Quantum Logic Gates 2 – Pauli Gate

Following the series “Quantum Logic Gates”, let’s talk today about the most intuitive of all quantum gates, the quantum logic gate created by Wolfgang Pauli that has his name. There are 3 kinds of them: Pauli X, Pauli Y and Pauli Z.

Wolfgang Pauli, creator of Pauli’s matrix

Pauli X Gate or NOT Gate

In essence, the quantum logic gate NOT, also known as Pauli X gate acts identical to the classic logic gate NOT. As we can see in the diagram below, two inputs, with their respective values of A|0> and B|1>, have their outputs inverted, going to A|1> and B|0>.

This gate, which acts on only a single Qubit, has the diagram below used to represent it in a quantum circuit. The actuation of this gate is equivalent to a rotation of 180º, or π radians, on the x axis of the Bloch sphere, which is a representation for Qubits that we have already covered in this post and in this one as well.

In short, the quantum logic gate NOT or Pauli-X gate, inverts the logical value of an input |0> to |1>, and an Input |1> to |0>. It receives this “Pauli X gate” name, on account of the matrix used to represent it, which is the matrix of Pauli:

The author of the bible of Quantum Computation, “Quantum Computation and Quantum Information”, Michael A. Nielsen, released a video on youtube telling us a little more about this logical gate, as we can see below:

 

Pauli Y Gate

The quantum logic gate Pauli Y, acts on a single Qubit. The actuation of this gate is equivalent to a rotation of 180º, or π radians, on the y-axis of the Bloch sphere, transforming a value of |0> to i|1> and a value of |1> to –i|0>. It receives the name of Pauli Y gate, by the matrix of Pauli that represents it:

It is drawn with the following diagram, in the quantum circuits:

In this video below, we can see around 25 seconds the action of the Pauli Y gate in a Bloch sphere:

 

Pauli Z gate

Just like its sisters, Pauli Y and Pauli X, this gate acts on a single Qubit. The actuation of this gate is equivalent to a rotation of 180º, or π radians, in the Z axis of the Bloch sphere. It maintains the initial state |0> unchanged and maps |1> to -|1>. Because of its nature, it is also called a phase-flip gate / phase-shift gate, a special case of this quantum gate category. It receives the name of Pauli Z gate, because of the Pauli matrix that represents it:

It is drawn with the following diagram, in the quantum circuits:

In this video below, we can see around 28 seconds the action of the Pauli Z port in a Bloch sphere:

 

That’s all for now folks! Next week we will talk about Fredkin and Toffoli gates.

Reference:
Série: Portas lógicas quânticas 2 – NOT gate
Série: Portas lógicas quânticas 3 – Pauli Y gate
Série: Portas lógicas quânticas 4 – Pauli Z gate

Quantum Logic Gates 1 – Genius At Work!

In the classical world, so-called logic gates make up circuits, which are the basis of all computing. Logic gates are essentially transistors that allow or not the electric flow of energy, which associated in different ways implement a boolean logic that allows to create diverse operations.

Integrated Circuit

Before we enter the dimensional portal of quantum bizarre, we will review some concepts of classical computation. Let’s look at some of the main classic logic gates:

Book Review – Quantum Computers

Jon Schiller’s Quantum Computers book, released in 2009, is a good study for those who want to learn more about quantum computing. The book, available only in English through Amazon in this link, brings several basic knowledge, and some advanced, within the thematic of quantum computing.

Jon Schiller Book

The book was born out of a lecture on quantum computing, which the author attended at a seminar at the California Institute of Technology, Caltech, which prompted curiosity, resulting in a survey of academic articles, and searches on google, resulting in the book.

The book is divided into 9 main chapters and 4 appendices, being:

• Chapter 1: Introduction
• Chapter 2: How a Quantum Computer Works
• Chapter 3: Timeline and references to quantum computers
• Chapter 4: How Quantum Computers Differ from Classic Computers
• Chapter 5: What problems can a quantum computer solve
• Chapter 6: What dangers exist for privacy with quantum computers
• Chapter 7: How Quantum Computers Store Data
• Chapter 8: When you can buy a quantum computer
• Chapter 9: IBM’s efforts in quantum computing
• Appendix A: Definitions used in quantum computing: Shor Algorithms
• Appendix B: Glossary of terms of quantum computing: Entaglement, Heisenberg’s uncertainty principle and Qubit
• Appendix C: The Einstein-Podolsky-Rosen Paradox (EPR)
• Appendix D: What’s new in the internet about quantum computers

The topics of this book will be further detailed in future posts. This book is very rich in diverse information, however in some points it goes deep in the mathematical aspect that can take some lay people off the subject. In some aspects the book is dated, due to developments in the area, but for the most part the book brings many relevant topics and a relatively accessible language.

Look forward to the next posts in which we will use this book (and others) as a reference for the study of this grand and intriguing universe of quantum computing!

Quantum hugs to all!

Reference:
Resenha do Livro “Quantum Computers”

Book Review – Programming The Universe

The book “Programming The Universe” was written by Seth Lloyd, professor of the famous MIT. Having worked with big names in physics like Murray Gell-Mann, Lloyd brings several considerations from his view of quantum physics and quantum computing in his book. Available in amazon at this link.

Seth Lloyd’s Book

The main thesis of the book is that the whole universe can be understood as a large quantum computer that computes and generates information in the interactions of its fundamental particles. To explain this thesis, Lloyd attempts to conceptualize in his book the various fundamentals of computation, quantum mechanics, complexity theory and tries to unite the fundamentals of computation with those of quantum mechanics to try to explain a little the history of the universe, by Big Ben, watching the universe as a great quantum computer.

A big Quantum Computer named universe

Lloyd demonstrates in his book that the universe computes, that is, does computing, recording and transforming information into its expansion movements, through the laws of entropy, which according to the book: “If we can look at matter on the atomic scale, we could see the atoms dancing randomly. The energy that drives this randomness is called entropy. Entropy is the information required to specify the random movements of atoms and molecules, very small movements for us to see. Entropy is the information contained in a physical system that is invisible to us.”

Earth = MC²?

Lloyd passes in his books on the various quantum foundations, such as “phantasmagoric action at a distance”, the heisenberg uncertainty principle, the particle / wave duality of quantum elements, entanglement, the schrodinger cat, and other quantum foundations we are exploring here in this blog.

This was the quantum book hint this time, look forward to more books soon !!

Reference:
Resenha do Livro “Programming the Universe”

Quantum Computing and Business!

In addition to all interest in the advancement of science and new paradigms of computing, quantum computing will represent many new business opportunities for the companies involved. With an eye on the gold mine, IBM, with its IBM Q, is already mapping the possibilities for businesses and companies.

Quantum Mine Gold

With the goal of building a quantum system with a processing power of 50 Qubits, IBM already glimpses possibilities in business in the fields of:

• Medicine: with the possible discovery of new medicines and materials.
• Logistics: with the discovery of ultra efficient paths through their algorithms.
• Financial Services: with the modeling of financial models, investment models and the mapping of risk factors.
• Artificial Intelligence: glimpses the possibilities with massive quantum processing, which will allow extensive searches on images and videos.
• Security Services: Using all the quantum power to keep information and data safe in the cloud using IBM services.

Along with companies such as Samsung, JSR, Honda, Hitachi Metals, Canon and Nagase, IBM has created a consortium to explore and share their research in the field of quantum computing and other areas.

That’s it folks, let’s wait and see what innovative new business will come out of this new quantum model. If with classical computing the IT industry was able to build this incredible world we live today with smartphones, applications and games, the possibilities for the quantum paradigm are unimaginable!

References:
A Computação Quântica e os Negócios!