What is Quantum Computing and why is needed?
Quantum computing is a revolutionary method of computing and solving certain types of tasks using the quantum-mechanical phenomenon of superposition and entanglement (explained later). However before we look into how quantum computers work, we must understand how classical computers work and why we need quantum computers. A classical computer represents information as bits (binary integers) using different states of electrical charge. This information can be processed with the use of transistors – the smallest building block of a computer. A collection of transistors can form a logical gate and a collection of logical gates can form a module process e.g. addition/multiplication. From here, computers are able to perform a plethora of tasks. For years the growth in information technology has been accurately modelled by Moore’s Law – The number of transistors on a microchip doubles every two years whilst the cost halves. This has meant double the processing. However this rate of development will begin to decline as we see limitations in the physical size of transistors. A typical transistor today is only fourteen nanometres, five hundred times smaller than a red blood cell. Approaching the quantum level, the functionality of transistors will struggle due to the phenomenon of quantum tunnelling – where electrons can make unpredictable movements beyond barriers they theoretically shouldn't be able to pass. However it is these exact processes scientists have been studying and attempting to utilize for their own advantage. Here comes quantum computers.
Representing information at the quantum level
Just like classical computers, a quantum computer must be able to represent information before it can process it. In classical computers we have bits which represent a one or a zero. However in in quantum computers we have ‘qubits’ which can represent a zero, a one or both a zero and one. This does not make any sense yet, so lets take a look at an example of a real world qubit. Qubits can be made using an electron, a nucleus or a photon. Lets take a look at how an electron can be used.
Imagine a phosphorus atom, embedded into a silicon crystal. The phosphorus outer electron has a dipole or a magnetic orientation, which we can imagine as ‘spin up’ or ‘spin down.’ We can think of this to be our qubit where ‘spin up’ represents a one and ‘spin down’ represents a zero. The dipole is dependant on the energy state of the electron. At a higher energy state the electron will spin up and at a lower energy state the electron will spin down.
At room temperature the qubit will have enough thermal energy to fluctuate frequently between energy states. Therefore using specialist equipment, the apparatus can be kept just a couple of hundredths of a degree above absolute zero. This means the qubit is stable, without energy and represents a zero. To change it to a one, a strong magnetic field can be applied to the qubit and its orientation will change as it gains energy. A superconducting magnet is used to apply this magnetic field. It now stores a one and this is how qubits can be written to. However should we change the amount of energy applied, the energy level of the qubit could be in-between the two values therefore the qubit is representing neither a one nor a zero, but both. Its fluctuating energy level and degree of rotation will provide a probability as what value it takes when it is measured (e.g. 37% zero and 63% one). This is called superposition and is how a qubit can represent both values at the same time. This is incredibly useful for some types of calculations which we will see later.
The process of reading a qubit is slightly more complicated. The qubit is an electron which is part of a phosphorus atom which is embedded in a silicon crystal. This atom lies close to a special type of transistor. The transistor is comprised of a line of electrons, ordered by their energy levels. When the qubit has the required energy level, it will jump into the transistor as it has more energy than the other electrons. This means the transistor has an extra electron and becomes charged. Therefore a positive charge is applied over the transistor which can be detected. If the voltage is present, we know the qubit held a one and if it isn’t, we know the qubit held a zero.
Calculations with quantum computers
A qubit can be any proportion of both states e.g. 37% zero and 63% one. As we saw before this is called ‘superposition.’ When a qubit or a sequence of qubits is not being measured, each qubit represents both values. Therefore a string of twenty qubits represents all the possible combinations of twenty normal bits at once. Moreover when an operation is applied to a series of qubits through a quantum gate, a sequence of qubits is also the result. This means that the result is all the possible answers for all the possible inputs. This is obviously no use though. Therefore clever algorithms such as the Grover algorithm are used to decide what the correct answer is based on the inputs. An important property of qubits is what’s known as ‘entanglement.’ This is where qubits will change their state instantaneously with the change to a neighbouring qubit. This means the values of other qubits can be deduced without having to measure them. This is important for determining the correct solution to a qubit calculation.
Qubit calculations work by treating the direction of magnetism (energy state dependent) as a 3D vector within a sphere. Matrix calculations can therefore be applied to the vector to determine the value of the resultant qubit. Through properties such as entanglement, the values of other qubits can be determined from the single calculation.
Being able to represent many binary values simultaneously (in parallel) makes quantum computing especially effective for solving problems typically associated with brute force. For example when cracking a password, the sequence of qubits already represents the correct value and smart algorithms can deduce what the discrete value of the password is. Problems which would take classic computers theoretically millions of years can take quantum computers merely minutes. However quantum computers will not replace classical computers. They have strengths when calculating the solutions to some types of problems, however great weaknesses when it comes to others. A classical computer can even be quicker at calculating some types of simple problems. Therefore it is very unlikely you will ever see desktop quantum computers.