Quantum Computing
Quantum Computers are computers that exploit some of the strange features of
quantum mechanics to perform data functions. They were first theorized by
professor Richard Feynman in a lecture in 1982 and since then have become a
very prominent area of study and speculation. By some it has been said to be the
future of computing while others claim it is a dead end and will never be worth
the money, which has been invested into the projects.
What is a Quantum Computer?
A classical computer handles data with bits, a bit will have an on or on off setting,
it could for example be imagined as being a current flowing or no current flowing
with these two states representing 0 and 1 which are the two letters that make
up the binary numeral system in which all data on computers is stored.
Therefore in a classical computer each bit can perform one calculation at a time
(0 or 1). In recent years the default way to improve classical computer
performance has been to reduce the size of the transistors in the processor.
However when transistors get to a certain minute size the effects of quantum
mechanics will begin to make them less reliable and generally have detrimental
effects on their performance. Therefore another form of computer is being
sought which would be able to overcome this seemingly fundamental barrier to
increasing the power of computers.
Quantum computers take advantage of two quantum phenomena Superposition
and Entanglement. Superposition is essentially the strange state that a particle
can be in when it is in two states simultaneously for example in the famous
Schrodinger’s cat experiment the cat is said to be in a superposition because it is
considered to be in a in the two states of dead and alive simultaneously. There
are ways that we can take a particle and put it into a superposition of states in an
experiment, here is an example: if we were to have an atom of some element. We
know that the atom has a property called spin, which can be in a state of either
up or down; these are two completely coherent states. We can flip the spin of an
atom (from up to down or vica-versa) if we subject it to high intensity
microwaves for a very short period of time. If we know the specific length of time
it takes to flip the spin of the atom we can very easily subject the atom to
microwaves for half of that period of time and then the atom will be in a
superposition of the two states up and down. In this way a quantum computer
can perform calculations on both states simultaneously. By performing two
calculaions simultaneously we are essentially saying (in accord with the many
worlds theory) that the qubit is performing two calculations in two worlds at the
same time.
The second quantum phenomena which a quantum computer takes advantage of
is that of entanglement. Entanglement is an idea whereby if a particle, for
example a photon, were to interact with another photon the two of them would
become entangled and will remain so even when separated over long distances.
For two entangled particles their quantum states are relatable for example if we
were to measure the spin of one of our particles and it measured up we would
know that the other photon’s spin would be down. If in a quantum computer all
the qubits are entangled it allows us to perform more calculations
simultaneously as measuring one qubit will have an effect on another entangled
qubit.
The main draw of a quantum computer is the exponential growth in the number
of calculations that can be performed as we add more and more qubits compared
to a normal computer, which shows a linear growth with the addition of more
bits. If for example we had two bits we would be able to perform two
calculations simultaneously however if we had two qubits we would be able to
perform 4 because the qubits are in a superposition and entangled
simultaneously (00, 11, 10, 01) while with 3 qubits we can perform 8
calculations simultaneously and the rise is exponential the more and more qubits
we are able to entangle
The problems with quantum computing
Now you may wonder what has stopped us so far from creating a quantum
computer to rival the classical computers we are all familiar with there are many
practical reasons but probably the most troublesome is that of decoherance. It is
based on the importance of taking into account quantum objects interactions
with the environment in which it is situated. If for example we have a particle in
superposition it could become entangled with a macroscopic object, the
superposition has now been forced upon a complex system of trillions of atoms
and cannot be maintained and decoheres. This is an irreversible process
therefore if the qubits of a quantum computer were to decohere all the
information they were processing would be lost. Therefore a quantum computer
would have to rely upon the qubits being completely isolated from their
environment which obviously is quite a difficult proposition or rely upon the
qubits decohering slowly enough that the computations can be effectively
carried within the time period prior to decohering, we could slow decoherance
down by keeping the computer at very low temperatures for example.
Here we see one of the key problems in constructing a fully functioning, reliable
and sufficiently powerful quantum computer that the very quantum phenomena,
which it relies upon to function correctly, can in essence spell its downfall as
they are such delicate states, which we need to maintain for the processor to
function.
Uses of quantum computers
It is very important to point out that a quantum computer is not essentially a
highly powerful classical computer it is a completely different machine. There
are many computational tasks that a quantum computer will not outperform it’s
classical counterpart. For example multiplication would not be performed any
faster on a quantum computer than it can be done on classical computer and will
be a far more complex process. However there are some areas of interest where
quantum algorithms have been devised which show that a quantum computer
would be significantly faster than classical computing the most famous and
possibly the most revolutionary is the quantum-factoring algorithm
In 1994 Peter Shor devised his quantum algorithm for the factoring of numbers
on a quantum computer. His algorithm represented a major turning point in the
development of quantum computing it represented the first evidence of a task
that a quantum computer would definitely be able to perform faster than a
classical computer. The difficulty of factoring large numbers for classical
computers is the basis of the majority of modern cryptographic systems. For this
reasons quantum computing started to catch the eye of major organizations such
as banks and whole governments who concerned about the security of their
communication channels looked to invest money into the development of
quantum computing (it is also prompted more investment into an alternative
method of cryptography but we’ll get onto that later).
Most current cryptographic systems rely on this basic principle: say we have two
prime numbers 2293 and 3457 it is very easy for us with a computer to times the
two numbers together to get 7,926,901 but if you were given this number and
told to find the two prime factors that is far more difficult. Cash prizes have been
offered by the RSA often over the last 25 years or so to those who can factor
numbers of certain lengths for example RSA-100 is a number with a hundred
digits RSA-200 has 200 digits and so on. There has been offered a $100,000 prize
for the factoring of RSA-1024 which has yet to be claimed. It is theorized that a
quantum computer would be able to factorise large numbers in relatively short
periods of time for example it could in theory factorise RSA-140 in a matter of
seconds.
The important thing is that Shor’s algorithm has been proved to work, IBM
demonstrated the factoring of the number 15 (into 5 and 3) in 2001 on a
quantum computer with 7 qubits although the experiment was criticized the feat
was repeated in 2012 on a less controversial machine. For many people in the
field of quantum computing factoring represents the most important potential
use of a quantum computer but others believe there are many other potential
uses which we are yet to discover, in the same way in the early days of the
classical computer people would never have imagined that a computer would be
able to perform the sort of tasks they are capable of now. (‘But in the long run I
do not expect factoring to one of the most important applications of quantum
computing” (J. Preskill))
The other main quantum algorithm in existence at this time is Grover’s algorithm
for searching an unsorted database. In a database containing N items we can use
Grover’s algorithm to find an item with specific criterion in a time of order N1/2
where as on a classical computer it would find the item in time in the order of N.
This suggests a major speed up when N is large but negligible difference when N
is a small number. This shows another example of a task at which we can be sure
a quantum computer would outperform a classical one (although it must be
noted Grover’s algorithm doesn’t give an answer for definite but instead with
very high probability).
There are other areas in which a quantum computer could be potentially useful
outside the area of calculation and that is through the simulation of quantum
systems which are to complex to be simulated by a classical computer. In his
lecture Feynman suggested that the idea of simulation would potentially be the
main use of a quantum computer.
Will it be useful?
In conclusion we know that a quantum computer would be ‘useful’ in the sense
that it could in some areas outperform classical computers however scientists
are split on whether we will discover that many alternative uses for them past
what we already know and also on the subject as to whether it is possible to
build a quantum computer large enough with enough entangled qubits to be of
particular use. The key point is that physicists have been searching for a
fundamental physical law that would prevent a large scale quantum computer
from being constructed and they are yet to find one but practically it will
undoubtedly be a hugely difficult task. There are many different ideas around as
to whether a large-scale quantum computer will ever be created or among those
who thin they can when. For example Scott Aronson a great believer in the
potential of quantum computing (who has even gone as far as offering a
$100,000 prize to anyone who can prove that a quantum computer could never
be built) said ‘It was more than 100 years between Charles Babbage and the
invention of the transistor, so I feel life if we can beat that, then we’re doing well’
while IBM (one of the main researchers in quantum computing) have stated that
practical quantum computers could be placed in businesses and maybe even
homes within the next ten years. A quantum computer would undoubtedly useful
if we knew how to build and sustain one