Download QUANTUM COMPUTING

2013 CHPC NATIONAL MEETING AND
CONFERENCE
Cape Town, South Africa
QUANTUM COMPUTING: PROSPECTS AND REALITY IN HIGH
PERFORMANCE COMPUTING APPLICATIONS
Nkundwe Moses Mwasaga
Dar es Salaam Institute of Technology
[email protected]
+255 754 461965
United Republic of Tanzania
QUBITS OR BITS
•
•
•
As we know, classical bits, by definition, exist in one of two
different states at any given time – a zero or a one. With
quantum mechanics, however, we are permitted to have a
zero and a one at the same time present in one physical
system. In fact, we are permitted to have an infinite range
of states between zero and one – which we called a qubit.
The number of states a qubit could occupy is infinite
because in principle we can tweak the ratio of probabilities
in which the states 0 and 1 occur to any desired accuracy.
When with certainty we have either 0 or 1 then this
reduces to the classical case.
Deutsch proposed ia quantum generalization of the TM
system. The basic idea is that - rather than the pair of
initial conditions determining a particular action of the
read/write head - they determine all possible actions of
the head with a given probability. As one might expect, this
does not change the range of possible computations that
can be carried out on the system (there are certain types
of computation that are impossible on a TM/QTM), but it
does allow the possibility of operation using quantum
parallelism.
State
Probability
0000
0
0001
0
0010
0
0011
0.0143707
0100
0.105507
0101
0.105507
0110
0
0111
0
1000
0.774615
1001
0
1010
0
1011
0
1100
0
1101
0
1110
0
1111
0
2012 NOBEL PRIZE
• In 2012 Serge Haroche, a
Frenchman, and David J. Wineland,
an American, were awarded the
Nobel Prize in Physics in Quantum
Computing
• The way we view the universe was
completely overturned at the turn of
the century with Planck’s discovery
that electron energy states come in
discrete units called quanta.
• A super-small logic gate-one that
consisted, say, of a single photonwould obey different, quantummechanical laws
WHY QUANTUM COMPUTING?
So why does quantum mechanics help here? Why can’t we do
factorization and search problem with our normal everyday
computers?
Well the point is that, yes we can, and we do use our computers
for factorization and search problem, but as the size of the prime
factor or list to be searched grows, it takes longer and longer to
get an answer. Quantum physics helps with these kinds of
problems, because unlike a conventional computer which checks
each possibility one at a time, quantum physics allows us to
check multiple possibilities simultaneously.
THE ARCHITECTURE OF QUANTUM
COMPUTERS
In terms of the make up of quantum computers,
qubits could be encoded in atoms, subatomic
particles, many-atom clusters, in light, or indeed
in some combination of these.
However, researchers are working on the
medium to store, say, 1000 qubits or more in a
superposition state, for long enough to assist
with more complex calculations.
QUANTUM COMPUTER
“Typical atoms useful for quantum computation usually need to be at a
temperature close to absolute zero (around 1 billionth of a kelvin)”
QUANTUM COMPUTATION SPEED-UP
Thinking of computation as a process that maximizes
mutual information between the output and the input i.e.
the question being asked, we can think of the speed of
computation as the rate of establishing mutual
information, i.e. the rate of build up of correlations
between the output and the input.
Furthermore the fact that qubits offer a higher degree of
mutual information than is possible with bits, directly
translates into the quantum speed-up that has been
proved in Shor’s and Grover’s algorithms.
QUANTUM PROPERTIES
The main quantum properties are:• superposition
• interference
The quantum property of superposition allows one photon to
explore four different possibilities at the same time, and
ultimately, through interference of the different paths, will
compress them into a definite single outcome (i.e. the element
searched in searching database problem)
SOME APPLICATIONS OF QUANTUM
COMPUTING
Two of the most successful applications of quantum computing
are :
• factorization of large numbers (used in various security
protocols,) and
• searching a large database (used in many optimization
techniques)
FACTORIZATION OF LARGE NUMBERS
The factorization of large numbers problem is important, as
much of modern day cryptography is based on the difficulty of
factoring large prime numbers.
SEARCHING A LARGE DATABASE
• The searching large database problem is important because
any problem in nature can be reduced to a search for the
correct answer amongst several (or a few million) incorrect
answers i.e Optimization problem. Example is Travel Salesman
Problem
• Searches are so ubiquitous that they range from you
searching for a file on your computer to a plant searching for a
molecule in order to convert the sun’s energy to useful work.
QUANTUM COMPUTING IN SECURITY USING
FACTORIZATION
Security is important in many aspects of life. Just as you want
your credit card details to be secure when you are paying for
something, governments and various companies want their
documents to be securely stored and unavailable to the public or
other governments or companies. Security can be enhanced by
Quantum factorization.
EXAMPLE OF FACTORIZATION IN CLASSIC
COMPUTING
For, example, it is very easy for computers to
multiply two numbers. You can check it yourself.
Take two one-hundred digit long numbers (they are
huge,
like
for
example
the
number
10000000000000000000000000000000000000000
00000000000000000000000000000000000000000
000000000000000000) and ask a computer to
multiply them together. This, the computer will be
able to execute in a split second, and you’ll hardly
notice that it’s taken any time at all.
EXAMPLE OF FACTORIZATION IN CLASSIC
COMPUTING
On the other hand, finding factors of a large number is
very difficult. This is because there are simply many
possibilities to explore.
Imagine the 100. What are its factors?
Two times 50 is equal to 100. But so is 4 times 25. Or 5
times 20, or 10 times 10.
The number of factors grows quickly and finding all of
them presents a great difficulty for any current
(classical) computer (it’s exponentially slower than
multiplying numbers in the first place).
EXAMPLE OF FACTORIZATION IN QUANTUM
COMPUTING
How is it that a quantum computer can factorize
efficiently? The explanation, first presented by
Shor and now known as Shor’s algorithm, is that
a quantum computer, by exploiting the quantum
principle of superpositions, can exist in many
different states at the same time.
EXAMPLE OF FACTORIZATION IN QUANTUM
COMPUTING
Imagine a single computer in a superposition of being in many
different spatial locations at the same time. In each of those
locations you can configure the machine to divide your number
by a different number to search for factors. And this is a massive,
high speed-up, since one quantum computer is now
simultaneously performing all these divisions, one in each
different spatial location.
And, if one of them is successful – we have our factors!
EXAMPLE OF SECURITY IN BANKING
INDUSTRY
• Have you ever wondered why your PIN (personal
identification number) is secure when you withdraw money
from an ATM (Automatic Teller Machine)?
• How come that neither the bank staff know your PIN? Why do
they not obtain it when you type it into the ATM and steal
your money?
EXAMPLE OF SECURITY IN BANKING
INDUSTRY
The reason is that the ATM machine performs the following
operation.
• When you type in your PIN with the intention of
withdrawing the money, this (usually a four to six digit
number) gets multiplied by a huge (say a 500 digit) number.
• The resulting number (a number 504 digits long) is then
checked by the bank. And if it is in the database, you will be
allowed to proceed with your transaction.
• But, and this is the crucial but, the bank cannot figure out
your PIN from the 504-digit long number that they have in
their database.
• It would simply take them a very long time – longer than
the age of the Universe with current computers!
EXAMPLE OF CHALLENGE TO SECURITY OF
BANKING INDUSTRY USING QUANTUM
COMPUTING
The punch-line of all this is that, using a quantum computer, we
can factorize numbers very quickly. If we have a quantum
computer with 10,000 quantum bits, we could factor a 500-digit
number in a few seconds.
And that would be the end of most current security!
SEARCH ALGORITHM USING QUANTUM
COMPUTING
Lov Grover, on the other hand, in 1996, was interested in an
altogether different problem. Grover wanted to know how to
design an efficient search algorithm using the mass parallelism
offered by a quantum computer.
SEARCH ALGORITHM USING QUANTUM
COMPUTING
Lov Grover idea can be explained through the following example:
Suppose that someone gives you access to a library containing a
lot of unsorted books. If you want to find a particular book, then
you simply have to search through all the books until you find
the one you are looking for.
SEARCH ALGORITHM USING QUANTUM
COMPUTING
• If there are a million books to go through and, if it takes a
second to check each book, that could take a two weeks (one
million seconds is equal to about two weeks)!
• A quantum computer could speed things up greatly and
would only take a thousand seconds (instead of a million) and
this is what Grover managed to prove.
SEARCH ALGORITHM USING QUANTUM
COMPUTING
• In a list with four entries (say 00, 01, 10, 11) we would
normally require a maximum of three searches to find the
right one. This is because you would have to look at each of
the elements and, if you are unlucky, the first three elements
will not be the ones you are looking for.
• Quantum search can, on the other hand, search a fourelement quantum database in only one step. The interesting
thing is as the size of the database increases so does the
quantum advantage.
QUANTUM COMPUTING IN CLIMATE
CHANGE STUDIES
• Most fascinating application of a quantum computer lies in
simulating complex physical systems e.g. our atmosphere
• Being able to predict the climate more accurately is not only
important to make our lives more pleasant; it could be crucial
for our survival on Earth.
• And for this, we definitely need better understanding of the
evolution of various weather patterns.
CHALLENGES OF QUANTUM COMPUTING
Any quantum computation that wants to be more efficient than
its classical counterpart has to be able to deal with two issues:-
• to make a measurement in order to extract the answer
• the effect of environmental noise
CHALLENGES OF QUANTUM COMPUTING
The main limitation of quantum computation geared towards
solving classical problems is that we ultimately have to make a
measurement in order to extract the answer, given that the
question we are asking requires a definite answer.
CHALLENGES OF QUANTUM COMPUTING
A far more serious inefficiency is the effect of environmental
noise which is, in practice, has poised difficulties to control.
EXAMPLE OF QUANTUM COMPUTER
• Zero degrees Kelvin, or absolute zero, is the coldest temperature that can possibly be
measured. It's the temperature at which every single atom that constitutes an object
stops moving, and therefore stops generating heat.
• The inside of D-Wave Systems' quantum computer is kept at a balmy .02 degrees
Kelvin. That's about -460 degrees Fahrenheit.
THANK YOU VERY MUCH
Quantum computers force a higher order of information processing than we can
currently achieve. They are the smallest and fastest gadgets that the laws of
physics currently allow us to construct.
“Quantum computers are faster than you can imagine”