Quantum computing is based on a principle in quantum mechanics called the superposition of states . In this case, the physical nature of an unobserved object in real time is defined by a mixture of the possible states the object can be in. The key concept here is unobserved

This is an incredibly confusing and counter-intuitive concept which is likely to remain that way, even after some explanation. Let's begin by considering the dilemma of the cat pictured below:

In this case the cat, more specifically Schrodinger's cat, is enclosed in a box with a hammer suspended above a glass vial that contains a gas that is deadly to cats (please try this at home). The box is closed. At any given time the cat may have randomly joseled the hammer apparatus thus causing it break the vial thus killing the cat. However, the cat is unobserved (assume the box is soundproof). So if you ask the question after you have placed the cat in the box: Is the cat alive or dead? your intiution tells you that you don't know and your intitution further tells you that the cat is either alive or dead. Your intution is incorrect.

What we know about physically about the cat is that it has two possible states of existence in the observed world.

• State 1: The Cat is Alive
• State 2: The Cat is Dead

Seems simple enough. However, since the cat is in the box, the cat is in the unobserved state. In that case, the correct response to the question Is the cat alive or dead? is the disturbing: The (unobserved) cat is both alive and dead .

More specifically if you say just put the cat in the box, the answer would be The cat is 50% dead and 50% alive. In other words, the physical state of the unobserved cat is a superposition of its two possible observed states. This situation is no different than flipping a coin in your hand and then closing your hand around the flipped coin. The unobserved coin is 50% heads and 50% tails.

Only when the coin/cat is actually observed, is its physical state determined. Note: most people think this stuff is bullshit - it is not - it is a deep maysterious consequence of Quantum Mechanics. For further confusion, please consult this YouTube video.



Now, let's consider the case of leaving the cat in the box, in the unobserved state, for a substantial period of time. You might expect, unlike the case of the coin in your enclosed hand, that as time goes on, the probability inside the box of the cat hitting the hammer thus extinguishing itself would increase. So maybe a week later the answer to the question Is the cat alive or dead? is now 20% alive and 80% dead. Hence the unobserved cat is now in a new information state.

Previously its unobserved state was 50% alive - 50% dead. Now its in a new information or bit state. It is this principle of superposition that Quantum computing seeks to exploit in the sense that a single physical object (e.g. the cat) at any given time can be in a single information state among many many possible states, as long as the cat is unobserved. The unobserved cat is in two states simultaneously: The main principle of quantum computing lies in the ability for a simple 2-bit system of alive or dead (heads or tails, 1 or 0) to, in fact, represent more than just two bits. This will be fully discussed later. Meanwhile, back to quantum mechanics.

The other tenet of quantum mechanics, which is the physical reason that transistors work, is that there is no such thing as a physical energy barrier. There remains some probability, objects can tunnel through physical barriers. This is not so astonishing as it sounds. Objects are made of atoms and when two objects interact, its possible that the atoms comprising each object can simple pass through one another. Now this never happens in the macroscopic world, but it happens frequently in the microscopic world. This figure below visualizes this process of quantum tunneling:

So if on the left hand side of the yellow barrier which represents the barrier to the flow of electrons, I have some collection of electrons with insufficient energy to actually penetrate the barrier, there is still some probability that some or all of these electrons will get through the barrier. Again, this is how transistors work and because of quantum mechanics the overall energy input (e.g applied voltage) associated with electronic circuits is much lower than it would if quantum mechanics did not exist.

The final important aspect of quantum mechanics is known as The Uncertainty Principle which states that:

an observer can not simultaneously know the position and momentum of any particle to absolute certainty

Consider the following case. I want to know the exact position of some electron in an atom but I have no way to directly observe the electron. To know when the electron is, I have to shine a laser on the atom and bounce a photon off the particle. That is, to observe the electron, I have to put energy into the atom from the outside world and that will change the way the atom behaves. More specifically, as soon as the photons from the laster interact with the electron, they have transferred momentum to the electron and it moves. Therefore, as soon as I have detected the spatial position of the electron, momentum from the photon interaction has been transferred to the electron and its position has changed. This uncertainty is an intrinsic limit in nature, not an artifact of measurement