## Quantum Computing – Random Ideas

Spooky, bizarre and mind-boggling are all understatements when it comes to quantum physics. Things in the subatomic world of quantum mechanics defy all logic of our macroscopic world. Particles can actually tunnel through walls, appear out of thin air and disappear, stay entangled and choose to behave like waves.

According to Niels Bohr, the parent of the orthodox’ Copenhagen Interpretation’ of quantum physics,’ Anyone who isn’t shocked by quantum theory hasn’t understood it’. Richard Feynman, one of the founding fathers of quantum field theory remarked,’ I think I can safely say that nobody understands quantum theory’.

Quantum mechanics deals with the survey of particles at the atomic and subatomic levels. The term was coined by Max Born in 1924. Though the theory works to provide accurate predictions of phenomena at the subatomic scales, there’s no real understanding of why it works, what it really means or what implications it has for our world picture. Ergo, the best we can do is present you with the central mystery at the very heart of quantum mechanics and show you the way its theoretical structure works to provide real world predictions. Once you decide to go down the rabbit hole, the wonderland of quantum physics, will keep you enthralled forever. So here we go.

As seen by a layman, quantum mechanics seems to be more like a bizarre phenomenon or science fantasy flick, full of jargon and complicated mathematical equations. However, it is easier to respond to a look at the foundations of quantum mechanics, provided one is not baffled by the fact that every electron is a particle, as well as a wave at the same time. In fact, the truth is even stranger. Electron cannot fall on each side of the particle/wave dichotomy. It is only described by a wavefunction or state vector, that can calculate the probability or likelihood of finding a particle. The theory sets fundamental limitations on how accurately we can measure particle parameters, replacing classical determinism with probabilistic determinism. The theory describes just about every phenomena in nature, ranging from the blue of the sky with the organization of the molecules that make organic life possible.

## Everything You Always Wanted To Know About Quantum Computing

Quantum mechanics arose as a superior theory, due to the fundamental failure of classical mechanics to describe several atomic phenomena. With the discovery of electron, by J.J. Thomson, in the year 1897, the idea of classical physics was proved to be inapplicable at the atomic level. Classical physics, which was governed by Newton’s laws of motion and Maxwell’s laws of electromagnetism, was used to determine and predict the movement of particles. But this theory was unable to explain the following three critical and world famous experiments.

Neils Bohr was liable for a third breakthrough in 1913 when he devised a quantum mechanical model of the atom, involving fixed orbitals for the electrons. His model correctly explained the range of hydrogen and the stability of atoms. These according to classical physics should be unstable and decay in less than 1 millionth of a second.

When ultraviolet light is shone on certain metal surfaces, electrons are emitted. This phenomenon, whereby electrons in atoms get liberated by the absorption of energy from incident light, is called the photoelectric effect. Classical electromagnetic theory predicted that the amount of electrons emitted and their kinetic energy is dependent on the intensity of light reflected from the surface. However, experiments had shown that the energy and many of electrons was a function of frequency. Using Planck’s energy quantization rule (E = hν), Albert Einstein conceptualized light as a stream of photons, successfully explaining the photoelectric effect in the area of light frequency. Thus light, which was yet known to become a wave, was now known to hold a dual character-that of a wave and a particle.

The next breakthrough occurred in 1905, when Einstein explained the photoelectric effect, whereby electrons are emitted from a metal plate upon which light is being shone. Once again, classical physics couldn’t explain the photoelectric effect properly. By postulating the presence of photons, particles of light, Einstein was able to correctly explain the effect.

Classical electromagnetic theory couldn’t explain the optical line emission or absorption spectra, arising from gases and liquids. Bohr’s atomic model, based on angular momentum quantization and quantized energy levels provided accurate experimental values of optical spectra for Hydrogen, thus providing further validation to the quantization approach.

All these phenomenological developments and heuristic theory laid groundwork for the old quantum theory. It was further amended by scientists like W. Heisenberg and E. Schrödinger to form the new quantum theory on the basis of central principle of the wave nature of matter particles.

To understand the quantum realm, you need to unlearn and unplug yourself from classical intuition-which serves us either in the macroscopic world, but is eminently useless in here. Let us peel off our classical intuition layer by layer.

Experiments like the photoelectric effect demonstrated particle wave duality of light. If light waves behaved like particles, could matter particles also behave like waves? This was the question asked by Louis de Broglie, a French physicist and answered through his PhD thesis in 1924. He hypothesized the existence of Matter Waves corresponding to every particle, whose wavelength would be inversely proportionate to the momentum of the particle.

Experiments conducted by Davisson and Germer at Bell Labs in 1927, conclusively proved the wave nature of particles. The duo fired electrons at a crystallized nickel target to observe wave-like diffraction patterns. Such a pattern was only observed for light waves till date. Thus it was conclusively proved that particles behave like waves and vice versa.

In 1926, Erwin Schrödinger formulated an equation that described the behaviour of these matter waves. He successfully derived the energy spectrum of Hydrogen atom, by treating orbital electrons as standing matter waves. Max Born interpreted the square of amplitude of these waves to become the probability of finding associated particles in a localized region. All these developments led to the creation of quantum mechanics as a scientific theory, well grounded in experiment and formalism. The wavefunction describing any particle in quantum mechanics is a matter wave, whose form is computed through the utilization of Schrödinger equation. Ergo, matter waves form the central most important aspect of quantum mechanics.

The fundamental limitation on accuracy is quantified in the form of the Planck’s constant. No matter how accurate your measuring equipment is, it is singularly impossible to minimize the error in measurement to fewer than the Planck’s constant. This is because a particle being a matter wave, is inherently delocalized (spread out in space). The more accurately you know the position, more uncertain you’re about the momentum and vice versa. Generally, the uncertainty principle is applicable to any dual set of complementary physical quantities that cannot be measured with arbitrary precision.

Since we cannot measure the position of a particle accurately, the entire idea of a fixed orbit or trajectory goes for a toss. You can no longer plot the trajectory of a particle on a graph, like in Newtonian mechanics. The particle itself being a wave has its position spread out in space. The entirety of information about particles is encoded in the wavefunction Ψ, that is computed in quantum mechanics, using the Schrodinger equation-a partial differential equation that can set the nature and time evolution of the wavefunction.

Once we have Ψ (the wave function)-for a system, the probability of a particle’s position is set by the square of its modulus-│Ψ│2. So we have basically given up on predicting the position of a particle accurately, because of the uncertainty principle. All we can do is predict the probabilities. One unnerving consequence of this fact is that, until a measure is made, the particle essentially exists in all positions! This paradox was put forward famously in the form of the Schrödinger’s cat in the box thought experiment.

This is a hypothetical experiment in which a cat’s put inside a box, with some equipment which releases poisonous gas, on detection of beta particles emitted by a radioactive source. Since beta emission is random by nature, there’s no way of knowing when the cat dies.

There is no way of knowing whether the cat is dead or alive, until the box is opened. So until we look inside, according to quantum theory, the cat is both dead and alive! This is the fundamental paradox which was introduced by the theory. It’s one way of illustrating the way quantum mechanics requires us to think. Until the position of a particle is measured, it exists in all positions during the same time, just like the cat is both dead and alive.

What we have introduced you to here, is only the proverbial end of the iceberg. Quantum mechanics allows one to think of interactions between correlated objects, at a pace more rapidly than the speed of light (the phenomenon known as quantum entanglement), frictionless fluid flow in the form of superfluids with zero viscosity and current flow with zero resistance in superconductors. It may one day revolutionize the way computers operate, through quantum computing. It also laid the foundation of advanced theory of relativity, knows as quantum field theory. This underlies all of particle physics.

At the initial stage, you might find your brain circuits getting fused, while trying to capture the basics of quantum mechanics. However, as you dig deeper into quantum wonderland, into the intricacies and complexities of equations and see the application in real life, the fascination goes on rising, revealing beauty at the most fundamental level. The world isn’t just what is seen by naked eyes, but something which is much beyond our comprehension. Quantum mechanics has revolutionized the study of physics, and opened the gateway to see new horizons.