I wrote this article some 2 years back on my older blog. Now, since I made a shift of blog, I thought of including this particular article from my older one and since I am including this here after such a long span, I have added a few things and modified it a bit.
A guy once asked me that what is my limit to find a number’s nth root. I replied that I can find only the square roots and my speed is very slow. He then said, “Dude, you are not just slow, you are also very weak with numbers. Shakuntala Devi found the 24th root of a number so long that it might take you one whole minute at your fastest reading speed to read it, in mere 50 seconds and that too exactly! Shocked?!”
This is a simple example that shows that there exists many shorter and simple algorithms that we need to implement to make calculations easy.
Quantum computing is trying to implement all these algorithms. One of the newly found algorithms – Shor’s algorithm can increase calculations’ speed exponentially. By a few 1994 algorithm methods, it would take 8,00,000 years to factorize 250 digit number & 1025 years to factorize 1,000 digit numbers. Recently, a new algorithm was developed which can do this in few million steps.
A quantum computer is a device for computation that makes direct use of quantum mechanical phenomena, such as superposition & entanglement, to perform operations on data.
A classical computer has a memory made up of bits where each bit holds either a one or a zero. A quantum computer maintains a sequence of qubits (quantum binary digits). A single qubit can hold a one or a zero or importantly, a quantum superposition of these. In general, a quantum computer with n qubits can be in up to 2n different states simultaneously in contrast to single state occupied by normal computer. This is to say that in quantum phenomena, if there were 10 pens in front of me, and if I were asked which pen am I going to use for writing, the reply would be all 10 simultaneously. Interesting, isn’t it?
Simplest implementation of qubits can start with two spin states – “up” and “down”. Rest all states for a given qubit would be formed by a combination of these states only. But the fact is that any two discrete and sufficiently spaced consecutive Eigen values can be used for implementation of qubit like +1/2 and -1/2 or +1 and -1 or 0 and 1 on our number system.
For a two-bit register on a classical computer, the computer at any time is in any one of the four possible states – 00,01,10,11. Since, they are just discrete non-negative numbers (p,q,r,s), their probability adds up to give one.
But, when we consider a two-qubit register, we get a 4-D vector (p,q,r,s) called a wave function with complex coefficients. This complex coefficient brings the difference between the two vectors – one obtained from classical computation & the second vector of quantum computing. Now, since, this happens to be a wave function of complex coefficients, the sum of squares of coefficients’ magnitudes add up to give one. Being a wave function, superposition principle comes into play and we get interference pattern between different computational paths.
To say in simple words, in quantum computing we would have to keep track of all 2n complex coefficients for our system to manipulate data.
Quantum computation preserves the Euclidean norm, i.e., their sum of squares adds up to one. Generally, the quantum computational operations are rotations. Since, any rotation can be reversed, quantum computations are reversible.
After computation, a classical computer gives a definite two-bit string as a result. On the other hand, a quantum computer destroys the original quantum state. Quantum algorithm gives the result with a certain probability of accuracy. But, by repeated computation, we can get the most accurate answer (more or less like the one we do with the help of Numerical Analysis).
A quantum computer can very efficiently break many of the cryptographic systems in use today. They can also break through many of the so-called secure web-pages and emails. Thus, a quantum computer can be a very effective tool in breaking a large cryptic key and decrypt the code.
There also exists quantum cryptography that uses digital signature schemes to protect the data.
The attempt to guess the secret key makes a quantum computer a severe attacker on symmetric ciphers such as Triple DES & AES.
Not only this, quantum system problems (related to physics & chemistry) can also be solved by the help of quantum computing. It has been estimated that these computers can speed up the problem solving approach to such an extent that a year taking problem could be solved in seconds.
NMR techniques are the evolution of quantum computation. Molecular magnet and fullerene-based ESR computer can be future generation quantum computers. Some other future generation quantum computers can be Bose-Einstein condensate-based and spin-based quantum computers.
One thing that you would have marked in this article is that everything that I said that Quantum computer can do is written as “can” do. I mean I just suggested a possibility. This is because we directly work on atoms and the quantum entanglement which is not easy to control. And, you know the best part? The world record, until last year, for quantum computation was set by IBM and the problem was “3 * 5 = 15”! Yes, you read it right. The reason this was a landmark was that the computation was done totally on atoms utilizing its wave nature. Even a minor disturbance hampered the system.
With some advances, a supercomputer, JUGENE, did factorization on 42 bit quantum computers.
Going off the topic, a researcher recently developed a new form of chess that makes it difficult for even a supercomputer to estimate the opponent’s next move, thus helping a human to atleast let him compete.
Ending it, for the lovers of these two fields, quantum physics and computing, this definitely is a place to be and for the guys who want to do a research, this is the ideal platform to begin because the potential is huge and you have almost everything to discover and develop.