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A touch of history

Quantum Mechanics as a subject rose from one single question that was bothering Scientists of the time, and is still debatable now.**"Is light a particle or wave"?**

Similar confusion reigned over the nature of electrons, which behaved like particles, but then it was discovered in electron diffraction experiments, performed in 1927, that they exhibit wave behavior. So do electrons behave like particles or waves? And what about photons?

This great challenge was resolved with the discovery of the equations of quantum mechanics. But the theory is not intuitive, and its description of matter is very different from our common experience.

The Bloch sphere is a representation of a qubit

### The Real Deal

The Bloch sphere is a representation of a qubit

Quantum computing is essentially exploiting the laws of quantum mechanics to process information. A traditional computer uses “bits,” which encode either a zero or a one.Quantum computers aren't limited to two states; they encode information as quantum bits, or qubits, which can exist in superposition. Which makes them better machines for computation.

To really understand superposition we need to look at one work of Alan Turing, "The Turing Machine".

To really understand superposition we need to look at one work of Alan Turing, "The Turing Machine".

The Turing machine, developed by Alan Turing in the 1930s, is a theoretical device that consists of tape of infinite length that is divided into little squares. Each square can either hold a symbol (1 or 0) or be left blank. A read-write device reads these symbols and blanks, which gives the machine its instructions to perform a certain program.

Explained Here:

Now think of a quantum Turing machine where the long tape is in a quantum state as does the read-write device.This means that the symbols on the tape can be either 0 or 1 or a superposition of 0 and 1, in other words the symbols are both 0 and 1 (and all points in between) at the same time. While a normal Turing machine can only perform one calculation at a time, a quantum Turing machine can perform many calculations at once.

Now think of a quantum Turing machine where the long tape is in a quantum state as does the read-write device.This means that the symbols on the tape can be either 0 or 1 or a superposition of 0 and 1, in other words the symbols are both 0 and 1 (and all points in between) at the same time. While a normal Turing machine can only perform one calculation at a time, a quantum Turing machine can perform many calculations at once.

Quantum computers also utilize another aspect of quantum mechanics known as entanglement.

Entanglement is an extremely strong correlation that exists between quantum particles, that two or more quantum particles can be inextricably linked in perfect unison, even if separated by great distances. The particles remain perfectly correlated even if separated by great distances. The particles are so intrinsically connected, they can be said to “dance” in instantaneous, perfect unison, even when placed at opposite ends of the universe. This seemingly impossible connection inspired Einstein to describe entanglement as “spooky action at a distance.”

Quantum Tunneling is something that most of us have heard and is the most misunderstood property of a quantum system. Let us take for example the phenomenon of tunneling. If we can’t tell exactly where something is then it follows that we can’t tell exactly where it’s been or where it will be(Classical/Newtonian Mechanics). The best we can hope for is where it most probably will be. So there’s a small chance that a ball thrown repeatedly at a barrier(for instance a wall) could just tunnel through the barrier, appearing almost magically on the other side. We don’t see this often because a ball is pretty big and its 'uncertainty' pretty small. But if we deal with matter on the subatomic scale it becomes much more likely. It’s made use of commonly in modern electronics and in a real way allows for life on earth. To see why, let us trace the creation of a photon in the sun. The light from the sun that we see, two light atomic nuclei (hydrogen) collide, forming a new element(helium), and in the process light is released. But these nuclei are both positively charged and so repel each other. Only if they have enough energy can they overcome this potential barrier and fuse. But if you do the math, the nuclei in the sun don’t have enough energy. The sun’s just not hot enough, yet, the sun shines, and it does so because of tunneling. Just like our physical barrier, there’s a chance that our particle could be on the other side, and so the sun shines.

Entanglement is an extremely strong correlation that exists between quantum particles, that two or more quantum particles can be inextricably linked in perfect unison, even if separated by great distances. The particles remain perfectly correlated even if separated by great distances. The particles are so intrinsically connected, they can be said to “dance” in instantaneous, perfect unison, even when placed at opposite ends of the universe. This seemingly impossible connection inspired Einstein to describe entanglement as “spooky action at a distance.”

Quantum Tunneling is something that most of us have heard and is the most misunderstood property of a quantum system. Let us take for example the phenomenon of tunneling. If we can’t tell exactly where something is then it follows that we can’t tell exactly where it’s been or where it will be(Classical/Newtonian Mechanics). The best we can hope for is where it most probably will be. So there’s a small chance that a ball thrown repeatedly at a barrier(for instance a wall) could just tunnel through the barrier, appearing almost magically on the other side. We don’t see this often because a ball is pretty big and its 'uncertainty' pretty small. But if we deal with matter on the subatomic scale it becomes much more likely. It’s made use of commonly in modern electronics and in a real way allows for life on earth. To see why, let us trace the creation of a photon in the sun. The light from the sun that we see, two light atomic nuclei (hydrogen) collide, forming a new element(helium), and in the process light is released. But these nuclei are both positively charged and so repel each other. Only if they have enough energy can they overcome this potential barrier and fuse. But if you do the math, the nuclei in the sun don’t have enough energy. The sun’s just not hot enough, yet, the sun shines, and it does so because of tunneling. Just like our physical barrier, there’s a chance that our particle could be on the other side, and so the sun shines.

They speak about multi-verse which is an another theory to explain why these subatomic particles behave the way they do, which was first explained Hugh Everett in the 1950's that the complicated and ill-defined parts of quantum mechanics, they're all happening when you measure/observe something, what he said was, when a quantum object/system interacts with another quantum system, the world 'splits', you get 2 worlds from 1 world, and these systems will never interact again. [This is a concise form of it, but the real expressions are far more complicated.(Read more on Wikipedia)]

### The Result

Nope, quantum computers will not serve as a replacement to classical computers. The computational power of a quantum computer is immense and can be applied to solve problems that seem impossible with a classical machine.

So we can use all these properties of a quantum system and apply it in information processing which can help us in a number of ways. As we saw in the above video, they spoke about Optimization problems and Optimization problems are some of the most complex problems to solve.

Imagine you are building a house, and have a list of things you want to have in your house, but you can’t afford everything on your list because you are constrained by a budget. What you really want to work out is the combination of items which gives you the best value for your money. This is an example of a optimization problem, where you are trying to find the best combination of things given some constraints. Typically, these are very hard problems to solve because of the huge number of possible combinations.

Imagine you are building a house, and have a list of things you want to have in your house, but you can’t afford everything on your list because you are constrained by a budget. What you really want to work out is the combination of items which gives you the best value for your money. This is an example of a optimization problem, where you are trying to find the best combination of things given some constraints. Typically, these are very hard problems to solve because of the huge number of possible combinations.

These types of optimization problems exist in many different domains - systems design, mission planning, airline scheduling, financial analysis, web search, cancer radiotherapy and many more. They are some of the most complex problems in the world, with potentially enormous benefits to businesses, people and science if optimal solutions can be readily computed.

One more application being, Simulation of physical environments. Many things in the world are uncertain, and governed by the rules of probability. We have, in our heads, a model of how things will turn out in the future, and the better our model is, the better we are at predicting the future. We can also build computer models to try and capture the statistics of reality. This is really a concise idea on quantum mechanics and quantum computing.

The subject is vast and requires substantial amount of patience to understand it. Although if you think you understood it...you haven't - as quoted by the great Richard Feynman. Well, go explore this ocean of opportunities.

Additional link: [Link] -> It's a great reference on this topic.

The subject is vast and requires substantial amount of patience to understand it. Although if you think you understood it...you haven't - as quoted by the great Richard Feynman. Well, go explore this ocean of opportunities.

Additional link: [Link] -> It's a great reference on this topic.

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