Update README.md

Signed-off-by: Fabiana 🚀  Campanari <[email protected]>

Author: FabianaCampanari

README.md

@@ -1,110 +1,118 @@
+
+ \[[🇧🇷 Português](README.pt_BR.md)\] \[**[🇺🇸 English](README.md)**\]
+
+ <br>
+
+
 # **Great Minds of Quantum Computing**
 
 A tribute to some of the brightest minds who have shaped the field of quantum computing. This repository highlights their fundamental contributions, innovative concepts, and the formulas that made them famous.
 
-
+ <br>
 
 ## 1. Richard Feynman
 ![Richard Feynman](path/to/image/feynman.jpg)
 - **Formula**: \( S = \int \mathcal{L} \, dt \)
 - **Explanation**: Feynman introduced the concept of particle paths using the path integral to describe quantum mechanics. This approach revolutionized our understanding of quantum state evolution.
 - **Contribution**: Feynman is widely recognized for his innovative ideas in quantum physics, particularly regarding the simulation of quantum systems. He proposed that a quantum computer could simulate quantum phenomena that are inefficient for classical simulations.
 
+ <br>
 
 ## 2. David Deutsch
 ![David Deutsch](path/to/image/deutsch.jpg)
 - **Formula**: N/A (universal quantum computing model)
 - **Explanation**: Deutsch developed the theory of quantum computing, showing that a quantum computer can simulate any physical system. He advocates that quantum computing is a tangible reality, not just a theoretical concept.
 - **Contribution**: Deutsch is considered the father of quantum computing, having defined the concept of a universal quantum computer. His ideas paved the way for quantum algorithms and research into quantum technologies.
 
-
+ <br>
 
 ## 3. Albert Einstein
 ![Albert Einstein](path/to/image/einstein.jpg)
 - **Formula**: \( E_k = h \nu - \phi \)
 - **Explanation**: Einstein explained the photoelectric effect, where the energy of electrons is quantized, introducing the idea that light can behave both as a wave and as a particle.
 - **Contribution**: Although Einstein was skeptical about the interpretation of quantum mechanics, his fundamental discoveries, such as wave-particle duality and relativity, laid the groundwork for modern physics and influenced the understanding of quantum mechanics.
 
-
+ <br>
 
 ## 4. Niels Bohr
 ![Niels Bohr](path/to/image/bohr.jpg)
 - **Formula**: \( E_n = -\frac{Z^2 R_H}{n^2} \)
 - **Explanation**: Bohr's model of the hydrogen atom revolutionized physics by quantizing the energy levels of the electron.
 - **Contribution**: Bohr was instrumental in developing quantum theory and proposed the principle of complementarity, which suggests that quantum phenomena can be described by different models depending on the experiment.
 
+ <br>
 
 ## 5. Werner Heisenberg
 ![Werner Heisenberg](path/to/image/heisenberg.jpg)
 - **Formula**: \( \Delta x \Delta p \geq \frac{\hbar}{2} \)
 - **Explanation**: Heisenberg's uncertainty principle establishes fundamental limits on the precision with which we can know a particle's position and momentum.
 - **Contribution**: Heisenberg introduced matrix mechanics, which was one of the first approaches to quantum mechanics. His view that we cannot simultaneously know certain properties of a particle changed how we interpret quantum nature.
 
----
+ <br>
 
 ## 6. Erwin Schrödinger
 ![Erwin Schrödinger](path/to/image/schrodinger.jpg)
 - **Formula**: \( i \hbar \frac{\partial}{\partial t} \psi = \hat{H} \psi \)
 - **Explanation**: Schrödinger's equation is fundamental to quantum mechanics, describing how the quantum state of a system evolves over time.
 - **Contribution**: Schrödinger is known for his contributions to quantum mechanics, especially for introducing the wave function, which provides a probabilistic description of particle behavior.
 
-
+ <br>
 
 ## 7. Paul Dirac
 ![Paul Dirac](path/to/image/dirac.jpg)
 - **Formula**: \( (i \gamma^\mu \partial_\mu - m)\psi = 0 \)
 - **Explanation**: Dirac's equation unified quantum mechanics and relativity, predicting the existence of antiparticles and laying the foundation for quantum field theory.
 - **Contribution**: Dirac is famous for his work that established the basis of quantum field theory, connecting quantum mechanics with relativity, and for predicting the existence of positrons, the electron's antiparticle.
 
----
+ <br>
 
 ## 8. John von Neumann
 ![John von Neumann](path/to/image/von_neumann.jpg)
 - **Formula**: \( \langle \psi | \hat{A} | \psi \rangle \)
 - **Explanation**: Von Neumann formulated the mathematical foundation of quantum mechanics and introduced the measurement theory, which became fundamental to understanding wave function collapse.
 - **Contribution**: He is known for his work on the mathematical interpretation of quantum mechanics, especially formalizing quantum states and measurements.
 
----
+ <br>
 
 ## 9. John Bell
 ![John Bell](path/to/image/bell.jpg)
 - **Formula**: \( |E(a, b) + E(a, b') + E(a, b) - E(a', b')| \leq 2 \)
 - **Explanation**: Bell's inequality is a crucial tool for testing quantum mechanics and exploring non-locality and quantum entanglement.
 - **Contribution**: Bell formulated his famous inequality to show that quantum mechanics predicts correlations between particles that cannot be explained by local theories, leading to important experiments on entanglement.
 
----
+ <br>
 
 ## 10. Peter Shor
 ![Peter Shor](path/to/image/shor.jpg)
 - **Formula**: N/A (factorization algorithm)
 - **Explanation**: Shor's algorithm is a groundbreaking discovery that enables the efficient factorization of integers, challenging the security of current cryptographic systems.
 - **Contribution**: Shor is one of the pioneers in using quantum algorithms to solve complex computational problems, leading to a new field of research in applied quantum computing.
 
----
+ <br>
 
 ## 11. Lov Grover
 ![Lov Grover](path/to/image/grover.jpg)
 - **Formula**: N/A (search algorithm)
 - **Explanation**: Grover developed an algorithm that accelerates search in unsorted databases, reducing time complexity from \( O(N) \) to \( O(\sqrt{N}) \).
 - **Contribution**: Grover's algorithm is a milestone in quantum computing, demonstrating that searching data can be dramatically accelerated through quantum techniques.
 
----
+ <br>
 
 ## 12. Claude Shannon
 ![Claude Shannon](path/to/image/shannon.jpg)
 - **Formula**: \( H(X) = -\sum p(x) \log p(x) \)
 - **Explanation**: Shannon is regarded as the father of information theory, introducing the concept of entropy as a measure of the amount of information in a message.
 - **Contribution**: His theories laid the groundwork for digital communication and cryptography, also influencing research in quantum computing regarding information transmission.
 
----
+ <br>
 
 ## 13. Alexander Holevo
 ![Alexander Holevo](path/to/image/holevo.jpg)
 - **Formula**: \( I(X:Y) \leq S(\rho) \)
 - **Explanation**: Holevo's bound establishes limits on the information that can be extracted from a quantum system, influencing the development of quantum communication protocols.
 - **Contribution**: Holevo significantly contributed to quantum information theory, establishing foundations for understanding the potential of quantum communication and data compression.
 
----
+ <br>
 
 ## Contributions and References