- ℹ️ REPO DESCRIPTION
- 🎓LEARNING RESOURCES
- 🎛️ FUNDAMENTAL PRINCIPLES OF QC
- 🐱💻 QUANTUM Computing (FINALLY 🙃)
- 🔎 REFERENCES
- 📒 GLOSSARY
- 🎓 CITATION
This repository contains the following information regarding
graph TD
A[Quantum<br>Computing<br>Primer<br>] --> A1[Learning<br>Resources]
A --> |Low<br>Math<br>Proofs|A2[Quantum<br>Theory]
A --> A3[Quantum<br>Computing]
%% A1 Boxes
A1 --> A11[Quantum<br>Physics+Mechanics]
A1 --> A12[Quantum<br>Computing]
%% A2 Boxes
A2 --> A21[Brief<br>Quantum<br>Physics]
A2 --> A22[Brief<br>Quantum<br>Mechanics]
%% A3 Boxes
A3[Quantum<br>Computing] --> A31[Overview]
A3 --> A32[QC Tools]
A32 --> A321[Packages<br>Tools<br>Test<br> maybe...]
⚠️ Information contained is subject to my own interpretation, which has been kept to a minimum. The bulk of the information has been referenced. I cannot guarantee 100% accuracy😟.
👉 Many concepts contained are an oversimplification of very deep physics and quantum physics/mechanics. Where examples of the application of equations are lacking. I may come back to that at a later time🙄.
🥅 The goal is to understand enough to start experimenting with the various quantum cloud services, open source packages and find some real world high impact application 🎪.
I have also added 🍌TLDR block to each section, for fast understanding 😉.
These are going to links to resources which have simplified explanations, that are not math heavy. With a greater focus on videos rather than papers. Note all of these sources have been studied for the content in this repository.
| N | Source | Url | Synopsis |
|---|---|---|---|
| 1 | Animation describing the dual behavior of a particle as both a wave and a particle | ||
| 2 | - Physics lecture on understanding Quantum Mechanics, thisi branch exists because standard laws of physics are modified at a subatomic level | ||
| 3 | Understanding quantum computing in light of quantum physics concepts. Qubits the fundamenetal processing unit of QC | ||
| 4 | 📷Slides | 📷 Quantum Physics Infographics | Simplified understanding of QP by comparison to the macro world |
| 5 | Source video for Fig 3: Components of QP | ||
| 6 | Animation superposition of quantum states of an electron and decoherence (time taken for the superposition to disappear) | ||
| 7 | 📃Paper | 📃 Quantum States & Superposition | Mathematical discussion of Quantum States & Superposition |
| 8 | Animation quantum teunneling effect, ie., quantum particles can pass through objects | ||
| 9 | Animation style explanation of a wave functions | ||
| 10 | Short documentary on the uncertainity principle | ||
| 11 | 📰Article | 📰 What Is Planck's Constant, and Why Does the Universe Depend on It? | Article discussing the origins and applications of the planc's constant in modern media |
| 12 | Discussion of mathematical operators that enable physical observables in quantum mechanics | ||
| 13 | Explanation of Quantum Entanglement from FermiLab | ||
| 14 | Description of the standard model of particle physics - which are the fundamental building blocks of everything in the universe | ||
| 15 | General video about dark energy, cosmic radiation and particle accelaration experiments | ||
| 16 | Story and description of the discovery of he Higgs-Boson from CERN the laboaratory that disovered the particle | ||
| 17 | Description of the LHC - The Large Hadron Collider at CERN | ||
| 18 | Simplified explanation of the Higgs-Boson particle from Fermilab | ||
| 19 | Simplified explanation of mechanism of higgs boson imparting mass to a particle | ||
| 20 | Explanation of the SPIN or Intrinsic Angular Momentum, which can't be described as a spinning top | ||
| 21 | Visualizing a quantum computing vectors space referred to as Bloch Sphere which is a Qubit. | ||
| 22 | |||
| 23 |
🍌 TLDR - Above media is more entertaining than reading the following text
To understand QC we have first to have understand important concepts of quantum physics. The knowlege tree looks like the following -
flowchart TD
A[Quantum\nComputing] --> B(Define\nQuantum)
A --> C(Quantum<br>Physics)
C --> C1(Quantum<br>Mechanics)
A --> D(Standard<br>Model<br>Particle<br>Physics)
D --> D1(Quantum<br>Particles)
C <--> D1
Fig1: QC knowledge tree
🍌 TLDR - Quantum means the smallest and simplest unit of thing
Quantum physics is the study of matter and energy at the most fundamental level. It aims to uncover the properties and behaviors of the very building blocks of nature.
Fig 2: Current landscape of understanding of physics
Fig 2 - Illustrates the evolution of our understanding of physics. Until more recent times due to the advancement of experimental technologies, Quantum Theories are only now being observed & proved. Please note that their are active efforts of utilizing the Quantum Phenomenon for computing purposes, but our general understanding of it is quite poor.
flowchart TD
A[Quantum<br>Physics] -->|Objects<br>described as<br>|A1(Wave<br>Functions)
A1 -->|Measuring|B
subgraph B [Particles Seen]
direction LR
B1(Particle Wave<br>Duality) o--o B2(Measurement<br>Problem)
end
A1 -->|Consequence|C
subgraph C [Quantum Phenomenon]
direction LR
C1[Superposition] o--o C11[Entanglement]
C11 o--o C2
C2[Quantum\nTunneling] o--oC3[Heisenberg<br>Uncertainity<br>Principle]
C3 o--o C4[Energy<br>Quantization]
end
Fig 3: Components of QP
Fig 4: Wave Particle Duality
One of the most counterintuitive concepts in physics – the idea that quantum objects are complementary, behaving like waves in some situations and like particles in others.
These particle waves are referred to as matter waves, Luis de Broglie first proposed that all matter has a wave function associated with it. These matter waves are a central part of the theory of
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Fig 5: QP Measurement Problem
According to the Copenhagen Interpretation (being debated), which states that during measurement, the observer gets a subjective perception of what is going on in the quantum space, which means that these particles exhibit the property of non-locality. Non-locality which basically means, no observed particles have an absolute location in space. Sub atomic particles are expressed as wave functions ($ \Psi $) ie., only an approxmation of its actual location is known based on mathematical probabilities and the exact location of the particle is unknown.
The Measurement Problem states that these wave functions abruptly collapse into a particle in a point of space in time during observation, whose beahvior is unknown.
| Superposition | Decoherence |
|---|---|
 |
 |
Fig 6: Quantum Superposition & Decoherence
Superposition or Quantum Superposition is defined as the ability of a sub atomic particle (such as an electron) to be in multiple quantum states all at the same time, but when observed only has one state. In the case of an electron which gets excited (jumps to a higher energy state) in the presence of electro magnetic radiation (e.g Magnetic Field), it exists in both a high energy state and a low energy state at the same time. These are also referred to as SPIN(also referred to as (angular momentum) This is deduced from the wave patterns during its observation. An important term to also know at this point is decoherence which is when superposition can no longer be measured.
This principle states that a system (such as a group of quantum particles) exist in all possible states at the same time, only after measurement it falls to one of the states that form the superposition. This destroys its original configuration
The superposition principle is the idea that a system is in all possible states at the same time, until it is measured. After measurement it then falls to one of the basis states that form the superposition, thus destroying the original configuration. The superposition principle explains the "quantum weirdness" observed with many experiments.
Superposition principle equation states that a statefunction(
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| Pics | Pics |
|---|---|
 Fig 6.1: Spin or angular momentum of quantum particles |
 Fig 6.2: Spin or other particles of the Standard Model |
Amongst the poperties of quantum particles one of them is referred to as spin or intrinsic angular momentum. This property although referred to as spin is not actually spinning like a top, but this property describes its behavior in the presence of an electro-magnetic field experimentally. This property is observed but not understood and has no likeness in classical physics, which is broadly referred to as
- Fig 6.1 - Describes a simplified view of the spin in the presence of an electro-magnetic field. For sake of simoplicity it is referred to as spin-up(
$s=+\frac{1}{2}$ ) or spin-down($s=-\frac{1}{2}$ ), these have been observed experimentally when the stream of particles group themselves in the presence of an electro-magnetic field. - Fig 6.2 - Describes these spins in the observed and hypothesized particles of the Standard Model of Particle Physics.
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Fundamental Law of Quantum Mechanics
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Where the function
Fig 6.1: 3d Illustration of a wave function
Fig 7: Quantum Entanglement or Spooky Action
In Quantum Theory, Quantum Entanglement is most bizzare and mysterious properties of quantum particles, which states that two subatomic particles can be intimately linked to each other even if seperated by billions of years light years in space ie., any change induced in one particle will affect the other. The mechanics of this behavior is unknown.
These two particles share a common unified quantum state, such that any observation of one of these particles will provide information about the other entangled particles. And any action to one of these particles will invariably impact the others in the entangled system.
Fig 8: Quantum Tunneling
Quantum Tunnelling is a phenomenen which has no counterpart in classical physics, it states that particles can penetrate a potential energy barrier with a height greater than the total energy of particles. In simple terms quantum tunnelling is where an atom or a subatomic particle can appear on the opposite of a barrier that should be impossible for the particle to penetrate. This is an important property in understanding energy production models of the sun.
Fig 9: Light microscopy for measuring speed and momentum
A principle of the quantum realm referring to the measurement of a particle. As we have discussed so far, that a sub atomic particle displays both a wave and particle like behavior, measuring both the position and speed becomes a challenge. The Heisenberg Uncertainity Principle states that it is impossible to know exactly both the position & speed of a particle. And the more effort is done to measure these properties, the less accurate the results.
In order to see a particle, light has to reflect of the particle and enter our viewing appartus. But the problem occurs when the photons emitted from the device that tries to measure the particle, these photons(light) transfer energy (momentum in the form of Kinetic energy) when striking the particle. This changes the momentum and speed of the particle under observation. So this light when reflected of the particle enters the viewing apparatus is already carrying inaccurate and altered information.
The Heisenberg Uncertaining Principle equation is the product of the uncertainity in position (
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Fig 10: Quantization of energy
Energy is quantized in some systems, meaning that the system can have only certain energies and not a continuum of energies, unlike the classical case. This would be like having only certain speeds at which a car can travel because its kinetic energy can have only certain values. We also find that some forms of energy transfer take place with discrete lumps of energy. While most of us are familiar with the quantization of matter into lumps called atoms, molecules, and the like, we are less aware that energy, too, can be quantized. Some of the earliest clues about the necessity of quantum mechanics over classical physics came from the quantization of energy.
Max Planc used that idea that atoms and molecules (quantum realm) act like oscillators to absorb and emit radiation. ie., the energy within these particles are not constant, but due to constant absorbtion and emission the energy is quantized. He is also credited for discovering constant proprtionality which is instrumental in calculation of physical quantities in the quantum mechanics. This proptionality is referred to as the planc's constant.
Planc's postulate for the energy state (
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🍌 TLDR - The above are the most basic building blocks of Quantum Physics. These properties are exploited in Quantum Computing
The following diagram is an illustration of the Standard Model of elementary particles as described by the particle theory in physics.
Fig 11: Standard Model of Particle Physics - Brief
| Pics | Pics |
|---|---|
 Fig 11.1: Standard Model of Particle Physics - Particles, Conservation Laws, Standard Model Interactions, Force Interactions |
 Fig 11.2: Standard Model Brief from CERN - The European Organization of Nuclear Research |
The Standard Model of Particle Physics is scientists current best theory to describe the most basic building blocks of the universe. It explains how particles called quarks (which make up protons and neutrons) and leptons (which include electrons) make up all known matter. It also explains how force carrying particles, which belong to a broader group of bosons, influence the quarks and leptons. This standard model is represented by the Standard Model Equation
Fig 11.3: Brief explanation of the Standard Model Equation
| Pics | Pics |
|---|---|
 Fig 11.3: Higgs Particle represenation in the Standard Model by CERN |
 Fig 11.4: Higgs Particle relationship in the Standard Model |
In 2012 CERN - The European Organization of Nuclear Research. Discovered the Higgs-Boson Particle (often referred to as Higgs - which was theorized by Peter Higgs ), during a particle collission experiment in the Large Hadronic Collide (LHC) at CERN which is the worlds largest and most powerful particle accelerator capable of accelerating particles (protons p+ to the speed of light (
It was detected via statistical analysis of large amounts of data which was collected by the ATLAS & CMS detectors, after the collisions occur.
| Pics | Pics |
|---|---|
 Fig: 11.5: Map of the LHC collider |
 Fig 11.5.1 : Geolocation of LHC collider tunnel, border of switerland and france - gooogle maps. |
 Fig 11.6: Components of the Dipole from 11.7 |
 Fig: 11.7 A chain of LHC dipole magnets inside the tunnel |
 Fig 11.8: Atlas Dector Schemaics |
 Fig 11.9: CMS Dector Schemaics |
Characteristics of the Higgs (
| Pics | Pics |
|---|---|
 Fig 11.10: Higgs Particle Generating Event in LHC |
 Fig 11.11: Higgs Particle generation diagram |
Fig 12: Higgs Mechanism also referred to as the Mexican Hat Potential is how particles acquire mass in the higgs-field
-
It is the fundamental particle associated with the higgs field. Which gives mass to other particles. This field is also thought to play a role in the big-bang. The higgs mechanism is how particles acquire mass.
- This mechanism starts with the premise that the universe is filled with a spin-zero field. Then guage bosons (are force carrier particles) & fermions interact with this field and acquire mass.
-
It is highly unstable particle that quicjly morphs into other particles, and is only occassionally produced in a particle collider.
-
It gets its own mass by interacting with the higgs-field. It is a
$zero \ spin \ particle$ whose mass is$125\ GeV$
🍌 Every thing can be broken own into smaller units. The most commonly known unit is the molecule. molecules in turn are made of smaller particles, and so and so forth until we reach the limits of observation.
All matter in the universe can be subdivided into two classes based on their spin.There are two classes of quantum particles, those with a spin multiple of one-half, called fermions, and those with a spin multiple of one, called bosons.
The spin quantum number of fermions can be (
The spin quantum number of bosons can be (
flowchart LR
A[Quantum<br>Particles] --> A1[Main Category <br> Fermions]
A --> A2[Main Category<br>Bosons]
A --> |Essentially<br>Fermions|A3[Hadrons <br> Combination of <br> Quarks & Antiquarks]
%% Fermions
A1 --> |Held <br> together|Ab1[Gauge<br>Bosons <br> force carrier particles]
%% Spin
A1 --> |Spin|A11[Spin = multiples of '1/2']
A2 --> |Spin|A21[Spin = multiples of '1']
A3 --> |Spin|A31[Spin = 1/2 multiple of <br> h=h/2pi]
%% Spin Number
A11 --> |Spin<br>Quantum<br>Number| A111[s = '+1/2' <br> s = -1/2'<br> s = + or - 1/2]
A21 --> |Spin<br>Quantum<br>Number| A211[s = +1 <br> s = -1 <br> s = 0 <br> multople of + or i]
A31 --> A3111[Mesons]
A31 --> A3111b[Baryons]
A3111b --> A32[Nucleons]
A3111b --> A33[Hyperons]
%% Box Examples
A111 --> a1x[Leptons, <br> Quarks, <br> Electrons, <br> Protons, <br> Neutrons]
A211 --> a2x[Force Carrier Particles <br> Mesons]
a1x --> a1x1[Including<br>Anti-Particles]
The fundamental building blocks of the universe are
🍌 Every thing is made up of smaller units, called elements of matter, these inturn are further made up of quantum particles. Many particles exist naturally, and some exist only in certain conditions.
graph TD
A[Quantum<br>Mechanics] --> A1[Hilbert<br>Space]
A --> A2[Harmonic<br>Osciallator]
A --> A3[Transformations<br> and Symmetries]
A --> A4[Angular<br>Momentum]
A --> A5[Identical<br>Particles]
A --> A6[Time Independent<br>Perturbation Theory]
Fig 13: Illustration of the interpretation of Quantum Mecahnics based on the principlels of Quantum Physics as described in the previous sections
| Quantum Physics | Quantum Mechanics |
|---|---|
| Major branch of science | Branch of Quantum Physics |
| Describes the particles | Describes their various interactions |
| Defined as Quantum physics is a branch of science that focuses on systems explained by theories such as quantum mechanics and quantum field theory. Scientists and researchers focus on this area in order to use this knowledge to understand the behaviour of particles at the subatomic level. However, sometimes we use the terms “quantum physics” and “quantum mechanics” interchangeably. | Defined as Quantum mechanics is the set of principle that explains the behaviour of matter at atomic (or subatomic) scale. The word ‘quantum’ itself describes a fundamental concept of quantum mechanics – the quantized or discrete nature of matter and energy. |
https://digbib.ubka.uni-karlsruhe.de/volltexte/wasbleibt/57355817/57355817.pdf - Ref for principles of QM
https://www.damtp.cam.ac.uk/user/dbs26/PQM.html - This is more concise
To Do Items
- Describe hilbert space
- Describe Schrodinger equation
- Describe principles of Quantum Mecahnics
- Talks about EigenStates
Linear Algebra is the language of Quantum Computing. The most important methematical quantity of QC is the
In QC often we deal with state vectors which are vectors which point to a specific point in space which corresponds to a particular Quantum State. These states are visualized as a Bloch Sphere which represents a
flowchart TD
A --> B
Under Construction
Now that we have a firm grasp (😁) of the important fundamental of QC, the following are a curated sources for some experimentation
Majority of the references will be
- Header Quantum Entanglement Gif - Actual source of image is not described. The illustration is factual as described HERE.
| n | Term | Expansion |
|---|---|---|
| 1 | QC | Quantum Computing |
| 2 | QP | Quantum Physics |
| 3 | QP | Quantum Mechanics |
| 4 | SMP | Standard Model of Particle Physics |
@misc{m0ham3dxx, title={M0ham3dx/quantum-computing-primer: Quantum computing primer githb repositroy research paper}, url={https://github.com/m0ham3dx/Quantum-Computing-Primer}, journal={Quantum Computing Primer - Github Reserarch Paper Respository }, publisher={https://twitter.com/m0ham3dxx}, author={m0ham3dxx}}