Alan Turing devised the Turing machine in the 1930s – a theoretical device that consisted of a tape divided into small squares that could either hold a 0 or a 1. Today’s conventional computers are very much similar to the Turing machine. They manipulate bits – binary digits, 0 and 1. In contrast a quantum computer uses qubits – quantum bits, a superposition of 0 and 1 that is both 0 and 1 at the same time.

A number of physical objects can be used as a qubit – atoms, ions, electrons, or even photons. The spin of an electron makes it an ideal candidate for representing a qubit. Electrons are basically tiny magnets, and will align with a magnetic field. This lowest energy state is called spin down or the 0 state. If we applied some energy we could as well put it against the field, in the 1 state or spin up. Thus far, this is no different from a classical bit. But the funny thing here is that the electron can be in both states at once. When you measure the spin, it’ll either be up or down. But before you do so, it exists in a quantum superposition of both the states.

For a single qubit two coefficients indicate the probability of finding the electron in either 0 or 1 state. Now consider two such qubits in a system. Now when measured they can be 00, 01, 10 or 11. Before measuring though, the system is in quantum superposition of all the 4 states. Thus there 4 coefficients to determine the state of the 2 spin system. Hence we see that two qubits actually hold 4 bits of information. Now for a 3 spin system there would be 8 such coefficients. If we keep going, we’ll find that the amount of equivalent information held by N qubits is equal to that held by 2^{N} classical bits. This power of exponentiation gives a quantum computer its inherent parallelism which allows it to carry out many more computations at once while a classical desktop computer would work on one.

Although the qubits can occur in any combination of states, when measured they must fall to one of the basis states. Thus the final state after processing must not be a complex combination of superposition of states since there’s no way you could measure a superposition. Thus the algorithm applied to get the final result must be such that the final result is measurable. Quantum computing is not necessarily faster in all cases. It is only useful when the superposition states can be used for some computational parallelism. This is only when they excel in speeds and performance in comparison to classical computing. Quantum computing cannot give you a faster internet, or a better playback of high definition videos. This is why conventional computers like your laptops, smartphones are not going anywhere. But the fact that you’re able to program the qubits to represent all possible inputs simultaneously, and process them at once, means that you could solve hugely enormous, complex problems that would otherwise take centuries or even millennia with conventional computing.

Protons not photons

No it’s photon. http://goo.gl/nSFR6