol uh which

allows us to transfer the population

from state zero to state two without

populating state one. This protocol is

well known for its robustness and high

fidelity. And to achieve this efficient

population transfer, it is required the

two photon resonance condition which

implies that the parameter delta has to

be nearly equal to zero. And then in

this case, one of the instantaneous

again states states of the system is a

dark state which does not have a

component along state one.

This protocol is also based on the

application of counterintuitive pulse

sequence. Which means that first we

apply omega s pulse that couples the

states one and two and then while

gradually turning it off we turn on

omega pulse which couples the states uh

zero and one. And in this situation if

the system evolves a diabetically

starting from state zero then it will

always follow the dark state and that's

why the population will be transformed

from 0 to two without populating state one.

one.

Here I want to point out two things.

First um uh here we define the

efficiency of the protocol by the

parameter s which is the population of

state two at the end of the time

evolution of the system. This parameter

is important because later we will see

that we will use this to train our

machine learning model. And the second

point is um our main goal here is not to

achieve an efficient population transfer

but we are just exploiting this protocol

in order to get information about the

noise that affects the system. In fact

we will see that we will get more

information from the imperfections.

Um so our main goal here is to

distinguish among five different types

of noise uh with the help of machine

learning. Among these five types there

are three non-marovian quasistatic noise

and two marovian noise. Here quasyatic

implies that both the random variables

x1 and x2 remain constant during a

single trajectory but change their

values in the next trajectory.

And uh for the non-marovian uh noise

case uh based on their energy

correlations we have three subclasses.

First the correlated noise where x2 is

equal to ea x1. The correlation

parameter I here always is positive. The

second class is anti-correlated noise

where it always assumes negative values.

And the third class is uncorrelated

noise where x1 and x2 are completely

independent of each other.

And for the marovian noise uh it is

delta correlated in time and as per the

energy correlations we have correlated

and anti-correlated noise.

Now uh for the non-marovian

uh noise um

um okay now for the non-marovian noise

we can for a single noise realization we

can solve the dynamics of the system

using time dependent stringer equation

and we can calculate the steerup

efficiency by taking average over all

possible realizations of the noise and

for the marovian case um as the system

is ruled by zero mean and delta

correlated noise. In this case, we are

able to derive a lean blood master

equation and the efficiency can be

calculated using the formula below

and uh um so we propose the following uh

protocol. As we will use supervised

learning which requires label data set

and to generate this um we apply syup

protocol under three different driving

conditions. when omega pax is equal to

omega s max. When omega pax is greater

than omega s max and when omega pax is

less than omega s max where this omega

pax and s max are the amplitudes of the

pump and stokes pulses and the

efficiencies calculated under these

three driving conditions goes as input

to the neural network. And of course the

labels are the five different noise

classes that I already mentioned. And in

fact in the output of the neural network

these are the probabilities that the

noise belongs to any of the five classes

that we have.

Now um this is um this is uh the main

result here. Each diagonal entry

represents the percentage of accurate

classification where the of diagonal

entries represents the um the the uh

percentage of error. Um and in the

y-axis here actually we plotted the true

levels of the noise in and in the x-axis

we plotted the predicted levels and from

here actually we can get three messages.

First that the neural network is able to

distinguish very well the non-marrobian

and marovian noise and the second

message is it is also able to

distinguish um very well almost with

100% accuracy the subclasses of the

non-marovian noise the energy

correlations of the non-marovian noise

and the third message is it fails to

distinguish the energy correlations uh

of the marovian noise and in fact we can

get an overall classification accuracy

of 80%.

And um if we and I mean uh if we simply

merge the two marovian uh subclasses and

make it a single one then from the

figure right here we can see that again

we uh achieve an classification accuracy

around 99%. And in the figure below here

uh here we plotted the training history

of the neural network considering both

four and five noise classes uh with

respect to the number of epochs. In the

figure left here we plotted the accuracy

and in the figure right here we plotted

the cost function.

Now until now we considered the ideal

efficiency measurement. Then uh we were

also interested to see how the

classification accuracy changes with

respect to the um number of finite

number of projective measurements and we

saw that around 2,000 measurements it

already reaches the the accuracy already

reaches the ideal case. So even if we

have a small statistical error in our

measurements still uh this methodology works.

works.

Now let's move to the second work um

which is 2 cubit quantum sensor for

detection of noise correlations by

machine learning. Here we u proposed a

design of 2 cubit sensor uh to detect

spatial and temporal correlation of

noise by expanding our ideas which is

which is used in the previous work.

And here we have two cubits with

energies epsylon 1 and epsylon 2

respectively. And they are coupled with

each other by xxising interaction. And

they are also driven by u two local

fields w1 and w2 and are also subjected

to local defasing noise.

So here then the question arises is it

possible to apply stup like protocol

also in this case. Um so let's first

look at the structure of the system. So

for simplicity we considered um that the

two cubits are identical so they have

the same energies and we can diagonalize

the system Hamiltonian into two

invariant subspaces. One is with even

parity, another one is with odd parity

and the corresponding values and states

are given in the table here. The even

parity states are um one 0 and one and

the odd parity states are three and two.

And uh now if we drive the two cubits

symmetrically so um we have so we have

w1 is equal to w2. Then the state three

is uncoupled with the rest and we are

left with three levels 0 2 and one which

is exactly what we need for the

application of syrup. Furthermore,

if we apply a two-tone pulse um where

the frequency small omega s is in

resonance with the transition 2 to1 and

small omega p is in resonance with the

transition 0 to2 and we perform rotating

web approximations um by neglecting the

fast oscillating terms and the terms

oscillating with uh g are neglected in

strong ultra strong coupling regime.

Then we have the ladder configuration

and we have exactly the steerup

Hamiltonian. Okay. But this is um just

uh this is the ideal case just for the

illustrative purpose. But anyway for our

simulations and analysis we use the full

system without any approximation and in

fact we get more information from the

non idealities.

um and uh in fact the presence of noise

disturbs everything. So it induces

fluctuations in the energy levels 0 and

one and also causes coupling between

state two two and three and couplings

between the states zero and one. Uh in

the figure right here we plotted the

populations for the four levels and uh

we see that even if there is a small

amount of noise present the state three

gets populated and this is actually

useful for uh detecting the correlations

uh between the noise and again like the

previous work uh we use the similar

noise uh classes but uh here the the

noise are temporal and specially uh

correlated and also we here we included

the uncorrelated marovian noise. So in

total we have six noise classes and this

is the result. So again we have the

three messages. The neural network is

able to distinguish very well the

non-marovian and marovian noise. The

second message is it is also able to

distinguish the special correlations

within the non-marovian class. And the

third is it it is able to distinguish al

also also the special correlations of

the uh marovian class of course with

certain amount of errors and overall we

can get an classification accuracy of um 86%.

86%.

Okay. So in summary we saw that it is

possible to combine quantum control and

machine learning to detect noise

correlations in multi-level quantum

systems. We exploit uh the sensitivity

of startup or situp protocol for

detecting noise correlations in

three-level system. It is it is possible

to distinguish very well the

non-marovian and marovian uh noise and

it is also possible to uh distinguish

the energy correlations in the

non-marovian class almost with 100%

accuracy but it here it fails to

distinguish the energy correlations in

the marovian uh class. Instead for the

two two cubits uh sensor um the neural

network is able to distinguish also the

space space correlations in marovian

noise uh class with around 80% accuracy.

Now let's uh move to the third um and

final uh work which is m machine

learning approach for detection of noise

gausianity in quantum systems. Um so

until now we did uh noise classification

based on their correlations um

correlations and so the next question

that comes that what is the statistical

signature of the noise sources is it

gausian like it is often assumed in open

quantum system problems or it is non-gausian.

non-gausian.

So a stoastic process is said to be

gausian if it can be fully characterized

by its mean and two time autocorrelation

function. H in this case all the higher

order cumulants vanish. And one of the

examples of this kind of noise is

electromagnetic noise. Instead for the

nonausian noise this is not the case.

The higher order cumulants are non zero

and they can also have relevant effects

in the deep coherence. And uh some

examples of this kind of noise are

impurities and 1 / f noise in

superconducting and semi semiconducting

devices. So note that um noise with the

same power spectra can be gausian or

non- gausian. For example, random

telegraph noise and on stanul and back

noise both of them have um have same two

time autocorrelation function thus the

same spectra but RTN is non-gausian

while O is gausian so they have

different effects on the system for the

RTN the important parameter is the

switching rate while for the stanul and

vectors the important parameter is the

um inverse of correlation time. Here we

plotted uh one realization of both type

of noise and in this work our goal is to

use a single cubit as a probe together

with machine learning to detect

gausianity and characterize these uh noises.

noises.

So here we considered um cubit which is

coupled with n number of bstable

fluctuators each mimicking random

telegraph noise. uh the cubit

Hamiltonian is given by H cis where

epsylon is its energy and delta is the

coupling and the h noise is given by the

random telegraph noise multiplied by

their coupling sum over all random

telegraph noise is coupling by

multiplied by their coupling strength

and here we assume that um the random

variable xt switches between two values

plus and minus one and the switching

rates between these two values are gamma

/ two.

Um now for simplicity we considered

purity phasing case. So we set delta is

equal to zero. And for um n um identical

fluctuators. So if uh the couplings are

the couplings of the fluctuators are the

same and their uh switching rates are

also the same. Then the an analytical

expression for the coherence of the

cubit evolving under n identical rtn

sources is given by this expression here.

here.

And now something interesting happens.

If we increase the number of fluctuators

n and simultaneously decrease the

parameter g which is the ratio between

the coupling and the switching rate such

that ng² is equal to constant then the

cumul cumulative effect of all the rtn

sources becomes equivalent to on stanul

and back noise which is a causian

process and the expression the the

expression for the coherence is reduced

to a form like this. And this is the

exact uh similar form if we consider

that the cubit evolves um under an

ownback noise with mean zero and

exponential correlation time.

Um so here we analyzed two scenarios.

First that the environment is composed

of finite number of identical earth

fluctuators. Here n equal to once means

that the that the noise is strongly non non-gausian

non-gausian

and as we increase the number n it

becomes more and more gausian. So here n

acts as a me measure of gausianity. So

the machine learning task is to infer

two parameters the number n and the

switching rate gamma by observing the

temporal evolution of the system. And in

the second scenario uh we considered a

hybrid uh environment where the cubit uh

where one fluctuator is strongly coupled

with the cubit while the rest is uh

weakly coupled and the cumulative effect

of the weakly coupled ones uh become

equivalent to an onstand backto noise

and in this case actually the

environment has both gaussian and

non-gausian components. So in this case

the machine learning task is to infer

four parameters. The coupling strength

of the strong fluctuator VRTN its

switching rate gamma and the coupling of

the equivalent uh equivalent coupling of

the weak fluctuators V and its inverse

correlation time 1 / C.

And these are the uh results actually.

Here we measured the average of sigma x

at discrete times during the evolution

of the system. And the neural network

here predicts the two parameters n and

gamma. And in the pictures uh right here

we in the y-axis we plotted the

parameters that we want to estimate n

and gamma uh and in the x-axis we

plotted the number of test sample. The

black dots here represent the target

values while the orange dot is the are

the predicted values. And we can see

that the neural network is able to

predict uh the the value of n until 9

around 9. But after that it fails to

estimate the value of n because in this

case the evolution of the cubit becomes

very similar to the gausian uh evolution

and the neural network is not able to

distingu distinguish it anymore and

instead for the gamma uh the switching

rate it uh estimate uh it the neural

network is able to estimate it quite

well. For the second scenario instead we

try to estimate the four parameters as I

mentioned and we see that the most

difficult parameter to estimate is uh

the gamma the switching rate instead for

the other uh parameters we see that it

is able to estimate good good enough. So

um in summary here we saw that we

developed a datadriven framework for

characterizing gausian and non-gausian

noise using a single cubit as a probe.

We saw that uh using supervised learning

it is possible to infer key noise

parameters and we saw that the potential

of um machine learning as a powerful

tool for noise spectroscopy and for uh

outlook we are trying to apply um

unsupervised learning for the first two

um works and for the last work we are

also doing the similar analysis on 1 / f

+ one shops

and these are the publications that I

had during my PhD. The last two works

are not included in my thesis. Uh thank

Click on any text or timestamp to jump to that moment in the video

Most transcripts ready in under 5 seconds

One-Click Copy125+ LanguagesSearch ContentJump to Timestamps

Paste YouTube URL

Enter any YouTube video link to get the full transcript

Most transcripts ready in under 5 seconds

Get Our Chrome Extension

Get transcripts instantly without leaving YouTube. Install our Chrome extension for one-click access to any video's transcript directly on the watch page.

Add to Chrome — Free

Works with YouTube, Coursera, Udemy and more educational platforms

Get Instant Transcripts: Just Edit the Domain in Your Address Bar!

YouTube

←

→

↻

https://www.youtube.com/watch?v=UF8uR6Z6KLc

YoutubeToText

←

→

↻

https://youtubetotext.net/watch?v=UF8uR6Z6KLc

YouTube TranscriptPreparing your results…

YouTube Transcript:Quantum sensing of noise based on Machine Learning (Shreyasi Mukherjee)