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>
</div>
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!
Candidate Profile
By ludmilaasb
