Quantum Computers

Different Ways of Representing Information

What Good is a Qubit?

Why Fast Calculations Matter When You Can't Know the Answer

Where Can I Buy a Quantum Computer?

Different Ways of Representing Information

Computers are basically a fancy collection of switches. In a computer, a bit is like a switch—it is either on or off. For a computer, a "1" stands for on, and a "0" stands for off. It can be represented by anything that can have two states that can be switched from one to another. (Deutsch) No two ways about it: there are no in-between states. (In other words, no dimmer switch. Sorry.)

Today’s computers use capacitors, which are two parallel plates that hold electric charges between them. When the capacitors have a charge, it is "on" (or in computer-speak, a 1). When they don’t have a charge, they are "off" (or 0). In theory, bits could be represented by photons of different polarizations or electrons in different electric states.

Quantum computers, on the other hand, exploit the laws of quantum mechanics, which say that a particle, until observed, can exist in two states at once, which physicists call a superposition of states. [link to explanation] Now a qubit, or quantum bit, is like a bit. It could be any particle--a photon, atom, electron, or subatomic particle, and it has two states, on and off. Now the twist is that, until observed, a qubit can be both "on" (1) and "off" (0)—at the same time!

But when you do observe it, you will detect only one state or one number, at random. So, while this is pretty neat and stuff, it’s actually not too useful by itself.

A classical computer, like the one you’re reading this web page on right now, stores numbers in a series of bits. Your PC most likely uses either 16-bit or 32-bit systems to store information,
 The 3-bit sequence What it represents 000 0 001 1 010 2 100 3 011 4 101 5 110 6 111 7
but for simplicity’s sake, we’ll look at a system that uses three bits. There are eight possible ways of arranging these bits.

For every three normal bits, we can only represent one number, but three qubits can represent all eight numbers at the same time. Because each qubit can exist in both possible states (1 and 0) at the same time, three qubits can represent all possible configurations of the three bits simultaneously, and thus, can represent all 2^3 or eight numbers.

Four qubits can store 2^4, or 16 numbers simultaneously. Five qubits can store 2^5 numbers, or 32 numbers. Ten qubits could store 2^10 or 1024 numbers. A mere 250 qubits could store 2^250 or 1.8 x 10^75 different numbers at once. That’s an 18 followed by 74 zeroes, which is more than the number of atoms there are in the universe!

Despite these impressive numbers, qubits aren’t really more useful than normal bits for data storage. Those same quantum laws that allow an unobserved qubit to exist in two states at once also forces it to "chose" one random state when it is observed. Therefore, that same string of qubits that, when unobserved, can represent more numbers than atoms in the entire universe, when observed…only shows one. One random number.

Now this sounds pretty useless. You have this fancy little qubit that holds tons of information but only shows a random number—when observed.

What Good is a Qubit?

None! Actually, that was a shameless lie. Just read on.

So these qubits aren’t real useful in data storage. What are they good for?

Quantum computers are (theoretically speaking) vastly better than normal computers for certain types of calculations, such as factoring (finding the two numbers that, when multiplied, equal a given number) or searching a list.

Since a sequence of qubits can represent many different numbers at the same time, they can be manipulated simultaneously. So in a quantum computer, a mathematical operation can be performed on many numbers at the same time.

Now your normal desktop computer—or even a supercomputer—has to do things one at a time. But a quantum computer is like a massive parallel processor that does all of them at the same time. Returning to our 3-bit example, if we wanted to perform a mathematical calculation on each number from 0 to 7, a normal computer would have to do eight calculations sequentially. A quantum computer, however, could store all eight numbers in a superposition and manipulate them at the same time.

For instance, you want to find the two factors that when multiplied, equal 23843.

? x ? = 23843

Now you could probably take several hours trying out numbers by trial and error before you found the answer.

100 x 200, too small. 120 x 199, too small. 333 x 292, too big…

Your computer has do more or less the same thing before it can find out that

113 x 211 = 23843

But a series of qubits, representing all the possible factors, could manipulate them simultaneously to find the answer.

Although factoring 23843 by computer is practically instantaneous, as the size of the number grows linearly (1, 2, 3, 4…) , the number of possible factors grows exponentially (2, 4, 16, 256, 65536…). Current computers use brute force to try out all the possibilities. The current record for the largest factored number was 129 digits, and it took six hundred volunteers’ spare computer time to factor it. Trying to factor a number of 400 digits with even the fastest supercomputers today would take billions of years. (For comparison, the universe is approximately 10-15 billion years old.)

This may not sound like that large an advantage until you consider the huge numbers that could be involved.

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Why Fast Calculations Matter When You Can't Know the Answer

You might be wondering how it is possible to have a qubit do calculations, because, as we said earlier, when observed, a qubit spits out a random number.

The trick is, you can know the answer, just not with 100% certainty.

You have to manipulate the qubits without "observing"—in other words, measuring or interacting with them.

How do they get the answer, then? After the blind manipulation of the qubits, they are cycled through an algorithm several times, which narrows down the possible answers until the probability of the right answer showing up is extremely close to 100%.

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Where Can I Buy a Quantum Computer?

Woa there tiger! It should be made clear that the majority of the above information is still theoretical. In reality, quantum computing is still in early, primitive stages. Unfortunately, you can't go to your nearest computer shop and pick one up.

Currently, scientists have only succeeded in building very simple quantum computers that process just one or two qubits. Several groups from MIT, Harvard, and Berkeley managed to make the first crude elements of a quantum computer using, of all things, a thimbleful of chloroform. Using nuclear magnetic resonance (which is like MRI, magnetic resonance imaging), the researchers manipulated the "spins" of the quantum particles within the nuclei of the atoms. One alignment of spin represented 0 and another represented 1. Researchers can manipulate the spins of the particles so that there is an equal chance of them being at 0 or 1. According to quantum mechanics, until those particles are observed, they exist in both states at the same time, a superposition of 0 and 1. (see Bell's Inequality and the EPR Paradox)

There are many approaches to quantum computers, but some of the main obstacles are maintaining coherence, the indeterminate superposition of states, for longer periods of time than a few nanoseconds and processing the quantum data.

In the future, quantum computers will most likely consist of three main things: entangled particles (see Bell's Inequality and the EPR Paradox), quantum teleportation, and logic gates.

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 Interference Make sure you see the Interactive Interference Illustration. The Photoelectric Effect Quantum Schozophrenia Quantum Computers How tomorrow's desktops might work. Quantum Cryptography The unbreakable code. Main Quantum Physics Page Have a question on this page? Uncertain about quantum theory? So was Heisenburg. Talk about it here.