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Photons can also be used as the fundamental building
blocks of a quantum computer. Quantum computers
are often said to be much faster than normal, or
“classical” computers, but what does this mean?
To answer this, we need to look at how computers actually
operate. Some problems are hard for a computer to solve,
while others are easy. An example of an easy problem is
multiplication: in just a few steps you can multiply two
relatively large numbers. Going in the opposite direction
—finding the prime factors of a number—is a much harder
problem. In practical computing terms this means that it
takes many more steps in the factoring computation to get
to the final answer than are needed for the multiplication
computation. For example, it is relatively easy to work out
by long-multiplication that 19 times 23 is 437. However, it
takes much longer to factor 437 into 19 and 23. Try it with
the number 3953.
On a classical computer, the fastest method—or algorithm—
for factoring large numbers is the “number sieve algorithm”.
If N is the number you wish to factor, the classical computer
needs about exp[1.9 (log N)⅓] steps. For large N this is a
very big number! On the other hand, a quantum computer
can do this computation in much fewer steps. Much, much
fewer: (log N)3. We call this an exponential speed-up. If
both computers run at the same clock cycle, the quantum
computer will be much faster than the classical computer.
You can see how much faster in this app: choose a large
number to factor, and see how much time a quantum
computer requires, compared to a classical computer.
USEFUL LINKS
www.ldsd.group.shef.ac.uk/QL
You may wonder what all the fuss is about. We care about
factoring a great deal! The asymmetry in hardness of
multiplication and factoring can be exploited to create
cryptographic codes in which encryption (via multiplication)
is fast, but decryption without a key is slow (factoring).
Light is the ultimate information carrier. It can be generated
with high efficiency and sent over huge distances using
optical fibres to transmit internet, TV, and telephone signals.
Our research aims to harness the special quantum properties
of light to make quantum computers a reality and provide
perfectly secure communications.
The cryptography used today is pretty much all based on this
mathematical property. If a quantum computer can quickly
factor very large numbers, all these cryptographic schemes
will be insecure. However, photons come again to the rescue:
as we saw above, in quantum cryptography we can use
photons to detect the presence of an eavesdropper.
The most detailed description of light uses quantum theory, which tells us
that light comes in small packets of energy called photons. These are neither
particles nor waves, and are best referred to as quanta. However, they do display
some properties of both particles and waves: photons can be detected at very
precise positions and times like particles and they exhibit interference like waves.
Because photons have these special quantum properties, they can be used
to process information in a fundamentally different way than ordinary light.
We can use them to create a perfectly secure communication channel via
quantum key distribution, and, in the future, we can use photons as the
information carriers in a quantum computer.
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8800 – DESIGNED AND PRODUCED BY
Grey Matter – www.usegreymatter.com
www.sheffield.ac.uk/physics
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It is now possible to build a communication system where
each pulse contains only one photon. Data is encoded via
the polarisation state of the photons. Although it is possible
for an eavesdropper to intercept the photons, these have
to be re-transmitted to try to conceal this interception.
However, single photons form a quantum system so the
act of measurement changes their properties. This change
can be detected by the two legitimate people using the
system. Hence, it is possible to construct a system secured
by the laws of physics, where any attempt to eavesdrop
can be detected.
This is a quantum cryptography system.
COMMUNICATING
WITH LIGHT
One reason why fibres can carry such large amounts of
data is that multiple wavelengths or colours can be injected
into the optical fibre. There is no interaction between these
different colours so at the far end of the fibre they can be
extracted and separated. A modern long distance system
might use 160 different wavelengths with each wavelength
carrying 10 gigabits per second to give a total capacity of
1.6 terabits per second. This is known as wavelength-division
multiplexing.
The demonstration is a single channel low data rate optical
fibre system. The amplitude of the audio signal is used to
vary (modulate) the frequency of the laser pulses. This is
referred to as frequency modulation (FM) which is much
less sensitive to interference than modulating the amplitude
(AM) and so results in a higher quality system. For a similar
reason FM analogue radio has a higher quality than AM radio.
Light from the laser travels across the breadboard via
a chopper wheel, which can be used to block the light,
confirming that it is carrying the data. The light is picked
up by an optical fibre and fed to a photo-detector and
amplifier. In a real fibre system the laser would inject light
directly into the fibre.
Each laser pulse is approximately 10 millionths of a second
(10 μs) long and contains one hundred thousand million
photons. With so many photons it is easy to ‘steal’ some
and use them to eaves-drop into the data. A beam splitter
can be moved into the laser beam, which splits off half the
light and directs this via the mirror onto a second optical
fibre and eavesdropper box.
QUANTUM
INTERFERENCE
OF PHOTONS
While photons behave as particles when they trigger
detectors and our eyes, they behave as waves when
they encounter each other. An important quantum
interference effect occurs when two photons enter
opposite sides of a beam splitter.
Beam splitters are often made out of cubes of glass, and can
be found in SLR cameras to divert half of the incoming light
to camera’s light sensors and the other half to the eyepiece.
Light is the ultimate data carrier. Optical fibres form
the backbone of the internet providing high capacity
date links between countries, large cities and more
recently to cabinets at the end of your road.
Using total internal reflection optical fibres guide ultra-short
pulses of laser light, with a modern system able to carry data
at the rate of 1.6 million bits per second along a single fibre.
This is equivalent to 43 DVDs every second or 25 million
simultaneous telephone calls. This is more than 10,000
times faster than current 4G rates. In research laboratories
data rates as high as 26 terabits/s have been achieved.
The Core
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Photonic systems combine both light and electronics
and can be shrunk down to sizes below one millionth of
a metre (1 μm). Nano-scale semiconductor objects known
as quantum dots can be used to produce a regular sequence
of single photons for use in quantum cryptography systems
and the quantum mechanical properties of the photons
can be used as the building blocks of an optical quantum
computer. The application of photons to quantum computing
is explored in the other areas of our exhibition.
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On a chip, these beam splitters are not made of glass cubes,
but are instead made of tiny semiconductor waveguides
routing photons closely to each other.
SINGLE PHOTON
CHALLENGE
A photon is the smallest
element of light, and just a
single photon can be used
as a carrier of information.
Devices that are able to
count single photons one by
one are called single photon
detectors and are one of the
key technologies required for
reliable quantum computing
and quantum communication
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How difficult is it to detect a single photon? An average
produces approximately 100 billion billions photons per
second. Digital cameras collect around half a million photons
for a single photograph. Human eyes are also very sensitive
organs, and we have made a demonstration setup in which
you can test your eyes against the single-photon detector.
Our source of photons is a light emitting diode (LED) that
generates short light pulses of various intensities. Light from
the LED is coupled straight to the optical fibre
and is split equally into three fibre outputs. Two are
connected to player’s oculars and one is connected to a
detector. You should be able to see dim flashes as the
photons hit your eye’s retina.
When a photon enters a beam splitter, it will randomly
choose the output, either crossing over or staying in the
same waveguide. When two photons enter from both sides,
you may expect that the two photons end up all over the
place, because they each independently and randomly choose
whether to cross over or not. However, this is not the case!
If the photons are identical in frequency (colour) they will
always emerge together on either exit of the beam splitter.
This purely quantum property of light is the key feature for
quantum computation.
For our exhibition we have made a large beam splitter
model in which you can explore this quantum behaviour
of the photons.
• Why does light reflect from flat
surfaces, like glass in windows?
limit
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photons that we can no
Scan here to watch our YouTube video explaining quantum interference