The Hindu Business Line : Of bits and qubits

It was Tamil New Year's Day and having completed the exams, the kids wanted to watch a movie. I logged into the Web and browsed. Luckily, I found a theatre and reserved the seats. As I pulled out my credit card to pay for them electronically, my brother stepped in with his `voluntary fraternal counsel' - "Don't give the credit card number over the Web".

I responded, "With secure transmission and powerful encryption techniques it is very safe. For your information, decrypting highly secure communications will possibly involve finding the factors of large numbers that have a couple of hundred digits and it will take today's computers many million years".

"Even with computers that run at teraflops?" chimed in my elder daughter and impressed me with her extra reading.

"Yes. A definite Yes! Unless you use Quantum computers".

What? Quantum computers... .? To explain, today's computers can process any piece of information (data, text, audio, video, images) so long as it can be digitised i.e., reduced into binary form using zeroes and ones. Commonly, the presence or absence of electric current is used to denote 1 and 0. In principle, one can choose any quantity that exists in one of two states, such as magnetisation on a hard disk (is it magnetized or not?) or charge on a capacitor (is there a charge or not?), to denote 1 and 0. This is similar to yesteryears, when switches and circuits were made using diverse technologies such as electromechanical relays, vacuum tubes, etc.

The electrons in an atom or molecule revolve around the nucleus. Additionally, they also rotate about their own axis and this is called spin. This spin can be clockwise or counter-clockwise. Can the direction of spin be chosen to denote one of two states like the presence or absence of electric current? Likewise can the polarisation state of a photon, or the atomic energy levels of an electron, or spin direction of an atomic nucleus in a magnetic field be used to denote the "1" or "0" state? Yes.

These binary digits are then called `qubits' - quantum bits. A qubit is a unit of quantum information. A number of qubits together constitute a quantum register. Quantum computers perform calculations by manipulating qubits. These quantum computers offer not only a lot of power but also potentially new algorithms that capitalise on the unique and strange characteristics of the quantum world.

PRINCIPLE OF SUPERPOSITION

Quantum mechanics is a branch of physical science dealing with the behaviour of matter and energy at the atomic and subatomic levels. This behaviour is not governed by the laws of classical mechanics. In the quantum world, at any time a subatomic particle can exist in more than one place i.e., it can exist in a state denoted by 0 or 1 or anything in between. This sounds unbelievable, but is true. How can an object be present in two places at the same time? How can I be turning right and left at the same time? These are questions that defy common logic but are meaningful and depict realistic possibilities in the quantum world. This concept is called the Principle of Superposition (see note at the end of the article).

Consider a 3 bit number denoted by 0 and 1. The possible combinations and the Arabic numerals they denote are given below.

At any instant, in a classical computer, the three bits can denote only one number between 0-7. But in a quantum computer, all the above eight numbers can be simultaneously denoted with a probability associated with each number. By adding a 4th qubit, the information that can be denoted can be doubled. With n qubits one can denote 2 n combinations simultaneously and that sure is big.

While a classical computer can perform only one operation with a single value, the quantum computer can perform eight operations simultaneously with all the eight values stored in the quantum register. Extending this idea, with n qubits, 2 n calculations can be done in parallel. The addition of one qubit doubles the power. That is a dramatic increase in power - made possible due to the superposition.

ENTANGLEMENT

Another important principle, Entanglement, is a quantum mechanical phenomenon in which the quantum states of two or more objects have to be described with reference to each other, even though the individual objects may be spatially separated. Consider one qubit "paired with" or "tied to" another qubit such that the change in the value (location or spin) of one influences the other. Then the two qubits are said to be entangled. In that case, if one them is observed/measured to be spin-up, then the other will have to be spin-down and vice versa. This is an advantage because observations of one are adequate to know the state of the other. Einstein famously called this phenomenon "spooky action at a distance". Entangled states are not natural and have to be created artificially.

Decoherence

Thus, while superposition permits the "creation" of many traditional computers running simultaneously, using entanglement, these `many' computers can be linked together to function as "parallel computers". That is a significant advantage. Yet, this large and powerful computer will also suffer from a limitation. An artificially created superposition will remain stable only for a very short time. When qubits interact with the environment, the superposition becomes unstable and the quantum state is reduced to either "0" or "1". This is called decoherence. With entanglement the influence of decoherence is significant, for if one qubit is affected, its `entangled counterpart' also gets affected. Scientists are researching to develop methods to prevent/minimise/delay decoherence.

QUANTUM COMPUTING TECHNOLOGIES

Quantum states can be produced and maintained by a variety of ways. ARDA (Advanced Research and Development Activity, an agency of US government) has published a Quantum Technology Roadmap (report no. LA-UR-04-1778) which lists the following techniques:

nuclear magnetic resonance (NMR) quantum computation

ion trap quantum computation

neutral atom quantum computation

cavity quantum electro-dynamic (QED) computation

optical quantum computation

solid state (spin-based and quantum-dot-based) quantum computation

superconducting quantum computation and

"unique" qubits (e.g. electrons on liquid helium, spectral hole burning, etc.) quantum computation.

For instance, the quantum states can be caused by trapping ions in a cavity or using light. Very low temperatures of the order of millikelvins (very close to absolute zero temperature possible on earth) are needed to maintain the quantum states stably.

The conditions necessary for any Quantum computing technology to be viable were given by DiVincenzo and hence are called "DiVincenzo criteria". They are:

It must be a scalable physical system of well-characterized qubits.

Meaning: This refers to a system where the number of qubits can be increased when needed.

It must have the ability to initialise the state of the qubits to a simple fiducial state.

Meaning: This refers to the capability to bring all qubits to a common reference state

The decoherence times must be longer than the gate-operation time.

Meaning: If decoherence sets in before gates open/close, then calculations cannot be performed. Typical decoherence times are of the order of nanoseconds. The decoherence times must be about 3-4 orders of magnitude larger than gate operation times.

There must be a universal set of quantum gates.

Meaning: In classical computers, logical gates take logical inputs and produce logical outputs. In the quantum computer, quantum gates are analogous to logical gates

There must be a qubit-specific measurement capability.

Meaning: To operate a quantum computer, it is necessary to be able to read out the state of a specific qubit with high accuracy (high probability).

Two additional criteria (necessary conditions) for quantum computer networkability are:

It must have the ability to interconvert stationary and flying qubits.

Meaning: This will allow different parts of the quantum computer to be connected at will and act as a bus permitting the movement of the individual qubits.

It must have the ability to faithfully transmit flying qubits between specified locations.

Meaning: The capability to convert qubits stored at specific points in the computer into flying qubits will be useful for scale-up and error correction. (This also poses the need to find ways to transmit information stored in a fixed qubit to a flying qubit).

RECENT DEVELOPMENTS

Ion traps are necessary to isolate the ions from the environment so that they don't docohere. Trapping the ions is a difficult task. On December 12, 2005 scientists at the University of Michigan created the first "quantum chip". The scientists have shown that ion traps can be produced using a semiconductor chip (of gallium arsenide), which was fabricated using molecular lithography (the same process used to produce conventional microchips). The chip had a precise cavity at the center. Electrodes protruded into the cavity. Laser was used to produce ions that got trapped and floated in the electrical field produced by the electrodes. Laser then manipulated the spin of the ion's free electron and flipped it between quantum states (up-spin denoting one and down-spin denoting zero). This is a first step in the process of producing a quantum chip capable of storing thousands of ions.

On February 13, 2007 D-Wave systems, based in Vancouver demonstrated the world's first commercial quantum computer. The Orion processor had an array of 16 qubits. The chips were fabricated out of superconducting niobium using traditional lithography and were cooled to near absolute zero temperature so that the quantum states are maintained. The company "plans to deliver field-deployable systems in 2008" (www.dwavesys.com) .

Quantum jumps of atoms, ions, electrons and other particles have long been detected by physicists. Recently on March 14, 2007, CNRS (Centre National de la Recherche Scientifique) in Paris reported the recording of the `birth, life and death' of a photon. When an atom absorbs a photon it is at state 1 and otherwise at state `0'. Hence this detection is significant for quantum information processing.

In the May 4, 2007 issue of Science, NEC, Institute of Physical and Chemical Research, or RIKEN, and the Japan Science and Technology Agency announced that they have developed a technique to control the time, two qubits are coupled. This is significant, for coupling and uncoupling of qubits is essential to quantum computation.

NEED FOR QUANTUM COMPUTERS

Today's computers, though powerful will soon be limited by the ability to dissipate the heat produced over a small area. The heat flux (heat produced per unit area) in the chips is more than that encountered by the space shuttle during re-entry into earth's atmosphere. Additionally, the miniaturisation of the microprocessor has doubled the computer power approximately every 18 months there by proving Moore's Law. Current chip manufacturing techniques (microlithography) can create pathways for current flow that are about 65 nanometers wide. (Intel recently announced that it plans to ship its first 45 nanometers chip, code named Penryn, later this year). For comparison, the diameter of hair is about 80,000 nanometers. Soon the width of the pathways may become comparable to that of the size of atoms. The behavior of particles in these small paths will be different and be governed by the laws of quantum mechanics (and not those of classical mechanics).

There are a still many problems that require large computing power and memory. Factoring large integers, discrete logarithms, and modeling and simulating quantum systems are NP (Nondeterministic Polynomial time) problems that cannot be solved using a classical computer. The solution for these problems will be useful in areas such as development of secure communications, development of advanced processes (single atom doping) in the semiconductor industry, nanotechnology and spintronics (short form for spin-based electronics, which utilizes the spin of an electron). An understanding of quantum processes can also potentially lead to discovery of new phenomena in mesophysics and nanophysics, which, in turn, can aid the development of new devices.

IMPLICATIONS OF QUANTUM COMPUTERS

Today's cryptography is based on the idea that factoring large numbers (as big as having 300 digits) needs immense computing power and impractical times (millions of years). The larger the number, the more difficult it is to crack the code. With the arrival of quantum computers these large numbers can be factored in realistic times rendering current cryptographic techniques futile. What is most important is the fact, that today's cryptographic messages can be retrospectively deciphered and that is a very big risk.

Quantum computers promise strong cryptographic techniques that cannot be cracked even by another quantum computer. Again, the principle of entanglement comes in very handy. An attempt to crack the code will disturb the system.

The possibilities are many. The difficult problems such as drug discovery can vastly be benefited by quantum computers. Areas such as biometrics, quantitative finance and pattern recognition also stand to gain considerably.

Despite all the promise and potential, quantum computers may not yield any advantage over classical computers for general purpose computation. That is a sigh of relief for all the programmers in the world today.

Note: This controversial duality in the existence or state of a subatomic particle is also a unique feature of light. Einstein first proposed that light can exist both as waves and particles and explained the photoelectric effect (and won the Nobel Prize). Electrons also exhibit wave and particle behaviour.

(The author is Consultant, Satyam Computer Services Ltd, and can be reached at chellaiah_s@satyam.com)