Tuesday, October 26, 2021

What is Quantum Computer and Quantum computing? How do Quantum Computers work? - Quantum bits

Quantum computer - Quantum computing - How do Quantum Computers work - How to build a Quantum Computer

Quantum bits: How to build a Quantum Computer

One of the most interesting properties of electrons is their spin (1). It is like a little arrow which is attached to the electron, making it into a tiny magnet. The tip of the arrow is in the direction of where the North Pole of that magnet points to.

Quantum computer - Quantum computing - How to build a Quantum Computer

The Spin States: Up or Down?

If you measure whether the spin points into a certain direction - say, up- or downwards - then there are only two possible answers. These are "The spin points upwards" and "The spin points downwards". There is nothing in-between, these are the only two possible outcomes of the measurement. In particular, the result will never be "The spin points sideways". The British physicist Paul Dirac has invented a neat little notation for these two possibilities. One writes these as |↑œ for "upwards and |↓ for "downwards".

The Qubit: Up, down, or In-Between

Now, this being a quantum system, the spin of the electron does not necessarily have to be in either the state |↑ or|↓, it can also be in a superposition of the two. Just as Schrödinger's cat can be both alive and dead at the same time(2), so the electron's spin can be both up and down, with certain possibilities. In fact, the spin can be any linear combination of |↑ and |↓. One writes this as

| ψ =   p  |↑  + q |↓  

The numbers p and q mean the following: If an electron has a spin like | ψ  with some numbers p and q, then, whenever you measure the z-component of the spin, you will get the result "upwards" with a probability of p, and the result "downwards" with a probability of q2. Well, since these are the only two possibilities, the probabilities better add up to 100%. Physicists don't like to use percentages, they rather like to use fractions between 0 (which is completely unlikely, i.e. 0%) and 1 (which is completely certain, i.e. 100%). So p and q need to be such that the sum of their squares adds up to 1. Every state of the electron's spin looks like some | ψ , maybe with different p and q - as long as p2 and q2 add up to 1!

If you have worked with computers before, you might have come to the following realization: If the spin can be up or down, then this seems perfect to store information. All data in our computers is expressed as a series of O's and 1's - called bits. But whether you use O's and 1's, or "on" and "off", or "current flows", "no current flows" does not matter - that is just the technical realization. The important point is that you need two different states, which encode the bit of information.

That's what the spin of the electron can do - if you measure it, it can be either "up" or "down". So to store information, you only need to have lots of spins, which are either in the state |↑ or |↓. But remember: Spin are not restricted to these two values, but can also attain any kind of superposition of these two values! This is why the spin of an electron is not called "bit", it is called "quantum bit", or qubit for short.

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A computer which could store and manipulate qubits instead of normal bits is often called a quantum computer, and it works fundamentally differently from the ordinary machines that we have in our offices and at home.

Because a qubit can also have the values "up" and "down", a quantum computer can do everything a normal computer can - and more! For instance, it can store more than one number in a piece of memory.

value of number in Qubit - Quantum Computer

For example, let us agree from now on that "spin up" means "1", and "spin down" means "0". Then, with a memory made out of four qubits, you could store, for instance, the number 5. In binary, the number five is represented with four bits as 0101, so in the quantum computer that would be |↓ |↑|↓ |↑. Similarly, the number 7 would be |↓|↑|↑|↑. But you could use any other qubit as well, for instance a qubit of the value

|  =   -1/2 (|↑ +|↓)

The four qubits could have the value |↓|↑ - then, the two numbers 5 and 7 would be stored, at the same time! If you were to read the memory now (that would be like measuring "all the spins"), you would get either 5 or 7, both with a 50-50 chance. But, and this is the important thing, performing calculations in a quantum computer is not measuring. So you can perform several different computations simultaneously, without collapsing the wave function of the spin (3). By the way, this is a question for the computer geeks: which numbers would be stored in the memory of the qubits read

|||| ?

Quantum bits - How to build a Quantum Computer -  Quantum Computer google - Quantum Computer IBM - Danger for Online Safety

A Danger for Online Safety?

To construct actual algorithms which make use of the power of quantum computers is actually quite complicated, but it can be done. Theoretically, there are several calculations which one could perform much much faster than with ordinary computers.

This is quite important, for instance, for online cryptography. The modern encryption algorithms are so safe, because they rely on the fact that apparently it is really, really hard to factorize a 90,000-digit number into its two prime factors. If you were to simply try all possibilities out by brute force, a normal computer would need about a century for that task. A quantum computer would achieve this much, much faster - a great risk for all encryption!

Quantum bits - How to build a Quantum Computer -  Quantum Computer google - Quantum Computer IBM - quantum computer algorithm

But rest assured, your online banking data is safe from encryption breaking (as long as no backdoor has been programmed into the banking code...), for two reasons: Firstly, even if we had quantum computers, one could simply use another encryption algorithm. If that would not rely on the prime factorization but on something else, we would be safe again. In fact, there are such algorithms, which quantum and normal computers would be equally bad at solving. We just don't use them right now on a global level, because it is not necessary.

quantum computer google - chief executive officer of Google - Sundar Pichai, with one of its quantum computers

Secondly, so far nobody has actually built a working, efficient quantum computer. There are some experimental designs, working with a few bits, but nothing ground-breaking (at least not at the time of writing this article). For the real deal, one would have to use lots and lots of qubits, and not measure them. 

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The power of qubits is that they can be in superposition of two bits, but only as long as nobody looks at them. It is really hard to shield them from the environment in such a way that they can be manipulated without measuring them, though. So in a manner of speaking, until we manage to keep Schrödinger's Cat reliably alive and dead for a long time, quantum computers are not something to reckon with yet.

This article is taken from:

Quirky Quarks: A Cartoon Guide to the Fascinating Realm of Physics

Tags: Quantum Computer, Quantum computing, Quantum Computer google, Quantum Computer IBM, How do quantum computers work, Quantum computer vs supercomputer

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