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Since the 1970s the computing power of processing chips has increased at an exponential rate every two years. This is follows Moore’s law which dictates computer chips speeds, it states that every two years the amount of transistors that can fit into one silicon chip (of the same size or smaller) doubles, which consequently doubles the computers processing power. However Moore’s law and current computing technologies are reaching their limits, as chips and transistors are reaching their smallest possible size at which they can function ordinarily.

Transistors work by acting as a gate for the current of electrons in a circuit to flow through, transistors can allowed the current to flow (on) or not allow it to flow (off).1 Transistors are used in computer chips as a way to encode functions using binary numbers, on being 1 and off being 0. The limits of transistors arise when they become so small (smaller than 7nm) that the electrons in the flow of current have a probability of ‘teleporting’ onto the other side of the transistor in a process called quantum tunnelling. 2 Quantum tunnelling allows some electrons to flow through transistors when they are supposed to prevent them from passing and causes problems in the operations of computer chips, restricting the capabilities of traditional silicon chips.

As a result of these limitations physicists and computer scientists are developing quantum computers which take advantage of quantum mechanics (quantum super-positioning and quantum entanglement) to allow quantum computers to overcome these problems. By taking advantage of these quantum computers can theoretically have superior overall computational speeds for certain tasks over traditional computers.

Where traditional computers use bits (0s and 1s) which are either the flow or lack of flow of electrons, quantum computers use qubits which can be any quantum system that takes two values. Some examples of qubits are the spin of a particle in a magnetic field (up/down, up being 1 and down being 0) or the direction of the polarisation of a photon. An example of a particle with spin would be the spin of an electron in a magnetic field. These two binary values act as the traditional 0s and 1s that traditional computers use. However were as bits can only have two values, qubits can be both the equivalent of 0, 1 or both at the same (a quantum super-position). 2 A quantum super-position is a state that two-state quantum systems (such as spin) take before they are measured where both states exist simultaneously. An example of a quantum super-position would be a particle like an electron having both an up and down spin at the same time until its spin is measured. Quantum super-positions collapse when the system is observed / measured at which point the system must take one of two values (e.g. spin up). It should be noted that when the system collapses there is an uncertainty on which state it will collapse into and there is a probability of it collapsing into each of the different states (which can be calculated). Quantum super-positions help to conserve things like spin and can help explain wave-particle duality of photons and particles. 3 Furthermore if you have a pair of particles both in super-positions connected through a quantum system, the state one particle collapses into when measured will directly affect the state of the other particle. This is called quantum entanglement. For example, if you measure the spin of one entangled particle as up, the other entangled particles spin will instantaneously become down without being measured. This means that the state of one entangled particle’s super-position affects the state of the other particle’s super-position. Entangled particles remain entangled even when separated by large distances and the collapsing of both super-positions remains instantaneous. 4 This has confused many scientists (including Einstein) as it seems to defy certain laws of classical physics.

An illustration of how super-positioning works in a quantum computer is this. In a conventional computer two normal bits can only exist as one of four possible values (01 for instance). Were as two qubits in a super-position can exist as all four possible values at once (00, 01, 10 and 11) until the qubits are measured, which is when only one value can exist (preferably the one you want). Therefore two qubits can hold more information than two bits at once. Expanding this illustration further, a conventional computer applies functions to a series of arguments (variables/values in computer language) to solve a problem. In quantum computers the states of a super-position can be thought of as arguments to a function. If you perform a function on a super-position you perform the function on each of the components of the super-position simultaneously 7, hence all possible outcomes can be computed much faster than conventional computers which would take more steps to compute. The amount of components of information a set of qubits can hold is 2n (n being the amount of qubits) were as the amount of information a set of bits can hold is 1, this makes quantum computers exponentially more efficient at completing tasks than normal computers. 20 qubits in super-positions can hold more than a million values (1048576) at once. This exploitation of super-positioning is what gives quantum computers their advantage in computing over conventional computers.

However once the outcome of the computation is measured the superposition will collapse and only one of the outcomes will be measured and the rest will be lost. This is important because most of the time only one of these outcomes will be your desired value, and because there is an uncertainty of which value the super-position will take when measured, there is a probability of your output being an undesired value. To solve this problem different quantum gates are applied to the qubits in super-positions. These work by using quantum entanglement and by rotating the qubits on one of their axis (x, y or z) which changes the direction their spin is measured relative to a magnetic field. Doing this changes the probabilities of each of the possible states that the super-position can collapse into. 5 What this basically means is that if you had a single qubit in a super-position with an equal probability of its spin being up as to it being down when measured it, you could essentially manipulate the qubits rotation to increase the probability of it being your desired outcome when measured (spin up for example). Although, this probability will most likely never be 100% because of the uncertainty of the super-positions. There are different quantum gates which rotate and entangle particles in different ways, which can be used in series to create algorithms that can be applied to qubits in super-position. By applying an algorithm to a super-position you apply it to all of the possible values (states) at once as oppose to a conventional computer which would apply the algorithm to the values one after the other. Because of the uncertainty of the super-positions there is still a small probability that the outcome you get will not be the correct / the desired outcome so the process may have to be done more than once to ensure a correct outcome. All this is essentially how quantum computers work and how there are able to complete tasks at fractions of the time that conventional computers can. It’s not that the steps take less time to complete it’s that there are exponentially less steps to complete because lots of them can be done simultaneously because of quantum super-positioning. 3

Quantum computers are however not currently a replacement for conventional computers for various reasons. For one, the more qubits you have in a quantum computer the more complicated and difficult it becomes to sustain the qubits and their super-positions in a stable state. Secondly quantum computers are often huge because of all of the technology required to make them work (some being the size of rooms). For instance to measure the spin of the qubits a magnetic field is used, this magnetic field is produced using a superconducting magnet which is very big. The processing chip with the qubits also has to be cooled to 0k (-293 degrees) to maintain the qubits spins as thermal energy would give the qubit enough energy to change spins. 6 All of these complicated conditions mean that quantum computers are only really advantageous in tasks that conventional computers could not solve, otherwise quantum computers do not offer a significant improvement considering how complicated and expensive they are. 3

In 2014 the largest calculation completed by a quantum computer was the factorisation 56153 (233×241) which was done using 4 qubits 9 and since 2014 there have been significant advances in quantum computing. IBM has developed a quantum computer with 50 qubits and google have developed a quantum processor with 72 qubits 8, both of these are the most advanced quantum computers to date but still have their limitations. The most complicated calculation completed using a quantum computer was a “two-colour Ramsey number” calculation which is a very difficult and complicated maths problem which was solved in 270milliseconds. 10 Quantum molecular simulations have also been done using quantum computers which conventional computers are not capable of simulating. This is important because scientists hope to use these simulations as they advance to gain a better understanding of quantum mechanics and our universe.

Although quantum computers are currently still not as powerful or versatile as conventional computers, it is expected that at they will soon surpass them in computational power, especially with current computers reaching their limits. In 1959 Richard Feynman first proposed the concept of using quantum mechanics as a form of computation in computers and in 1998 the first quantum computer demonstration was shown using two qubits. 11 Since then huge advancements have been made in the field of quantum computing and so it is very possible that the wide spread use of quantum computers could become a thing in a 25 or more years. When conventional computers were first invented they were the size of rooms and can now fit into your pocket, so who knows how quantum computers will evolve. Quantum computers will most likely never fully replace conventional computers as they are perfectly adequate for using the internet, playing games and writing long science projects.