physics369

[physics369]

Types of physics

Quantum Physics

Classical Physics

Celestial Physics

Meta-Physics

[physics369]

TENSOR:---> Raju Rai

Tensor is the part of study which is rather suitable for the mathematical formulation of natural laws in forms of which are invariant with respect to different frames of reference.

Maxwell's equations… originally consisted of eight equations. These equations are not “beautiful.” They do not possess much symmetry. In their original form, they are ugly. …However, when rewritten using time as the fourth dimension, this rather awkward set of eight equations collapses into a single tensor equation. This is what a physicist calls “beauty.” — Michio Kaku

* INVARIANT TENSOR:

1) It does not vary under co-ordinate changes.

2) Also we call isotropic tensor.

3) or  same components in all direction.

4) Ex, Kronecker Delta Symbol ,ε-Symbol and  K-rutkov’s tensor.

*  ε-SYMBOL TENSOR:

This is one of the invariant tensor which is third rank tensor and anti-symmetric in every pair of indices.

      (It’s odd permutation or cyclic in order with courtesy.)

From above picture it is cleared that if the i,j,k are even permutation or cyclic.

This picture also clear that the   εijk  called the Epsilon tensor, if this follows the above expression.

( Even permutation)                                                                  (Odd permutation)  

* DERIVATION:

(Courtesy: Stack exchange)

Summary:

The third rank epsilon-tensor is used to formulate the dual relation between an antisymmetric second rank tensor and a vector or vice versa, in three-dimensional space. 

THANK YOU , Raju Rai

E-mail:rairajupungwat1234@gmail.com

[physics369]

QUANTUM PHYSICS:-->Raju Rai

# Quantum physics: (क्वान्टम भौतिकी )

It is a branch of  physics which deals with the dynamics nature of particles. So it   provides a description of the physical properties of nature at the scale of atoms and subatomic particles. Quantum  theories are most successful theories till now for explanation of  quantum nature of particles.

# History of Quantum Theory:

At the end of the 19th century, physics consisted mainly of Classical mechanics, the theory of electromagnetism and thermodynamics. Classical mechanics was used to predict the dynamics nature of earthy bodies, Maxwell equations electromagnetism  provided the proper framework of radiation, matter  and particle and wave and for the interactions between matter and radiation can be explain by using thermodynamics. Because of overwhelming success of these theories  most of people believed that the ultimate description of nature had been achieved.

But at the turn of the 20th century classical/thermodynamics/electromagnetism    showed the unusual nature in two field of physics: They are

1) Relativistic Domain                   2) Quantum Domain

# Development of Quantum Theories:

1) Max-plank(1900): Father of Quantum physics, 

2) Einstein Quantum Theory(1905)

3) Niels  Bohr(1913)

4) Compton Discovery( 1923)

5) De-broglie’s(1923)

6) Heisenberg and Schrodinger equation(1925)

7) Max-Born(1927)

8) Dirac (1928)

THANK YOU, RAJU RAI

[physics369]

Quantum Gate:---Raju Rai

We are living in mysterious world where mathematics plays the vital role in every action and reaction. So what we know is we have three realm where we can apply mathematics mostly, they are Classical, Quantum and Huge body realm. on the basis of different realm’s phenomenon technology is growing in positive or negative direction. In this article i only write about classical and quantum technologies.

* Classical Technology:

We are living the classical world and it is very beautiful. We live here we need different facilities in context of technology. So to development of those facilities we should go through different fundamental things among from Circuits gates comes first because it is very building block of technology. In classical devices we use the gates, and they are:

1) Basic gates(OR, AND,NOT)

2) Universal gates( NAND, NOR)

3) Special gates(X-OR ,X-NOR)

OR gate is basic gate of electronics devices, which gives high output when there should be at least one high input. otherwise output will be low.

AND gate gives an output as 1 only when both of its input signals are 1 but gives an output as 0 when both or either of the input signals is 0.

NOT gate uses just one input to generate one output. A NOT gate inverts the input - the output is 1 (high) if the input is 0 (low),

NAND gate is an electronic logic gate that is a combination of an AND gate and a NOT gate, it is universal gate because we can make other gate on the basis of this gate. In this gate the out of will be invert of AND gate.

NOR gate is simply an OR gate followed by a NOT gate. The output is 1 only when all inputs are 0. Or the output is high when all the inputs are low. These are also called Universal gates since the earlier three gates can be realized by using the NOR gate.

X-OR gate  an abbreviation for “Exclusively-OR.” The simplest XOR gate is a two-input digital circuit that outputs a logical “1” if the two input values differ.

XNOR gate (sometimes referred to by its extended name, Exclusive NOR gate) is a digital logic gate with two or more inputs and one output that performs logical equality. The output of an XNOR gate is true when all of its inputs are true or when all of its inputs are false.

*Quantum Technology:

Now-days we trying to implement the quantum phenomenon(Super-position and Entanglement ) in many devices to get the highest form efficiency and speed. So we have quantum technology and to build that technology we need basic block of circuit that’s we called quantum gates. There are several gates:

1) Pauli X-gate

2) Pauli Y-gate

3) Pauli Z-gate

4) Hadamard gate

5) S-gate

6) T-gate

7) CNOT gate, CX gate

8) CZ gate

9) SWAP gate

10) TOFFOLI gate(CCNOT)

*Pauli-X gate:

The Pauli-X gate is a single-qubit rotation through \piπ radians around the x-axis.

CODE:

qc = QuantumCircuit(1)

qc.x(0) 

qc.draw()

* Pauli-Y gate:

The Pauli-Y gate is a single-qubit rotation through π radians around the y-axis.

CODE:

qc = QuantumCircuit(1)

qc.y(0)

qc.draw()

* Pauli Z-gate:

The Z-gate is a unitary gate that acts on only one qubit. Specifically it maps 1 to -1 and leaves 0 unchanged. It does this by rotating around the Z axis of the qubit by π radians (180 degrees). By doing this it flips the phase of the qubit.

CODE:

qc = QuantumCircuit(1)

qc.z(0)

qc.draw()

* Pauli H-gate:

H-gate is one of very important and interesting gate. which creates the super-position.   (H-gate) is a fundamental quantum gate. It allows us to move away from the poles of the Bloch sphere and create a superposition of |0⟩|0⟩ and |1⟩|1⟩

CODE:

qc = QuantumCircuit(1)

qc.h(0)

qc.draw()

* CNOT gate:

Controlled NOT gate (also C-NOT or CNOT) is a quantum logic gate that is an essential component in the construction of a gate-based quantum computer. It can be used to entangle and disentangle Bell states.

CODE:

qc = QuantumCircuit(2)

qc.cx(0,1) 

 qc.draw()

Note: For other gates, i will write next article.

THANK YOU:

[physics369]

Max-Cut Problem:--- Raju Rai

* Introduction:

Max-cut problem is one of important  graph partition problems, and it is  most difficult combinatorial optimization problem to solve. The main goal of max-cut problem is partition of set of vertices of graph  into two subsets, such that the sum of the weights of the edges having one endpoint in each of the subsets is maximum.  MAX-CUT is an important combinatorial problem and has applications in many fields including VLSI circuit design  and statistical physics, Data clustering that is Machine Learning.

“Protons give an atom its identity, electrons its personality.” ― Bill Bryson, A Short History of Nearly Everything

# QAOA:

The quantum approximate optimization algorithm (QAOA) is a general technique that can be used to find approximate solutions to combinatorial optimization problems, in particular problems that can be cast as searching for an optimal bit-string .

Steps of QAOA:

-  cost Hamiltonian.

-  mixer Hamiltonian.

-  Draw e−iγHCe−iγHC and e−iαHM.

-  Choose a parameter n≥1n≥1 and draw circuit.

- Prepare the initial state.

-  Measurement.

“Not only does God play dice but... he sometimes throws them where they cannot be seen.” ― Stephen Hawking

Note:  QAOA is the specification of cost and mixer Hamiltonians.

THANK YOU:

[physics369]

Quantum Computing:---Raju Rai

*Introduction:

Quantum Computing is latest computing technique based upon the quantum physics, Quantum computing began in 1980 when physicist  Paul Benioff proposed a quantum mechanical model of the Turing machine. Richard Feynman and Yuri Manin later suggested that a quantum computer had the potential to simulate things a classical computer could not feasibly do. Quantum Computer are very powerful, they can be used in certain specific purpose only, because of it’s sensitiveness. As we know classical computer stores the data in form of bits, but quantum computer stores the information in form of quantum-bits. Quantum bits follows the phenomenon of quantum physics like super-position, quantum   entanglement  et cetera.

* Why Quantum Computing?

Quantum computing are more power efficient than modern computing through the use of quantum tunnelling. They are expected to reduce power consumption from 1000 to 10000 times.  Quantum computers could speed up the learning process of AI, reducing thousands of years of learning to mere seconds, also it helps in field of medical to make the complex structure of medicines like HIV, Cancer etc.

* Companies who are racing in quantum computing:

Cold-Quanta. 

Microsoft. 

Zapata Computing. 

1QBit.

QC Ware. 

D-Wave Solutions. 

IBM. 

Honeywell.

Google

* Most important algorithm:

Deutsch–Jozsa algorithm.

Bernstein–Vazirani algorithm.

Simon's algorithm.

Quantum phase estimation algorithm.

Shor's algorithm.

Grover’s algorithm

Hidden subgroup problem.

Boson sampling problem.

Estimating Gauss sums.

Note: (Most powerful and interesting algorithm are Shor’s and Grover)

* Classical and Quantum gates:

In classical computer we, use the classical gates, Basic gate(NOT, AND, OR) , Universal gate(NAND, NOR)  and Special gates(X-OR,X-NOR) But in case of quantum computer we use the different gate called quantum gates:

List of quantum gates are listed below:

 Identity gate.

 Pauli gates (X,Y,Z)  Square root of NOT gate (√NOT)

 Controlled gates.

 Phase shift gates. Controlled phase shift.

Rotation operator gates.

 Hadamard gate.

 Swap gate. Square root of swap gate.

Toffoli (CCNOT) gate.

Each gate has their own quantum meaning and functions.

* Remember:

 Qubits represent atoms, ions, photons or electrons and their respective control devices that are working together to act as a computer memory and a processor.

THANK YOU:

[physics369]

Physics:---- Raju Rai

Physics is one of beauty of universe which explains the natural phenomenon . Physics can provides the essence of the universe  with help of  mathematics and mathematics walks under the physics. According to physicist working field ,Physics can be categorize into three realm:

a. Celestial realm - Relativity physics

b. Classical physics realm

c. Quantum physics realm

To provide the basic introduction of these realm, we need the higher level mathematics like  Tensor, Differential geometry,---- Newtonian mathematics like calculus ---- linear algebra etc. To go through the intuition of above realms:::

* Relativity:

 Relativity is the field of physics which explains the dynamics  behaviour of celestial body, and  it explains the speed limits light , frame of reference, gravity( it is curvature of space and time) time dilation , length contraction, black holes,   singularity  etc.==> To summarize relativity explains the how universe started from big bang and what is the role of gravity at celestial realm and how speed of light is mysterious and inherent phenomenon. 

==>  “Two things are infinite: the universe and human stupidity; and I'm not sure about the universe.” --- Albert Einstein

* Classical physics:

Classical physic the field of physics where we use the  Newtonian laws and mathematics. In classical physics we explains those phenomenon which are completely based upon the our observation, means we can feel, we can heal we can see   every that we can do governs by the classical physics.

==> “Classical physics is just a special case of quantum physics.”----- Philip Ball, Beyond Weird

* Quantum physics:

It is the field of physics having completely weirdness ,phenomenon. Actually this realm is realm of particles having size of fermi/planks level. This physics explains the dynamics nature of particles. Quantum physics governs the way the universe behaves at the scale of atoms, electrons and photons. Quantum physicists put the rules of this quantum world to the test and devise ways to stretch their boundaries. I personally dazzled the two phenomenon of quantum particle nature: 

a) Quantum Entanglement 

b) Super-position phenomenon

{Note: Next paper, i will write about a ) and b) }

“ At last ,i want to say physics is the composition of weirdness and simplest phenomenon , which we can explains by using the tool called mathematics, and i don’t want to say the mathematics only that tool which explains the weirdness and simple phenomenon of our universe. May be there will be something better than mathematics. But lets be good creature of the world and respect the mathematics and its  intuition )

==>“I think I can safely say that nobody understands quantum mechanics.” ---->  Richard Feynman

THANK YOU

[physics369]

Who know ,anti-matter and resolve the conflict between matrix mechanics and wave-mechanics.