# Deep Dive into the world of Quantum Mechanics & Quantum Computing
This was a School Project for Physics
Some information & pages has been redacted / removed for obvious reasons.
[https://lh3.googleusercontent.com/JWlu_REcb8fypYRnR3k1WOyPgMnaw5ChmKmGOTdWyOc2qEjPJN_475-MJEDMXUxsSFr1DHT7JQVqFr2z0l-j-GnRyRZcPy-i1Q-hM_7R5v_7D7dMHfBt0GHtagUvV0G56ngPPsXs](https://lh3.googleusercontent.com/JWlu_REcb8fypYRnR3k1WOyPgMnaw5ChmKmGOTdWyOc2qEjPJN_475-MJEDMXUxsSFr1DHT7JQVqFr2z0l-j-GnRyRZcPy-i1Q-hM_7R5v_7D7dMHfBt0GHtagUvV0G56ngPPsXs)
Author: Vimarsh Shah
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Physics Project
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# **Acknowledgement**
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I would also like to thank [IBM Quantum](https://quantum-computing.ibm.com/) for giving me the opportunity to use their Quantum Computers and experiment in their sandbox and a real cutting edge quantum computer. They also have amazing resources to understand quantum circuits.
# **Introduction: What is Quantum Physics**
Wikipedia states that: Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science.
Quantum Physics the term is believed to be coined in the 1920s with discoveries of Neih Bohr and Shrodinger. To most of us, it sounds like abstract maths, trying to explain laws that rule over our universe at the sub-atomic level, but it has far reaching applications and use cases- some of which unlock the gates of computing and level of understanding of the universe we did not have before.
Before there was Quantum Physics, there was so called “classical Physics”, all existing before Einstein’s theory of relativity and subatomic interactions. With its advent, not only could microscopic interactions be explained, but they could also be scaled to macroscopic level.
In quantum mechanics, particles have wave-like properties, and a particular wave equation, the Schrodinger equation, governs how these waves behave.
In this project we will be going through the history of major developments which were the basis of Quantum Mechanics and properties used in Quantum Computing. From experiments which changed how we saw particles and bizarre properties of entanglement, these phenomena have the ability to explain so many of our questions. Be it from computing exponentially faster, to finding out the history of the Universe or even transferring information (and hence matter) from one location to another.
All these effects could also enable us to create cutting edge neural networks able to understand the world, even humans have not the understanding of. [Quantum teleportation](https://physicsworld.com/a/atoms-teleport-information-over-long-distance/) is also a highly perceivable future where we will be able to transfer information at the speed of light (or even faster? - instantaneous?) without any need of physical connection between two points.
In this project we will also be using a real Quantum Computer and explaining its working and tech behind it. We will also be coding it using Logic Gates and try to break the encryption that is keeping the web safe.
Quantum Mechanics also has a lot of deep philosophical implications and other developments which will be beyond the scope of this project, the primary one being the Quantum Field Theory. Also abbreviated QFT - it describes all elementary particles as vibrational modes in fundamental fields that exist at all points in space and time through the universe. Quantum ElectroDynamics, QED, provides this description for one such field, the ElectroMagnetic field. The pillars of QED are the description of the behavior of the EM field and the description of the behavior of the electron via the [Dirac equation](https://en.wikipedia.org/wiki/Dirac_equation).
# **Rough Timeline of the events**
[https://lh5.googleusercontent.com/1IwH8Ii2MCteklNhbpYhzQLy25o-VXyWND1xC2I92LUG_kR3GBjkLALO8W1Z_bQWzi5lxG3KoOm9gKyaAO7_BtBI7bBoUCF1s-AGJ2c7uzdbbsHNiOWepYe6IQKGnXnFeid5Obzd](https://lh5.googleusercontent.com/1IwH8Ii2MCteklNhbpYhzQLy25o-VXyWND1xC2I92LUG_kR3GBjkLALO8W1Z_bQWzi5lxG3KoOm9gKyaAO7_BtBI7bBoUCF1s-AGJ2c7uzdbbsHNiOWepYe6IQKGnXnFeid5Obzd)
[Courtesy of Andrew Alexander, taken from imgur](https://imgur.com/RbndZgZ)
# **Black Body Radiation**
In 1900, a German physicist Max Planck was experimenting in trying to understand the different colors that are emitted when a body is heated and sought to explain the distribution of colors emitted over the spectrum in the glow of red-hot and white-hot objects, such as light-bulb filaments. When making physical sense of the equation he had derived to describe this distribution, Planck realized it implied that combinations of only certain colors (albeit a great number of them) were emitted, specifically those that were whole-number multiples of some base value. Somehow, colors were quantized! This was unexpected because light was understood to act as a wave, meaning that values of color should be a continuous spectrum. What could be forbidding atoms from producing the colors between these whole-number multiples?
Since the early 19th century spectrometers and other devices had shown that all different elements emit and absorb just specific colours of light - called spectral lines. It was found to be one of the more reliable methods to determine elements that stars, distant planets and galaxies were made off, researchers were still confused about why they gave the specific lines in the first place. Max Planck proposed a mathematical model in which the thermal radiation given off by an element was proportional to the harmonic oscillations happening inside the atom. The quantum of energy for each oscillator, according to Planck, was proportional to the frequency of the oscillator; the constant of proportionality is now known as the Planck constant. The Planck constant, usually written as h, has the value of 6.63×10−34 J s. So, the energy E of an oscillator of frequency f is given by
[https://lh4.googleusercontent.com/twCnd58lSG-OSFWrASggk42Qt1HQ0pJ4pQGP-xUNZAG5wxTIn0SPWuAlHSeVZam9SUwDDGTyGo_h5YF5mYAPcRnamSBM9dKlHA2phr8SrtBYczRBvAPW_RtKbcLmX-kZqbJ9MNw3](https://lh4.googleusercontent.com/twCnd58lSG-OSFWrASggk42Qt1HQ0pJ4pQGP-xUNZAG5wxTIn0SPWuAlHSeVZam9SUwDDGTyGo_h5YF5mYAPcRnamSBM9dKlHA2phr8SrtBYczRBvAPW_RtKbcLmX-kZqbJ9MNw3)
To change the color of the radiating body, it is necessary to change the temperature. > Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T, when there is no net flow of matter or energy between the body and its environment.
This was further researched upon in 1913 when Niels Bohr applied Planck's hypothesis of quantization to Rutherford's 1911 "planetary" model of the atom, which postulated that electrons orbited the nucleus the same way that planets orbit the sun. According to Bohr electrons were restricted to "special" orbits around an atom's nucleus. They can only "jump" between special orbits, and the energy produced by the jump or released when jumping to a lower level causes specific colors of light to be absorbed by atom or observed as spectral lines. Though quantized properties were invented as a mere mathematical trick, they explained so much that they became the founding principle of Quantum Mechanics.
# **Light is quantized**
In 1905, Albert Einstein took an extra step. He suggested that quantization was not just a
In 1905, Einstein published a [paper](http://www.esfm2005.ipn.mx/ESFM_Images/paper1.pdf) , in which he envisioned light traveling not as a wave, but as some manner of "energy quanta." This packet of energy, Einstein suggested, could "be absorbed or generated only as a whole," specifically when an atom "jumps" between quantized vibration rates. These individual packets of light beams were called photons. This would also apply, as would be shown a few years later, when an electron "jumps" between quantized orbits. Under this model, Einstein's "energy quanta" contained the Energy of a single photon of light “f” is given by the frequency multiplied by the Plank’s constant “h”.
[https://lh6.googleusercontent.com/jyK5Nrw_jTq_foNg1TDgjnVlQURGxkiv933HhkMTSILuKzWT5z1tnBXyKtiTF0mfh2dokQ1xiEG1QaccZd977_KYZIMbK7ar1OC5S_qYITUyPdXyuxJL8_53eiVHDxkA33ToiA8p](https://lh6.googleusercontent.com/jyK5Nrw_jTq_foNg1TDgjnVlQURGxkiv933HhkMTSILuKzWT5z1tnBXyKtiTF0mfh2dokQ1xiEG1QaccZd977_KYZIMbK7ar1OC5S_qYITUyPdXyuxJL8_53eiVHDxkA33ToiA8p)
For centuries, scientists had debated between two possible theories of light: Is it a wave or does it instead comprise a stream of tiny particles? By the 19th century, the debate was generally considered to have been settled in favor of the wave theory, as it was able to explain observed effects such as refraction, diffraction, etc. Maxwell had shown that electricity, magnetism and even light were all the phenomena of the electromagnetic field.
Eventually, however, the photon model became favored. One of the most significant pieces of evidence in its favor was its ability to explain several puzzling properties of the [photoelectric effect](https://en.wikipedia.org/wiki/Photoelectric_effect).
**The Photoelectric Effect**
Under the right circumstances light can be used to push electrons, freeing them from the surface of a solid. This process is called the photoelectric effect (or photoelectric emission or photoemission), a material that can exhibit this phenomenon is said to be photoemissive, and the ejected electrons are called photoelectrons.
It was first observed in 1887 by Heinrich Hertz during experiments with a spark gap generator (the earliest device that could be called a radio). In these experiments, sparks generated between two small metal spheres in a transmitter induce sparks that jump between two different metal spheres in a receiver. Compared to later radio devices, the spark gap generator was notoriously difficult to work with. The air gap would often have to be smaller than a millimeter for the receiver to reliably reproduce the spark of the transmitter. Hertz found that he could increase the sensitivity of his spark gap device by illuminating it with visible or ultraviolet light. Later studies by J.J. Thomson showed that this increased sensitivity was the result of light pushing on electrons.
Philipp Lenard, an assistant of Hertz, used metal surfaces that were first cleaned and then held under a vacuum so that the effect might be studied on the metal alone and not be affected by any surface contaminants or oxidation. The metal sample was housed in an evacuated glass tube with a second metal plate mounted at the opposite end. The tube was then positioned or constrained in some manner so that light would only shine on the first metal plate — the one made out of photoemissive material under investigation. Such a tube is called a photocell. Lenard connected his photocell to a circuit with a variable power supply, voltmeter, and microammeter. He then illuminated the photoemissive surface with light of differing frequencies and intensities.
[https://lh4.googleusercontent.com/5KOAkK-7ZGIaczISmuNH6ZB9DyhpPHAhZOTV1DAxyJl8RRfcCPFoNQterni6JZ7Fvj7lTeIOWNM9oMQ-gyLz-O2x6_3X_v7QXrTHSeDIM1Yqi8_yGC1590zf8wgSmZjY_yDAVOAv](https://lh4.googleusercontent.com/5KOAkK-7ZGIaczISmuNH6ZB9DyhpPHAhZOTV1DAxyJl8RRfcCPFoNQterni6JZ7Fvj7lTeIOWNM9oMQ-gyLz-O2x6_3X_v7QXrTHSeDIM1Yqi8_yGC1590zf8wgSmZjY_yDAVOAv)
Knocking electrons free from the photoemissive plate would give it a slight positive charge. This experiment did not create electrons out of light, it just uses the energy in light to push electrons that are already there around the circuit. The photoelectric current generated by this means was quite small, but could be measured with the microammeter. It also serves as a measure of the rate at which photoelectrons are leaving the surface of the photoemissive material. This was further developed to become solar panels in the modern age.
Robert Millikan in 1914, found that light with frequencies below a certain cutoff value, called the threshold frequency, would not eject photoelectrons from the metal surface no matter how bright the source was. He saw the following results:
[https://lh5.googleusercontent.com/8aF5UBkOjm5nP1QcanmSJaR3nVBUFaSMnxuMzQcjPaLjxoq70p6TsbctdXPtZFl0SMkdSfiJPDeCI-zGwqMdl0rctbv2P_-QELt0D8pC1wLSuZSlegmSLqnaj674GhRMMznBUlQv](https://lh5.googleusercontent.com/8aF5UBkOjm5nP1QcanmSJaR3nVBUFaSMnxuMzQcjPaLjxoq70p6TsbctdXPtZFl0SMkdSfiJPDeCI-zGwqMdl0rctbv2P_-QELt0D8pC1wLSuZSlegmSLqnaj674GhRMMznBUlQv)
This could not be directly explained by the realm of classical physics. There ought to be something they had not thought of. The classical model of light describes it as a transverse, electromagnetic wave. A wave model of light would predict an energy-amplitude relationship and not the energy-frequency relationship described above. Here was the thing: Scientists believed that if a light was of high enough intensity it should be able to knock the electron out of the orbit, but that didn’t happen. As mentioned earlier a lower frequency of light even at very high intensity was not able to remove the electron, whereas a higher frequency light especially UV rays were able to remove electrons for almost any material.
The two factors affecting maximum kinetic energy of photoelectrons are the frequency of the incident radiation and the material on the surface. Planck did not believe that radiation was actually broken up into little bits as his mathematical analysis showed. He thought the whole thing was just a shortcut that gave him the right answers. It was Einstein who recognised that Planck's contrivance was in fact a reasonable description of reality. What we perceive as a continuous wave of electromagnetic radiation is actually a stream of discrete particles. (called photons).
**Presence shown in the real world:**
The relationship between the frequency of electromagnetic radiation and the energy of each photon is why ultraviolet light can cause sunburn, but visible or infrared light cannot. It is also why even though there are lots of radio waves (WiFi and 5G!) they cannot damage the DNA as it is not powerful enough to knock an electron from any atom.
**What does it signify?**
The photoelectric effect showed the presence of light as quantised particles rather than an electromagnetic wave as was believed earlier. This would then set the foundation for a game-changing theory of Wave-Particle Duality.
# **Matter also Quantized**
Niels Bohr proposed a new model of the atom that included quantized electron orbits: electrons still orbit the nucleus much as planets orbit around the sun, but they are permitted to inhabit only certain orbits, not to orbit at any arbitrary distance. When an atom emitted (or absorbed) energy, the electron did not move in a continuous trajectory from one orbit around the nucleus to another, as might be expected classically.
Instead, the electron would jump instantaneously from one orbit to another, giving off the emitted light in the form of a photon. The possible energies of photons given off by each element were determined by the differences in energy between the orbits, and so the emission spectrum for each element would contain a number of lines. [[further reading](https://courses.lumenlearning.com/physics/chapter/30-3-bohrs-theory-of-the-hydrogen-atom/)]
When a gas is heated, it gives off light only at discrete frequencies. For example, the visible light given off by hydrogen consists of four different colors, as shown in the picture below. Balmer's formula explained how the frequencies of different lines were related to each other without explaining why, which Bohr could with reasoning.
# **Wave Particle Duality**
Light is not only just a wave but also particles called “photons” as mentioned earlier. But, if we just considered light to be made of particles called photons then it wouldn’t explain the phenomenon of reflection, diffusion. In fact, let’s just say we have two light sources crossing paths with each other - wouldn’t it create some sort of explosion or energy burst if particles collide? But it doesn’t. Hence, we consider light to also be a wave and a particle. This hypothesis with further research also expanded to all particles and all forms of matter.
Wave-particle duality refers to the fundamental property of matter where, at one moment it appears like a wave, and yet at another moment it acts like a particle.
Colliding particles will bounce off each other but colliding waves pass through one another and emerge unchanged. But overlapping waves can interfere - where a trough overlaps a crest the wave can disappear altogether.
The interference pattern of a wave incident on two holes in a screen. The holes can be seen near the bottom of the image. The waves above the screen show regions of destructive interference, where the wave crests overlap troughs and cancel out, and regions of constructive interference, where the wave crests overlap crests and reinforce. Tim Davis
[https://lh6.googleusercontent.com/OHRl1YvTNoolTREosiht_hmYi0jQC5_AQQ_SEpsVnLtGDC7LH2L0wOlY8ai-AimIQL3PvjZmDOzpVi3SHMW_VQwOFHUJP-ryzn0WMbH7C224UXxwP_mKy8w_19iE3s3qBnmu3lfq](https://lh6.googleusercontent.com/OHRl1YvTNoolTREosiht_hmYi0jQC5_AQQ_SEpsVnLtGDC7LH2L0wOlY8ai-AimIQL3PvjZmDOzpVi3SHMW_VQwOFHUJP-ryzn0WMbH7C224UXxwP_mKy8w_19iE3s3qBnmu3lfq)
This can be seen when parts of a wave pass through closely spaced holes in a screen. The waves spread out in all directions and interfere, leading to regions in space where the wave disappears and regions where it becomes stronger.
The image on the left shows an example of the double slit experiment invented by English polymath Thomas Young.
[https://lh4.googleusercontent.com/glFR1gMB2dvPxhVR4DLH4l-qlwO-qsVpF1vXw-lhZmJ5mVplPbe12kMtWW9x27z_uKWYEp32kLQT5g0qP5PYu5krP2OijeuUEKYM3MEBrpJ1YuU914jMu918eiOywMkR0XtTnqkZ](https://lh4.googleusercontent.com/glFR1gMB2dvPxhVR4DLH4l-qlwO-qsVpF1vXw-lhZmJ5mVplPbe12kMtWW9x27z_uKWYEp32kLQT5g0qP5PYu5krP2OijeuUEKYM3MEBrpJ1YuU914jMu918eiOywMkR0XtTnqkZ)
In double slit experiment a beam of light is directed through two narrow, closely spaced slits, producing an interference pattern of light and dark bands on a screen. If one of the slits is covered up, we would expect that the intensity of the fringes due to interference would be halved everywhere. But in reality, a much simpler pattern is seen, a diffraction pattern diametrically opposite the open slit. ([Wikipedia](https://en.wikipedia.org/wiki/Double-slit_experiment#:~:text=62-,Interpretations%20of%20the%20experiment,Like,-the))
[https://lh3.googleusercontent.com/-3Q0jAdK0CgHfA0LrBFxMFfXtN3E9UfyTdGapIa4oC2a-TByH6Momm1qRGHMzcHZW0ELXffz1tc-TTaMGeDEysRNhmCSI5H9D_LdTSsVklOupD2KJKfIGWPoUTm9GzKZD_r62Psh](https://lh3.googleusercontent.com/-3Q0jAdK0CgHfA0LrBFxMFfXtN3E9UfyTdGapIa4oC2a-TByH6Momm1qRGHMzcHZW0ELXffz1tc-TTaMGeDEysRNhmCSI5H9D_LdTSsVklOupD2KJKfIGWPoUTm9GzKZD_r62Psh)
**Significance**
Variations of the double-slit experiment have been performed using electrons, atoms, and even large molecules, and the same type of interference pattern is seen. Thus it has been demonstrated that all matter possesses both particle and wave characteristics.
Even if only one particle (e.g. photon or electron) is passing through the apparatus at a time, the same interference pattern develops over time. The quantum particle acts as a wave when passing through the double slits, but as a particle when it is detected. This is a typical feature of quantum complementarity: a quantum particle acts as a wave in an experiment to measure its wave-like properties, and like a particle in an experiment to measure its particle-like properties.
De Broglie expanded the Bohr model of the atom by showing that an electron in orbit around a nucleus could be thought of as having wave-like properties. In particular, an electron is observed only in situations that permit a standing wave around a nucleus. His treatment of quantum events served as a starting point for Schrödinger when he set out to construct a wave equation to describe quantum-theoretical events.
# **Spin and spinors**
Spin is one of two types of angular momentum in quantum mechanics, the other being orbital angular momentum. The orbital angular momentum operator is the quantum-mechanical counterpart to the classical angular momentum of orbital revolution and appears when there is periodic structure to its wave function as the angle varies. For photons, spin is the quantum-mechanical counterpart of the polarization of light; for electrons, the spin has no classical counterpart.
In the Stern–Gerlach experiment, silver atoms were observed to possess two possible discrete angular momenta despite having no orbital angular momentum. The existence of the electron spin can also be inferred theoretically from the Pauli exclusion principle—and vice versa, given the particular spin of the electron, one may derive the Pauli exclusion principle.
[Video on Spin - the quantum magnet](https://upload.wikimedia.org/wikipedia/commons/transcoded/9/9e/Quantum_spin_and_the_Stern-Gerlach_experiment.ogv/Quantum_spin_and_the_Stern-Gerlach_experiment.ogv.720p.webm) Spin is represented by [spinors](https://en.wikipedia.org/wiki/Spinor) which are not considered Tensors but do have direction. This also makes it plausible for an electron to have a preferred space for it to stay in.
# **Modern Quantum Mechanics**
Among many others, Erwin Schrödinger stands out as the one who showed chance was central to how the universe worked. And he produced an entirely new view of the microworld in the process. Attempting to solve problems with the theory of atomic structure, Schrödinger wrote an equation that determines how a probability wave, known as a wave function, evolves over time.
This was a huge step. It means that for a given electron at a given time, the probability that it is where you want it – or indeed anywhere at all – can be precisely calculated.
Schrödinger’s equation also has a profound consequence in the double-slit experiment. Depending on your opinion, it can mean several things. But there are two popular interpretations.
*Was Schrödinger’s cat a real pet?*
Whether Schrödinger’s famous thought experiment was based on a real cat is uncertain. But he did have a cat called Milton at Oxford University. He introduced the idea of a cat being both dead and alive, until being observed, to ridicule the popular interpretation of quantum superposition.
Either a particle somehow chooses which of many possible paths to follow to end up where it lands on the back screen. Or it takes all possible paths but only lives out one in our universe, the rest playing out in an ever-expanding number of parallel universes. There are still debates going on around both of these interpretations but they might also answer some questions of life in general and our stance in the Universe.
All of the postulates by these different scientists were put together as the “Copenhagen Interpretation”. Although this interpretation did have a lot of pitfalls and was [disproved](https://www.sjsu.edu/faculty/watkins/copenhageninterp4.htm). The current understanding is way more deep and complex.
**The Pauli exclusion principle**
The Pauli Exclusion Principle states that, in an atom or molecule, no two electrons can have the same four electronic quantum numbers. As an orbital can contain a maximum of only two electrons, the two electrons must have opposing spins. This means if one electron is assigned as a spin up (+1/2) electron, the other electron must be a spin-down (-1/2) electron.
**Application to the hydrogen atom**
Bohr's model of the atom was essentially a planetary one, with the electrons orbiting around the nuclear "sun". However, the uncertainty principle states that an electron cannot simultaneously have an exact location and velocity in the way that a planet does. Instead of classical orbits, electrons are said to inhabit atomic orbitals.
An orbital is the "cloud" of possible locations in which an electron might be found, a distribution of probabilities rather than a precise location. Each orbital is three dimensional, rather than the two-dimensional orbit, and is often depicted as a three-dimensional region within which there is a 95 percent probability of finding the electron.
[https://lh4.googleusercontent.com/TNPcoOI3-ZeuSd8EY_-cWBPqDviZhSsYRGS9BBN5wS9zSv9A_W-yCrybJm2S62DMlKQ6BJd4xDed-9G0JW4P8b1_sFZJ4nMOyu0nnTnJYZZ8mL2nlutTp48pk6VHp485wt_nelC-](https://lh4.googleusercontent.com/TNPcoOI3-ZeuSd8EY_-cWBPqDviZhSsYRGS9BBN5wS9zSv9A_W-yCrybJm2S62DMlKQ6BJd4xDed-9G0JW4P8b1_sFZJ4nMOyu0nnTnJYZZ8mL2nlutTp48pk6VHp485wt_nelC-)
Credit: [Wikimedia Foundation](https://en.wikipedia.org/wiki/Quantum_mechanics#/media/File:Hydrogen_Density_Plots.png)
# **Quantum entanglement**
In 1935 Einstein, Boris Podolsky and Nathan Rosen thought they had found a paradox in the equations of quantum mechanics. They showed that two particles that are entangled – linked in a quantum-mechanical sense – would communicate instantly over vast regions of space. But this meant information would be transmitted faster than light – forbidden by the theory of relativity.
The Pauli exclusion principle says that two electrons in one system cannot be in the same state. Nature leaves open the possibility, however, that two electrons can have both states "superimposed" over each of them. Recall that the wave functions that emerge simultaneously from the double slits arrive at the detection screen in a state of superposition. Nothing is certain until the superimposed waveforms "collapse". At that instant, an electron shows up somewhere in accordance with the probability that is the square of the absolute value of the sum of the complex-valued amplitudes of the two superimposed waveforms.
In a letter to Neils Bohr, Einstein labelled the phenomenon a 'spooky remote effect'. But in the 1950s, Chien-Shiung Wu showed that entangled particles indeed behaved as quantum mechanics predicted. Then in the 1960s, John Bell revealed that quantum mechanics is fundamentally nonlocal – meaning entangled objects are linked but do not communicate through spacetime – and therefore no paradox exists.
[[Reference Video](https://youtu.be/DbbWx2COU0E)]
# **Quantum Computers**
Quantum Computers can harness the unique information processing capability of quantum mechanics to exponentially optimize the time and energy needed to solve large complex problems. This could be the next big thing since the integrated circuit, that will transform the global market and life as we know it.
Imagine this, there are 10⁷⁸ to 10⁸² atoms in the visible universe, so a quantum computer with 265 qubits can store as many values as there are in the entire universe and we are looking to break that fold within the decade.
# **Limits of Human Technology**
For most of our history, human technology consisted of our brains, fire, and sharp sticks. While fire and sharp sticks became power plants and nuclear weapons, the biggest upgrade has happened to our brains. Since the 1960's, the power of Computers has kept growing exponentially, allowing computers to get smaller and more powerful at the same time.
[https://lh4.googleusercontent.com/9nBNWA6ZXfrC2c-ytIJQYbHkuzEUHdOE9_LPwuAu1nOD95V9UvL7awryj2KvP7rKP8pKBOM-eJ99fATgTWu2WIYrJ0gjkyAjq_2E7HXm4xPbpGslQj_vkKS9t8KHNnrL_p9PpVjz](https://lh4.googleusercontent.com/9nBNWA6ZXfrC2c-ytIJQYbHkuzEUHdOE9_LPwuAu1nOD95V9UvL7awryj2KvP7rKP8pKBOM-eJ99fATgTWu2WIYrJ0gjkyAjq_2E7HXm4xPbpGslQj_vkKS9t8KHNnrL_p9PpVjz)
But this process is about to meet its physical limits. Computer parts are approaching the size of an atom. A computer is made up of very simple components doing very simple things.
**Classical Computers**
Representing data, the means of processing it, and control mechanisms. Computer chips contain modules, which contain logic gates, which contain transistors. A transistor is the simplest form of a data processor in computers, basically a switch that can either block, or open the way for information coming through. This information is made up of bits which can be set to either 0 or 1.
Combinations of several bits are used to represent more complex information. Transistors are combined to create logic gates which still do very simple stuff. For example, an AND Gate sends an output of 1 if all of its inputs are 1, and an output of 0 otherwise. Combinations of logic gates finally form meaningful modules, say, for adding two numbers. Once we can add, we can also multiply, and once multiplication is possible, anything can happen.
[https://lh5.googleusercontent.com/CK-f6RtEx8DDd0-6p1YVEtNrpdYXUFCd-B9mNT8kvdixmffuX5W11Rq8kPAgsAX4wycHmnVxA1CdKdQS10gtUIOx0RfyXv1C2SbRgz8Y1Tj3OLzAP8u6muGWpIThHh0be3_KSCpP](https://lh5.googleusercontent.com/CK-f6RtEx8DDd0-6p1YVEtNrpdYXUFCd-B9mNT8kvdixmffuX5W11Rq8kPAgsAX4wycHmnVxA1CdKdQS10gtUIOx0RfyXv1C2SbRgz8Y1Tj3OLzAP8u6muGWpIThHh0be3_KSCpP)
Since all basic operations are literally simpler than first grade math, you can imagine a computer as just people solving small questions. Also, this was exactly how the term was coined.
However, with parts getting tinier and tinier, quantum physics is making things tricky. In a nutshell, a transistor is just an electric switch. Electricity is electrons moving from one place to another. So, a switch is a passage that can block electrons from moving in one direction.
Today, a typical scale for transistors is 7 nanometers, which is about 8 times less than the COVID virus' diameter, and 5000 times smaller than a red blood cell.
As transistors are shrinking to the size of only a few atoms, electrons may just transfer themselves to the other side of a blocked passage via a process called Quantum Tunneling.
[https://lh4.googleusercontent.com/ZRZOapxwQVV9z4MRTNt20naqULG2Gaew1R0tXeDF2BdnNghxn0vOcyxa3Js3hyxsJ_SznHRD1GOzeEOy_LA-xinMemCF7xHcWZEmF7MmfQXCNTCBNpmRJoqQVC2WD6tWVxVzNlYb](https://lh4.googleusercontent.com/ZRZOapxwQVV9z4MRTNt20naqULG2Gaew1R0tXeDF2BdnNghxn0vOcyxa3Js3hyxsJ_SznHRD1GOzeEOy_LA-xinMemCF7xHcWZEmF7MmfQXCNTCBNpmRJoqQVC2WD6tWVxVzNlYb)
In the quantum realm, physics works quite differently from the predictable ways we're used to, and traditional computers just stop making sense. We are approaching a real physical barrier for our technological progress. To solve this problem, scientists are trying to use these unusual quantum properties to their advantage by building quantum computers.
In normal computers, bits are the smallest unit of information. Quantum computers use qubits which can also be set to one of two values. A qubit can be any two level quantum system, such as a spin and a magnetic field, or a single photon.
1. There could be electrons which could be used as qubits. [Phosphorus electrons are quite popular in use in Quantum Computers](https://en.wikipedia.org/wiki/Kane_quantum_computer).
2. We could also use Photons as qubits and could be programmed using polarised filters.
0 and 1 are this system's possible states, like the photons horizontal or vertical polarization. In the quantum world, the qubit doesn't have to be just one of those, it can be in any proportions of both states at once.
This is called **superposition**. But as soon as you test its value, say, by sending the photon through a filter, it has to decide to be either vertically or horizontally polarized. So as long as it's unobserved, the qubit is in a superposition of probabilities for 0 and 1, and you can't predict which it'll be. But the instant you measure it, it collapses into one of the definite states. Superposition is a game changer.
*Experimenting*
I made a simple circuit that would just program a qubit and then read it. (Just a two bit number). And the quantum computer still resulted in reading the data differently from what it was programmed to.
This is also why there need to be multiple iterations for a reading because just due to the nature of qubits you are not sure of the value until you take the measurement.
[https://lh5.googleusercontent.com/ABgEZFhtm_MkdvWsDVLmd4eHb_eEercIbs1n6SXO5yRt9cAyZ_b2QxviEbB-ey8uGIF7_IyBeMK6O11w9Vd_n27Ly4J53s5n1Zf6EUTnGsLMIw9r1JfnwmhIARK_-YjvX4xbYtEG](https://lh5.googleusercontent.com/ABgEZFhtm_MkdvWsDVLmd4eHb_eEercIbs1n6SXO5yRt9cAyZ_b2QxviEbB-ey8uGIF7_IyBeMK6O11w9Vd_n27Ly4J53s5n1Zf6EUTnGsLMIw9r1JfnwmhIARK_-YjvX4xbYtEG)
---
Let’s consider four classical bits that can be in one of two to the power of four different configurations at a time.
That's 16 possible combinations, out of which you can use just one. Four qubits in superposition, however, can be in all of those 16 combinations at once. This number grows [exponentially](https://en.wikipedia.org/wiki/Quantum_complexity_theory) with each extra qubit. Twenty of them can already store a million values in parallel.
A really weird and unintuitive property qubits can have is Entanglement, a close connection that makes each of the qubits react to a change in the other's state instantaneously, no matter how far they are apart.
This means when measuring just one entangled qubit, you can directly deduce properties of it's partners without having to look.
**Qubit Manipulation** is another brilliant phenomenon as well. A normal logic gate gets a simple set of inputs and produces one definite output. A quantum gate manipulates an input of superpositions, rotates probabilities, and produces another superposition as its output.
So a quantum computer sets up some qubits, applies quantum gates to entangle them and manipulate probabilities, then finally measures the outcome, collapsing superpositions to an actual sequence of 0s and 1s.
What this means is that we get the entire lot of calculations that are possible with our setup, all done at the same time. Ultimately, we can only measure one of the results and it'll only probably be the one we want, so we may have to double check and try again.
So, while quantum computers will not probably not replace our home computers, in some areas, they are vastly superior.
# **Use Cases of Quantum Computing**
One of them is database searching. To find something in a database, a normal computer may have to test every single one of its entries.
**Grover’s Algorithm**
Grover’s algorithm demonstrates this capability. This algorithm can speed up an unstructured search problem quadratically.
Suppose you are given a large list of N items. Among these items is one item with a unique property that we wish to locate. We will call this one the winner, “x” . Think of each item in the list as a box of a particular color. Say all items in the list are gray except the winner “x”, which is red.
[https://lh6.googleusercontent.com/mbMiuceI8MzL-I1_N7uFUbj5qs3x0US0dDhgWDWXz9scSyunS907ViKDXYLxPP7nOh9AQx6YZCPP__Up_ELpOcN8CwZOcdAtrkORMK-dNJF6uCRf3NGamliqW8TpuvKPmeIVdTig](https://lh6.googleusercontent.com/mbMiuceI8MzL-I1_N7uFUbj5qs3x0US0dDhgWDWXz9scSyunS907ViKDXYLxPP7nOh9AQx6YZCPP__Up_ELpOcN8CwZOcdAtrkORMK-dNJF6uCRf3NGamliqW8TpuvKPmeIVdTig)
To find the red box – the marked item – using classical computation, one would have to check on average N/2 of these boxes, and in the worst case, all N of them. On a quantum computer, however, we can find the marked item in roughly *square root of [N]* steps with Grover’s amplitude amplification trick. {[more details](https://quantum-computing.ibm.com/composer/docs/iqx/guide/grovers-algorithm)}
*Testing out Grover’s Algorithm*
[https://lh4.googleusercontent.com/Va0IM4_6OovRnWATY4MQRkwikBTjS_VM4j87nAqDRYrJVzTecL5YmzfCPfPMKEx2ncKl9pSv75FBDign-Z_5vqaA8AEmLesPHFQGT_72ZPKCy6xtX6d92pAIZWNtCyUTTGIuuJ-z](https://lh4.googleusercontent.com/Va0IM4_6OovRnWATY4MQRkwikBTjS_VM4j87nAqDRYrJVzTecL5YmzfCPfPMKEx2ncKl9pSv75FBDign-Z_5vqaA8AEmLesPHFQGT_72ZPKCy6xtX6d92pAIZWNtCyUTTGIuuJ-z)
Quantum computers algorithms need only the square root of that time, which for large databases, is a huge difference. ****The most famous use of quantum computers is ruining IT security.
---
Right now, our browsing, email, and banking data is being kept secure by an encryption system in which you give everyone a public key to encode messages only you can decode. The problem is that this public key can actually be used to calculate your secret private key.
Luckily, doing the necessary math on any normal computer would literally take years of trial and error. But a quantum computer with exponential speed-up could do it in a breeze.
This is using the Shor’s Algorithm.
**Shor’s Algorithm**
The goal of encryption is to garble data is such a way so that no one who has the data
can read it unless they’re the intended recipient.
And the encryption of pretty much all private information sent over the internet relies immensely on one numerical phenomenon - as far as we can tell, it’s really really hard to take a really big number (prime) and find its factors using a normal, non-quantum computer.
Unlike multiplication, which is very fast (just multiply the digits together and add them up ), **finding the prime numbers that multiply together to give you an arbitrary, big, non-prime number appears to be slow** - at least, the best approach we currently have that runs on a normal computer - even a very powerful one - is very slow.
It’s due to quantum superposition and interference; they’re just taken advantage of by an algorithm developed by [Peter Shor](http://www-math.mit.edu/~shor/).
The encryption being mentioned here is called RSA. If somebody doesn’t have the factors, either they can’t decrypt the data, or they have to spend a really really long time or a huge amount of investment in computing resources finding the factors.
Our current best methods essentially just guess a number that might be a factor, and check if it is . And if it isn’t, you try again. And again. And again.
There are so many numbers to check that even the fast clever ways to make really good guesses are slow.
Basically, it works by guessing a random number and then turning it into a better guess. But, how can it turn it into a better guess? That is where Quantum Computing comes in. With the concept of Superposition you can give several inputs and get the probability of each input being a likelihood of a better guess. And here’s where quantum computing shines. If you can program the machine to [destructively interfere](https://www.ryanlarose.com/uploads/1/1/5/8/115879647/shor3.pdf) then you can simply eliminate a lot of outputs with low probabilities.
The problem we are trying to solve is that, given an integer N, we try to find another integer p between 1 and N that divides N. If we can find one, we can just divide and find the other one as well.
Shor's algorithm consists of two parts:
1. A reduction of the factoring problem to the problem of order-finding, which can be done on a classical computer.
2. A quantum algorithm to solve the order-finding problem.
The first part of the algorithm turns the factoring problem into the problem of finding the period of a function, and may be implemented classically. The second part finds the period using the quantum Fourier transform, and is responsible for the quantum speedup.
The second part is finding the period. Shor's period-finding algorithm relies heavily on the ability of a quantum computer to be in many states simultaneously (Superposition). To compute the period of a function f, we evaluate the function at all points simultaneously.
Quantum physics does not allow us to access all this information directly, though. A measurement will yield only one of all possible values, destroying all others. Therefore we have to carefully transform the superposition to another state that will return the correct answer with high probability. This is achieved by the quantum Fourier transform.
[Mathematical Explanation](https://www.quantiki.org/wiki/shors-factoring-algorithm)
[https://lh5.googleusercontent.com/Lm0sWCYe5zerI6u7DKKANMkIn_3guOPJ1XXhuzGXMS79lnOASrP0SAsApHiUv6r6RCbzsU72YnvbOQ3DUrVJNEdTdG-fpPqtgGON5wQIpv3vzxc4_F_oxu01VRQJwgptsFQxgMhZ](https://lh5.googleusercontent.com/Lm0sWCYe5zerI6u7DKKANMkIn_3guOPJ1XXhuzGXMS79lnOASrP0SAsApHiUv6r6RCbzsU72YnvbOQ3DUrVJNEdTdG-fpPqtgGON5wQIpv3vzxc4_F_oxu01VRQJwgptsFQxgMhZ)
**Trying it out**
In the image below we are trying to find out the value of r (in the equation above) which will then help to find the factors of the number.
[https://lh3.googleusercontent.com/_w_lVxt8cK45Ao-4yHKDCU-Dwwc3rJ96NVIyhrV8A4vkpvw4SmjlugSiG9WChv37Fu6B9t89Yj9zbCdvjKNVP024xm5tcOsGQ0aVyZm8-1aos25nBhmGZy--E-UJxxnd5jNSUoMk](https://lh3.googleusercontent.com/_w_lVxt8cK45Ao-4yHKDCU-Dwwc3rJ96NVIyhrV8A4vkpvw4SmjlugSiG9WChv37Fu6B9t89Yj9zbCdvjKNVP024xm5tcOsGQ0aVyZm8-1aos25nBhmGZy--E-UJxxnd5jNSUoMk)
Encrypting data isn’t a guarantee of protection - it’s a way of making it harder to access; hopefully hard enough that no one thinks it’s worth trying.
*Comparing it to Classical computer*
[https://lh5.googleusercontent.com/bDAIdAOWCcSzYiraizHXZFQKbL7N-DSI9FhxKEqLiG2E3WnFyrz09q7WsB0nmHtNqbele8h_z1xDTPiyGuYpHgwsgBQhuXARg4lbgWk66DXR2fZ9mG2uswcNQChoEcYobN3FOFMr](https://lh5.googleusercontent.com/bDAIdAOWCcSzYiraizHXZFQKbL7N-DSI9FhxKEqLiG2E3WnFyrz09q7WsB0nmHtNqbele8h_z1xDTPiyGuYpHgwsgBQhuXARg4lbgWk66DXR2fZ9mG2uswcNQChoEcYobN3FOFMr)
Quantum Computer’s definitely help in finding the factors quickly. But here comes the problem at this stage (I used a quantum computer with a maximum of 5 qubits). It is simply faster to brute force rather than use quantum mechanics and find out the solution. But over time as the number of bits that it can hold at such cold temperatures and also take accurate measurements this might actually be faster and it could break the internet.
Even my laptop executed it faster than the quantum computer did. Not to mention waiting times. There is a limited number of available quantum computers and hence I had to wait for a long long time to be able to execute my code.
---
Another really exciting new use is simulations. Simulations of the quantum world are very intense on resources, and even for bigger structures, such as molecules, they often lack accuracy.
So why not simulate quantum physics with actual quantum physics? Quantum simulations could provide new insights on proteins that might revolutionize medicine. Imagine doing all different combinations of protein folding and finding out new Cancer medicines or Vaccines.
Right now, we don't know if quantum computers will be just a specialized tool, or a big revolution for humanity.
# **Some Achievements**
In 2007 Switzerland used quantum cryptography for the first time in its National Council elections to combat vote tampering. And in 2017 Chinese physicists quantum teleported a packet of information from Tibet to a satellite 1,400 kilometres above the Earth's surface. Both of these achievements show the power of quantum technology in securing data. In October 2019 Google declared [Quantum Supremacy](https://www.youtube.com/watch?v=-ZNEzzDcllU) which basically means their Quantum Computer was able to solve a puzzle way faster than any normal computer could do. This is very optimistic but also frightening. At the pace of developments happening, it is very likely to see Quantum Computers being regularly used in products and services we use daily while also solving problems in parallel and achieving big feats in fields of medicines and cryptography.
# **Conclusion**
After all, true randomness can be achieved only by a Quantum device, because the silicon we use in our computers is still hardwired.
Quantum computers have the potential to revolutionize computation by making certain types of classically not possible problems solvable. Could we also make a Turning incomplete machine? While no quantum computer is yet sophisticated enough to carry out calculations that a classical computer can't, great progress is underway. A few large companies and small start-ups now have functioning non-error-corrected quantum computers composed of several tens of qubits, and some of these are even accessible to the public through the cloud (like IBM Quantum Lab). Additionally, quantum simulators are making strides in fields varying from molecular energetics to many-body physics and astrophysics calculations.
As small systems come online a field focused on near-term applications of quantum computers is starting to grow. This progress may make it possible to actualize some of the benefits and insights of quantum computation long before the quest for a large-scale, error-corrected quantum computer is complete.
We have no idea where the limits of technology are, and there's only one way to find out - Exploration!
# **Webliography**
1. [Quantum Mechanics: A First Course](https://www.edx.org/course/quantum-mechanics-a-first-course)
2. [Introduction to quantum mechanics](https://scholar.harvard.edu/files/david-morin/files/waves_quantum.pdf)
3. [Why Is Quantum Computing So Hard to Explain](https://www.quantamagazine.org/why-is-quantum-computing-so-hard-to-explain-20210608/)
4. [What Is Quantum Mechanics? Quantum Physics Defined, Explained](https://www.livescience.com/33816-quantum-mechanics-explanation.html)
5. [Quantum mechanics](https://www.iop.org/explore-physics/physics-stepping-stones/quantum-mechanics)
6. [Uncertainty in quantum mechanics: faith or fantasy? | Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences](https://royalsocietypublishing.org/doi/10.1098/rsta.2011.0179)
7. [Learn Quantum Computing with These Qiskit Projects | Qiskit](https://medium.com/qiskit/learn-quantum-computing-with-these-seven-projects-7478d90d125a)
8. [Quantum physics by NewScientist.com](https://www.newscientist.com/definition/quantum-physics/)
9. [Quantum Computers Explai*ned – Limits of Human Technology (Youtube - Kurgezagt)*](https://www.youtube.com/watch?v=JhHMJCUmq28)
10. *[How Quantum Computers Break Encryption |Shor's Algorithm Explained (Youtube- Minute Physics)](https://www.youtube.com/watch?v=lvTqbM5Dq4Q)*
11. *[Shor's factoring algorithm](https://www.quantiki.org/wiki/shors-factoring-algorithm)*
12. *[Introduction to quantum mechanics (Wikipedia)](https://en.wikipedia.org/wiki/Introduction_to_quantum_mechanics)*
13. *[Photoelectric Effect – The Physics Hypertextbook](https://physics.info/photoelectric/)*
14. *[Quantum Physics | Physics](https://courses.lumenlearning.com/physics/chapter/introduction-6/) **** Very useful guide by Lumen Learning*
15. [Explainer: what is wave-particle duality](https://theconversation.com/explainer-what-is-wave-particle-duality-7414)
16. [How Do You Create Quantum Entanglement?](https://www.forbes.com/sites/chadorzel/2017/02/28/how-do-you-create-quantum-entanglement/?sh=3044d4a41732)
17. [Your Simple (Yes, Simple) Guide to Quantum Entanglement](https://www.wired.com/2016/05/simple-yes-simple-guide-quantum-entanglement/)
18. [Shor's factoring algorithm](https://www.quantiki.org/wiki/shors-factoring-algorithm)
19. [Grover's algorithm - IBM Quantum](https://quantum-computing.ibm.com/composer/docs/iqx/guide/grovers-algorithm)
20. [Advanced single-qubit gates - IBM Quantum](https://quantum-computing.ibm.com/composer/docs/iqx/guide/advanced-single-qubit-gates)