Quantum entanglement is the process by which particles interact in such a way that their physical properties such as momentum, spin and polarisation perfectly correlate. In quantum computing this allows us to infer the state of a qubit based on the state of another qubit elsewhere in the computer, even if they are separated by space. This correlation is what makes quantum computers so much faster than classical computers because they don’t have to read/write to every qubit of data in order to measure/change their value. For any n qubits, 2^n classical bits are required to represent the same data because functions can be parallelised by way of quantum entanglement. This exponential increase makes it impossible to represent large memories of qubits with classical bits.

A problem arises when you want to measure the outcome of a calculation. Qubits are complex numbers that can code for an infinite amount of information but on observation, will only ever be either a 1 or a 0. This is because when they are read from by the quantum computer, a signal is sent to the qubit which forces it to become one state or the other. The qubit collapses either into a 1 or a 0. The resultant state is influenced by the superposed probability vector, however a probability vector of 0.8 “up” doesn’t guarantee an observed reading of “up” (1); therefore, multiple signals are sent by the quantum processor in order to ascertain a more reliable value.

Despite this issue with reading from memory comprised of qubits, the internal logic of a quantum computer can manipulate the data without forcing it into one of its two binary states. This is what allows quantum computers to output the processing power they do since during their calculations they can make use of particle superpositions.

The ability to put individual ions in a superposed state was discovered by Serge Haroche and David Wineland who were awarded the Nobel Prize for their work in 2012. Before the breakthrough, it was only possible to trap an array of “hot” (a few Kelvin) ions. Particles at room temperature are spread among millions of energy states; however, during Wineland’s experiments (a few microkelvin) they were measured to near 100% probability at “ground state” – the lowest quantum energy state. This advancement allowed for the demonstration of other thought experiments such as “Schrödinger’s cat” whereby on absorbing or emitting a photon, a single ion would change state and become the superposition of two other states; however, collapses into just one when measured. This is symmetrical to the design of a qubit.

The trapped ion approach to quantum computers utilises multiple oscillating and static electromagnetic fields to suspend charged particles in free space by interacting with the forces between the subatomic particles defined by Coulomb’s Law (relates force to the charges and distance between two stationary charged particles). Qubits are stored as the electronic states of these ions. This approach allows quantum information to be transferred relatively easily with a shared trap (another electromagnetic field). As well as trapping charged particles, lasers can be used to entangle and superpose qubits since the energy state of the particle determines the state of the qubit.

Another difficulty with the manufacture of quantum computers is the requirement of a temperature near to absolute zero. Quantum states are defined by voltage ranges typically of around 0.25V (e.g. 1.50-1.75V). If the quantum computer isn’t at a temperature of absolute zero, the particles will gain kinetic energy randomly causing a change in the measured voltages. This may change a qubit’s state from being measured as state A to being measured as state B if the voltage moves from the range defining one state to the range defining another. In addition to this, these cold temperatures and extremely large magnetic fields are required to entangle qubits in the first place. A low temperature, as stated by the Boltzmann distribution [next paragraph], allows spin to be more ordered, and a magnetic field induces a spin in a certain direction. This unitary polarisation is what forces particles into an entangled state. The Hamiltonian function outputs the state of a quantum system.

The output is positive when the center spin differs to either its adjacent spins or the external magnetic field and negative when it is the same (i.e. ferromagnetic behavior) such that all particles will switch in order to maintain a low energy state. The Boltzmann probability distribution with inverse temperature is a common representation of the probability that a given temperature will induce a higher energy state and cause a change in spin.

A fascinating prospect that quantum computers are vital for is the study of black holes. Quantum mechanics states that information is never lost; however, information that surpasses the event horizon of a black hole is thought to be impossible to retrieve since all information – including that of subatomic particles – is mixed up. This is known as the “black hole information paradox”.

Black holes evaporate over extremely long periods of time by emitting Hawking radiation – atoms created by sudden pockets of energy in the event horizon. When black holes emit Hawking radiation, they emit two entangled particles, one of which gains enough energy to escape the gravity of the black hole, and other falls back into it. It’s believed that by studying the state of Hawking radiation we can ascertain what is occurring inside the black hole. This process is known as the “teleportation” of information using quantum entanglement and can also be performed by dropping an entangled qubit into a black hole. This is a much faster alternative to waiting 10^67 years for a black hole of the sun’s mass to evaporate in order to reconstruct the information – as some physicists believe. In order to model the process whereby entangled particles are emitted from a black hole, quantum computers are used. This model was proved successful by a team at the University of Maryland and measured teleportation rates of up to 80%; a teleportation fails when the qubit decays by decoherence rather than being scrambled. The experiment modelled a three-qubit black hole inside a seven-qubit trapped-ion quantum computer and was deemed a success. An added benefit is that this process can be used to “benchmark” quantum computers which will become even more valuable as more and more advancements are made.

Bibliography:

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