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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,
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The
3-bit sequence
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What
it represents
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000
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0
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001
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1
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010
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2
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100
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3
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011
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4
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101
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5
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110
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6
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111
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7
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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.
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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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