Candidate profile

Ludmila Augusta Soares Botelho

Departamento de Física - ICEx - Universidade Federal de Minas Gerais

AM

Who

I'm a Scientist!

I?

Martial Artist

Nerd

Woman

Brazilian

Physicist

Diverse

Femminist

Programmer

Gammer

I'm a Scientist!

AM

WHO

I?

Quantum Information Theory

Scientist

Physics

Programming

Mathematics

Writing

Teaching

Comunication

  • MATLAB/Octave
  • Mathematica
  • Bash
  • Python
  • HTMLL + CSS

Programming

  • MATLAB/Octave
  • Mathematica
  • Bash
  • Python
  • HTML + CSS
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        <p>Programming</p>
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        <ul>
            <li>MATLAB/Octave</li>
            <li>Mathematica</li>
            <li>Bash</li>
            <li>Python</li>
            <li>HTML + CSS</li>
        </ul>
    </div>
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Experiment

Data

Quantum Mechanics

Data

Quantum State

Masters Thesis

2-1

$$\vert \alpha \rangle$$

signal

50/50

$$I_{21} = I_1 - I_2$$

Homodyne Tomography

Intensity \(\propto\) Photon number

Quadratures

\hat{n}_1=\hat{a}_1'^\dagger\hat{a}_1' \qquad \hat{n}_2=\hat{a}_2'^\dagger\hat{a}_2'\\ \hat{a}_1'=2^{1/2}(\hat{a}'-\alpha_{LO}) \qquad \hat{a}_2'=2^{1/2}(\hat{a}'+\alpha_{LO}) \\ \hat{n}_{21} = \hat{n}_{2} - \hat{n}_{1} = \alpha_{LO}^*\hat{a}+\alpha_{LO}\hat{a}^{\dagger} \\ \alpha = \vert\alpha_{LO}\vert(\cos{\theta} +i\sin{\theta}) \\ \hat{n}_{21} = \frac{1}{\sqrt{2}} \vert{\alpha_{LO}}\vert \left[ (\cos{\theta} +i\sin{\theta})(\hat{q} - i\hat{p}) + (\cos{\theta} +i\sin{\theta})(\hat{q} - i\hat{p}) \right]\\
\hat{n}_{21} = \frac{2}{\sqrt{2}}\vert{\alpha_{LO}}\vert\hat{q}_{\theta}
\langle{q_{\theta}}\vert\rho \vert{q_{\theta}}\rangle = \frac{1}{2\pi\hbar} \int_{-\infty}^{\infty} W(q_{\theta}\cos{\theta} - p_{\theta}\sin{\theta},q_\theta \sin{\theta} + p_{\theta}\cos{\theta}) \mathrm{d}p_{\theta}

Radon Transform

$$\langle{q_{\theta}}\vert\rho \vert{q_{\theta}}\rangle \rightarrow W(q,p)$$

$$W(q,p) \rightarrow \langle{q_{\theta}}\vert\rho \vert{q_{\theta}}\rangle  $$

?

W(q,p) = \frac{1}{2 \pi^{2}} \int_{-\infty}^{+\infty} \int_{0}^{\pi} pr(x,\theta) K(q\cos{\theta} + p\sin{}\theta -x) \mathrm{d}x \mathrm{d}\theta

Inverse Radon

K(x)= \frac{1}{2} \int_{-\infty}^{+\infty} \vert{\xi}\vert \exp{(i\xi x)} \mathrm{d}\xi

What about more general state?

Or Different types of measurements?

Convex Optmization

min

s.t

$$\rho \succeq 0$$

$$\mathrm{Tr}(\rho) = 1$$

  • Semi-definite programming

  • Fock Basis

$$\sum_{i \in \mathcal{I}} \Delta_i + \delta$$

$${\rho, \Delta, \delta}$$

$$\left\vert \mathrm{Tr}({E_i \rho) -f_i} \right\vert  \leqslant \Delta_i f_i$$

$$i \in \mathcal{I}$$

$$\mathrm{Tr}({ E_i\rho} )\leqslant \delta$$

$$i \notin \mathcal{I}$$

$$\vert q_{\theta}\rangle\!\langle{q_{\theta}}\vert= \sum \psi_n^*(q) \psi_m(q) \exp[i(m-n)]\vert{n}\rangle\!\langle{m}\vert$$

Representations

Discrete

Continuous

Quantum States

Discrete

Continuous

\vert \uparrow \rangle = \begin{bmatrix} 1\\ 0\\ \end{bmatrix}
\vert \downarrow \rangle = \begin{bmatrix} 0\\ 1\\ \end{bmatrix}
\vert 0 \rangle = \begin{bmatrix} 1\\ 0\\ \end{bmatrix}
\vert 1 \rangle = \begin{bmatrix} 0\\ 1\\ \end{bmatrix}

Convex OPTIMIZATION

  • Semi-definite programming

  • Fock Basis

$$\vert q_{\theta}\rangle\!\langle{q_{\theta}}\vert= \sum \psi_n^*(q) \psi_m(q) \exp[i(m-n)]\vert{n}\rangle\!\langle{m}\vert$$


% cleaning yalmip memory
yalmip('clear');

F = class('double');

% defining the SDP variables
Rho = sdpvar(df,df,'hermitian','complex');

% standard constraints
F=[Rho>=0];
F=[F,trace(Rho)==1];

% observables

Obs=projX_LARGE;


Prob = (medidas+noise);

DELTA = sdpvar(length(projX_LARGE),length(projX_LARGE),'full','real');
F=[F,DELTA>=0];

delta = sdpvar(1,1,'full','real');  
F=[F,delta>=0];


for i=1:length(projX_LARGE)
    for j=1:length(projX_LARGE)
        F=[F,trace(Rho*Obs{i,j})<=Prob(i,j)+DELTA(i,j)];
        F=[F,trace(Rho*Obs{i,j})>=Prob(i,j)-DELTA(i,j)];
    end
end

F=[F,trace(Rho*E_n)<=delta];


% cost function
E = sum(sum(DELTA))+delta;


ops = sdpsettings('solver','mosek','verbose',1);
ops.mosek.MSK_IPAR_NUM_THREADS=6;
SOLUTION=optimize(F,E,ops);


disp('DEBUGGING');
problema = double(SOLUTION.problem);
disp(yalmiperror(problema));

Rho = value(Rho);
DELTA = value(DELTA);
delta = value(delta);

min

s.t

$$\rho \succeq 0$$

$$\mathrm{Tr}(\rho) = 1$$

$$\sum_{i \in \mathcal{I}} \Delta_i + \delta$$

$${\rho, \Delta, \delta}$$

$$\left\vert \mathrm{Tr}({E_i \rho) -f_i} \right\vert  \leqslant \Delta_i f_i$$

$$i \in \mathcal{I}$$

$$\mathrm{Tr}({ E_i\rho} )\leqslant \delta$$

$$i \notin \mathcal{I}$$

arXiv:1911.09648v2 [quant-ph]

Add here:

Master's figures from thesis

 

 

 

Article figures

Positive Maps

  • Density Operator -> Moment Matrix
  • Entanglement Witness

(But Not Completely Positive)

Sep

$$\rho$$

$$\mathit{W}$$

Ent

$$M$$

$$\mathit{W}'$$

Did someone say "Applications"?

bosonic systems

bosonic systems

=   continuous variables

innovation

 relevant

urgent

 a robust quantum computing infrastructure

vanguard

novelty

vanguard

innovation

novelty

vanguard

 relevant

novelty

vanguard

 relevant

urgent

novelty

vanguard

 relevant

urgent

 a robust quantum computing infrastructure

Good Quantum Softwares/Computers

... and computational science!

=

Deep knowledge about Quantum Physics

and communication theory, mathematics, etc.

I AM

What

looking for?

I AM

What

looking for?

Some business card?

Thank you!

Dziękuję Ci!

Obrigada!

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