Quantum Computation: A Profusion of Possibilities

“A classical computation is like a solo voice—one line of pure tones succeeding each other. A quantum computation is like a symphony—many lines of tones interfering with one another.”

― Seth Lloyd

The Limit of Present-day Computers:

Computers are getting tinier as well as fast by the day, as the electronic components are getting smaller and smaller as predicted by Moore. But this process is about to meet its physical limit.

Electricity is the flow of electrons. Since the size of transistors is diminishing to size of a few atoms, transistors cannot be used as the switches because electrons may transfer themselves to the other side of the clogged passage by the process called quantum tunneling, which is the anomaly in which a subatomic particle goes through a potential barrier.

Quantum Computers: The Origin

The study of quantum computing is relatively new, credit for it must be given to Richard Feynman. He hypothesized that there were tasks that a quantum computer could perform exponentially better as compared to a classical computer. He observed that a classical computer could not stimulate a quantum mechanical model, without exponentially slowing down. At the same time, Feynman hinted that by using a device whose behaviour is inherently quantum in nature, one could simulate such a system without this exponential slowdown.

So, what is a quantum computer?

Quantum computer is device used for computation, which makes use of the quantum mechanical properties, such as superposition and entanglement, in order to perform data operations.

The basic principle of quantum computer is that the quantum properties can be used to represent and structure the data, and that some mechanisms can be built to perform functions with this data.

This is just the extension of classical computation in order to process the  quantum information (aka qubits), using quantum systems such as individual atoms, molecules, or photons. It has the potential to bring about a never seen before revolution in computer science. Current-day electronic computers are not fundamentally different from purely mechanical computers: their operation can be described completely in terms of classical physics. By contrast, computers could in principle be built to profit from genuine quantum phenomena that have no classical analogue, such as entanglement and interference, sometimes providing exponential speed-up as compared to classical computers.

How’s it Better?

The reason for all the fascination is that quantum computer scientists believe quantum computers can solve problems that are intractable for conventional computers. That is, it’s not that quantum computers are like regular computers, but smaller and faster. On the other hand, quantum computers work according to principles entirely different than classical computers, and using those principles can solve problems whose solution would never have been feasible on a classical computer. Computers that thrive on entangled quantum information could run exponentially faster than classical computers because n qubits require 2ⁿ numbers for their description. A few simple operations on these qubits can affect all 2ⁿ numbers through the use of quantum parallelism and quantum interference properties.

Quantum Algorithms

Most computational arguments require an amount of computer power or time that grows exponentially with the size of the problem, and large applications often exhibit rather erratic behaviour. They start at a reasonable pace, but then suddenly collapse, either due to running out of storage or failing to compute in a reasonable amount of time (those runtime errors). The inability of classical algorithms to compute such problems such as prime factoring or the travelling salesman problem (TSP) in polynomial time make them quite useless. Quantum algorithms offer a remarkable solution to these problems.
So, just like quantum mechanics all the quantum computational algorithms are probabilistic, they do not assure a hundred percent of success but a large probability of it. The probability of success can be improved by running the algorithm a number of times.

The Most Well known one of them is the Shor’s algorithm having an abundance of applications.

Shor’s Algorithm

Shor’s algorithm is a quantum algorithm for factoring a number N in O((log N)3) time and O(log N) space, named after the mathematician, Petr Shor.

The algorithm has two parts. The first part of the algorithm turns the factoring problem into the problem of finding the period of a function, and has classical implementations. The part two finds that period using QFT (Quantum Fourier transformation) and is responsible for the exponential speedup. I won’t go into details here, already some heavy words were used here.

This algorithm has significance due to the fact that with this algorithm, the public key cryptography might be easily broken, given a large quantum computer. RSA, uses a public key N which is the product of two large numbers which are prime. A way to crack the RSA encryption can be cracked, in order to do this N must be factored, but with the classical algorithms (general number field sieve (GNFS) algorithm), factoring becomes increasingly time-consuming as N grows large; more specifically, no classical algorithm is known that can factor N in time O((log N)k) for any value of k. By contrast, Shor’s algorithm can crack the RSA algorithm in polynomial time.

Shor’s algorithm was demonstrated in 2001 by a group at IBM, the group factored 15 into 3 and 5, using a quantum computer with 7 qubits. As n qubits can keep a track of 2ⁿ states at the same time, a quantum computer with 300 qubits can at any instance “take care of” 2³⁰⁰ states which is more than the number of atoms in the Universe!!

Possibilities in the Not so distant future:

Artificial Intelligence(AI)

The basic application for quantum computing has to be AI. AI has the principle of learning from experience and becoming more accurate as feedback is given, till the program appears to have “intelligence.”

This feedback is based on calculating the probabilities for many possible choices, and so AI is an ideal candidate for quantum computation. It promises to disrupt every industry, from automotive to medicine and it’s been said AI will be to the twenty-first century what electricity was to the twentieth.

Currently, D-wave is running an autopilot software on it’s quantum computer which is far too complex for the current computers. We have already reached the mark where AI is creating more AI, and so the importance would exponentially increase.

Cyber Security

Quantum computers can perform factorisation exponentially faster than digital computers, meaning public key-based security methods will soon become obsolete. Cryptography methods to counter this are currently being developed, though it may take time: in August 2015 the National Security Agency started to introduce a list of quantum-resistant cryptography methods.  There is also quite a bit of promise for devising quantum encryption methods using the one-way nature of quantum entanglement.This has already been demonstrated in several major cities.

Weather Forecasting

NOAA Chief Economist claims that nearly 29 percentage of the US GDP is directly or indirectly affected by the weather. The ability to better predict the weather could have enormous benefits to many fields, not to mention more time to take cover from disasters.

While it has always been the intention scientists, the equations overseeing such processes have a lot of variables, making classical simulation obsolete. As quantum researcher Seth Lloyd pointed out, “Using a classical computer to perform such analysis might take longer than it takes the actual weather to evolve!” This motivated Lloyd to show that these equations supervising the weather have an inherent wave nature which was the basic idea governing quantum computers, so the equations can be easily solved with it.

So, where can I get one!

So, why aren’t these quantum machines more common already? In a way, scientists are vying for perfection in imperfection. Quantum computers are susceptible to disturbances and other environmental effects, which causes their quantum states to flicker and perish, the devil known as decoherence.

To many experts, this is the challenge that’s holding quantum computing back. Even with utmost care, noise can slip into calculations. Scientists can only keep quantum information precise till the system is noiseless, to make a system noiseless it has to be kept under impractical conditions. To manufacture a commercial quantum computer one should have to keep all these things in mind. Although you can get yourself a quantum computer, it won’t come cheap. If you’re willing to spend around 15,000,000 $ (cess GST !), you can get your own D-Wave Quantum computer.

Summary:

As there is a limit to the fastness and compactness of current day computers, this can be easily solved with the advent of quantum computers. These computers harness the quantum mechanical properties to give a never seen before performance.However there are several pros and cons to it. With these computational giants, Even the uncrackable RSA can be cracked in polynomial time owing to the Shor’s algorithm. On the bright side, NSA has already made some quantum proof algorithms for cryptosecurity, AI and weather forecasting also look to have huge bonuses. An exact date for buying of portable quantum computers has not materialized yet but it’s expected to come in a decade or two.