CONCEPT – QUANTUM COMPUTING

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 CONCEPT – QUANTUM COMPUTING

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• What it is : Quantum computing (QC) focuses on developing computer technology based on the principles of quantum theory, which explains the nature and behavior of energy and matter on the quantum (atomic and subatomic) level. All computing systems rely on a fundamental ability to store and manipulate information. Current computers manipulate individual bits, which store information as binary 0 and 1 states. Quantum computers leverage quantum mechanical phenomena to manipulate information. To do this, they rely on quantum bits, or qubits.
• What will happen once a QC is made : It will be a leap forward in computing capability far greater than ever, with performance gains in the billion-fold realm and beyond. The QC will follow the laws of quantum physics, and gain enormous processing power through the ability to be in multiple states, and to perform tasks using all possible permutations simultaneously. Current centers of research in quantum computing include MIT, IBM, Oxford University, and the Los Alamos National Laboratory.
• First steps : The elements of quantum computing originated with Paul Benioff, working at Argonne National Labs, in 1981. He theorized a classical computer operating with some quantum mechanical principles. Later, David Deutsch of Oxford University provided the critical impetus for quantum computing research. 
• What is "Quantum Theory" : Quantum theory began in 1900 with a presentation by Max Planck, in which he introduced the idea that energy exists in individual units (which he called "quanta"), as does matter. It developed over 30 more years with some key ideas -

1. Energy, like matter, consists of discrete units, rather than solely as a continuous wave.
2. Elementary particles of both energy and matter, depending on the conditions, may behave like either particles or waves.
3. The movement of elementary particles is inherently random, and, thus, unpredictable.
4. The simultaneous measurement of two complementary values, such as the position and momentum of an elementary particle, is inescapably flawed; the more precisely one value is measured, the more flawed will be the measurement of the other value.

• Niels Bohr : He proposed the Copenhagen interpretation of quantum theory, which says that a particle is whatever it is measured to be (for example, a wave or a particle) but that it cannot be assumed to have specific properties, or even to exist, until it is measured. In short, Bohr was saying that objective reality does not exist. This translates to a principle called superposition that claims that while we do not know what the state of any object is, it is actually in all possible states simultaneously, as long as we don't look to check.
• Schrodinger's Cat : This cruel analogy explains it clearly. 

1. We have a living cat and place it in a thick lead box. 
2. There is no question that the cat is alive. 
3. We then throw in a vial of cyanide and seal the box. 
4. We do not know if the cat is alive or if it has broken the cyanide capsule and died. 
5. Since we do not know, the cat is both dead and alive, according to quantum law - in a superposition of states. 
6. Now we open the box to check.

• It is only now that the superposition is lost, and the cat must be either alive or dead. Till that time, both states were true.
• Multiverse theory : It holds that as soon as a potential exists for any object to be in any state, the universe of that object transmutes into a series of parallel universes equal to the number of possible states in which that the object can exist, with each universe containing a unique single possible state of that object. Also, there must be a mechanism for interaction between these universes that somehow permits all states to be accessible in some way and for all possible states to be affected in some manner. Both late Stephen Hawking and Richard Feynman expressed a preference for the many-worlds theory.
• Comparison of Classical and Quantum Computing :  

1. Classical computing relies on principles expressed by Boolean algebra, operating with a (usually) 7-mode logic gate principle, though it is possible to exist with only three modes (which are AND, NOT, and COPY). Data must be processed in an exclusive binary state at any point in time - that is, either 0 (off / false) or 1 (on / true). These values are binary digits, or bits. The millions of transistors and capacitors at the heart of computers can only be in one state at any point. While the time that the each transistor or capacitor need be either in 0 or 1 before switching states is now measurable in billionths of a second, there is still a limit as to how quickly these devices can be made to switch state. As we progress to smaller and faster circuits, we begin to reach the physical limits of materials and the threshold for classical laws of physics to apply. Beyond this, the quantum world takes over, which opens a potential as great as the challenges that are presented.
2. The Quantum computer can work with a two-mode logic gate: XOR and a mode we can call QO1 (the ability tochange 0 into a superposition of 0 and 1, a logic gate which cannot exist in classical computing). In a quantum computer, a number of elemental particles such as electrons or photons can be used (in practice, success has also been achieved with ions), with either their charge or polarization acting as a representation of 0 and/or 1. Each of these particles is known as a quantum bit, or qubit, the nature and behavior of these particles form the basis of quantum computing. The two most relevant aspects of quantum physics are the principles of superposition and entanglement.

• Three basic definitions : 

1. Superposition - It refers to a combination of states we would ordinarily describe independently. To make a classical analogy, if you play two musical notes at once, what you will hear is a superposition of the two notes.
2. Entanglement - It is a famously counter-intuitive quantum phenomenon describing behavior we never see in the classical world. Entangled particles behave together as a system in ways that cannot be explained using classical logic.
3. Interference - Quantum states can undergo interference due to a phenomenon known as phase. Quantum interference can be understood similarly to wave interference; when two waves are in phase, their amplitudes add, and when they are out of phase, their amplitudes cancel.

• Superposition : Think of a qubit as an electron in a magnetic field. The electron's spin may be either in alignment with the field, which is known as a spin-up state, or opposite to the field, which is known as a spin-down state. Changing the electron's spin from one state to another is achieved by using a pulse of energy, such as from a laser - let's say that we use 1 unit of laser energy. But what if we only use half a unit of laser energy and completely isolate the particle from all external influences? According to quantum law, the particle then enters a superposition of states, in which it behaves as if it were in both states simultaneously. Each qubit utilized could take a superposition of both 0 and 1. Thus, the number of computations that a quantum computer could undertake is 2^n, where n is the number of qubits used. A quantum computer comprised of 500 qubits would have a potential to do 2^500 calculations in a single step. But 2^500 is infinitely more atoms than there are in the known universe. 
• Parallel processing : This is true parallel processing - classical computers today, even so called parallel processors, still only truly do one thing at a time: there are just two or more of them doing it. But how will these particles interact with each other? They would do so via quantum entanglement.
• Quantum entanglement : Entanglement Particles (such as photons, electrons, or qubits) that have interacted at some point retain a type of connection and can be entangled with each other in pairs, in a process known as correlation . Knowing the spin state of one entangled particle - up or down - allows one to know that the spin of its mate is in the opposite direction. Even more amazing is the knowledge that, due to the phenomenon of superpostition, the measured particle has no single spin direction before being measured, but is simultaneously in both a spin-up and spin-down state. The spin state of the particle being measured is decided at the time of measurement and communicated to the correlated particle, which simultaneously assumes the opposite spin direction to that of the measured particle. This is a real phenomenon (Einstein called it "spooky action at a distance"), the mechanism of which cannot, as yet, be explained by any theory - it simply must be taken as given. Quantum entanglement allows qubits that are separated by incredible distances to interact with each other instantaneously (not limited to the speed of light). No matter how great the distance between the correlated particles, they will remain entangled as long as they are isolated.
• Taken together : Both taken together (quantum superposition and entanglement) can create an enormously enhanced computing power. Where a 2-bit register in an ordinary computer can store only one of four binary configurations (00, 01, 10, or 11) at any given time, a 2-qubit register in a quantum computer can store all four numbers simultaneously, because each qubit represents two values. If more qubits are added, the increased capacity is expanded exponentially.
• Quantum Programming : Perhaps even more intriguing than the sheer power of quantum computing is the ability that it offers to write programs in a completely new way. For example, a quantum computer could incorporate a programming sequence that would be along the lines of "take all the superpositions of all the prior computations" - something which is meaningless with a classical computer - which would permit extremely fast ways of solving certain mathematical problems, such as factorization of large numbers, one example of which we discuss below.
• Problems with QC : There are many obstacles still to be overcome. 

1. Interference - During the computation phase of a quantum calculation, the slightest disturbance in a quantum system (say a stray photon or wave of EM radiation) causes the quantum computation to collapse, a process known as de-coherence. A quantum computer must be totally isolated from all external interference during the computation phase. Some success has been achieved with the use of qubits in intense magnetic fields, with the use of ions.
2. Error correction - Because truly isolating a quantum system has proven so difficult, error correction systems for quantum computations have been developed. Qubits are not digital bits of data, thus they cannot use conventional (and very effective) error correction, such as the triple redundant method. Given the nature of quantum computing, error correction is ultra critical - even a single error in a calculation can cause the validity of the entire computation to collapse. There has been considerable progress in this area, with an error correction algorithm developed that utilizes 9 qubits (1 computational and 8 correctional). More recently, there was a breakthrough by IBM that makes do with a total of 5 qubits (1 computational and 4 correctional).
3. Output observance - Closely related to the above two, retrieving output data after a quantum calculation is complete risks corrupting the data. In an example of a quantum computer with 500 qubits, we have a 1 in 2^500 chance of observing the right output if we quantify the output. Thus, what is needed is a method to ensure that, as soon as all calculations are made and the act of observation takes place, the observed value will correspond to the correct answer. How can this be done? It has been achieved by Grover with his database search algorithm, that relies on the special "wave" shape of the probability curve inherent in quantum computers, that ensures, once all calculations are done, the act of measurement will see the quantum state decohere into the correct answer.

• What can QC achieve :

1. Medicine and materials - Physicians administer doses of radiation to treat cancer, and often patients feel sick after treatment. Physicians can harness the power of quantum computers to more accurately determine the dosage and pinpoint where the radiation should be applied. Chemists use computer-aided drug design to model compounds and their interactions. Quantum computers enable chemists to model extremely complex drug interactions, a task that would be impossible with classical computers.
2. Machine learning - Computer scientists are training computers to sense and respond like humans. Take, for example, when Watson won on “Jeopardy” in 2011. Using today’s classical computers to correctly identify an image of a cat requires the development of complex software and extensive, human-led training of the computer. Contrast that with how much easier it is to train a two-year-old child to recognize a cat. Quantum computers show great promise in bridging the gap between human and machine thinking.
3. Searching big data - Data is a new natural resource. More and more data is generated, stored and analyzed every day. Many data sets are becoming so large and complex that it is difficult to recognize patterns. Just think about how much weather data has been collected and how accurate today’s weather forecasts are. Forecasters need a different approach. The power of quantum computers can be used to find connections that today’s classical computers cannot.
4. Cryptography - Public-key cryptography is widely used to protect information residing on and in transit between classical computers. Keys are generated by multiplying two large prime numbers. Keeping the information secret relies on the difficulty of finding the prime numbers when only the multiplicative result in known. Quantum computers could threaten that type of encrypted information because they can identify those two prime numbers in a fraction of the time that classical computers require. Yet imagine if quantum computers could be used to strengthen post-quantum cryptography. That’s exactly what lattice-based cryptography will do.

• Summary : So, the defining property of a quantum computer is the ability to turn classical memory states into quantum memory states, and vice-versa. This is not possible with present-day computers because they are designed to ensure that the memory never deviates from defined informational states. We humans are classical beings and we can only observe classical states. That means the quantum computer must complete its task by returning to us a classical output. To produce these classical outputs, the quantum computer is obliged to measure parts of the memory at various times throughout the computation. The measurement process is inherently probabilistic, meaning that the output of a quantum algorithm is frequently random. The task of a quantum algorithm designer is to ensure that the randomness is tailored to the needs of the problem at hand. For example, if the quantum computer is searching a quantum database for one of several marked items, we can ask the quantum computer to return one of the marked items at random. The quantum computer succeeds in this task as long as it is unlikely to return an unmarked item.

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