1. QUANTUM COMPUTING: PROSPECTS AND REALITY IN HIGH PERFORMANCE COMPUTING APPLICATIONS Nkundwe Moses Mwasaga Dar es Salaam Institute of Technology moses.nkundwe@gmail.com +255 754 461965 United Republic of Tanzania 2013 CHPC NATIONAL MEETING AND CONFERENCE Cape Town, South Africa

2. 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 00000 00010 00100 00110.0143707 01000.105507 01010.105507 01100 01110 10000.774615 10010 10100 10110 11000 11010 11100 11110

3. 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 photon- would obey different, quantum- mechanical laws

4. 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.

5. 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.

6. 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)”

7. 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.

8. 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)

9. 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)

10. 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.

11. 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.

12. 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.

13. 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.

14. 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).

15. 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.

16. 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!

17. 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?

18. 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!

19. 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!

20. 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.

21. 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.

22. 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.

23. 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 four- element quantum database in only one step. The interesting thing is as the size of the database increases so does the quantum advantage.

24. 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.

25. 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

26. 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.

27. CHALLENGES OF QUANTUM COMPUTING A far more serious inefficiency is the effect of environmental noise which is, in practice, has poised difficulties to control.

28. 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.

29. 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”