TUTORIAL: Quantum for All (Roman Urdu Version)— Topic: Normalization (Beginner Level)

 


TUTORIAL: Quantum for All — Topic: Normalization (Beginner Level)

Mere "Quantum for All" safar mein, main hamesha apne students se kehti hoon: Kabhi kabhi universe humein ek "saaf" (clean) rasta deta hai. Mushkil square roots ka samna karne se pehle, humein perfect squares par maharat hasil karni hogi.

1. The Power of "Clean" Numbers: [6, 8] Challenge

The Problem: Farz karein ek simple qubit is unnormalized state mein hai: V = [ 6, 8 ]

Step 1: "Weights" Maloom Karein Hum entries ka square nikalte hain taake unki asli power pata chale.

  • Top Slot (6): 6 squared = 36

  • Bottom Slot (8): 8 squared = 64

Step 2: Weights ko Jama (Sum) Karein Inhein aapas mein plus karein taake total unnormalized value mil jaye: 36 + 64 = 100

Step 3: Normalization Factor (N) Nikalein Chonkay 100 ek Perfect Square hai, humein divisor ke liye ek saaf integer mil jayega: N = √100 = 10

Step 4: Final "Legal" Vector Apne purane numbers (6 aur 8) ko factor (10) se divide karein.

  • 6 / 10 = 0.6

  • 8 / 10 = 0.8 Normalized State |ψ> = [ 0.6, 0.8 ]

2. Staying Exact with Roots: [1, 2] Challenge

Kya hota hai jab math perfect 100 par khatam nahi hota? Research mein hum andaza nahi lagate, hum Exact rehte hain.

The Problem: V = [ 1, 2 ]

Step 1: "Weights" Maloom Karein

  • Top Slot (1): 1 squared = 1

  • Bottom Slot (2): 2 squared = 4

Step 2: Weights ko Jama Karein 1 + 4 = 5

Step 3: Normalization Factor (N) Nikalein Chonkay 5 perfect square nahi hai, hum symbol (root) ko barkarar rakhein ge taake 100% precision rahe: N = √5

Step 4: Final "Legal" Vector Normalized State |ψ> = [ 1/√5, 2/√5 ]

Researcher's Note: Qiskit aur hardware-aware research mein, hum decimal ke bajaye 1/√5 ko tarjeeh dete hain kyunki jaldi rounding karne se "probability leaks" paida hote hain.

3. Handling the "Phase": [3, -4i, √11] Challenge

Ab hum Ground Reality mein dakhil hote hain. Minus signs, imaginary "i", aur square roots ko ek sath kaise handle karein?

The Problem: V = [ 3, -4i, √11 ]

Step 1: "Weight" Check (Absolute Square) Secret: Weight calculate karte waqt minus sign aur "i" ko 'khamosh' (idle) rehne dein.

  • Top: 3 squared = 9

  • Middle (-4i): -i ko ignore karein, sirf 4 ka square lein. 4 squared = 16.

  • Bottom (√11): Square root ko khatam kar dega. √11 squared = 11.

Step 2: Weights ko Jama Karein 9 + 16 + 11 = 36

Step 3: Normalization Factor (N) Nikalein N = √36 = 6

Step 4: Final "Legal" Vector Ab hum "compass" (matlab -i aur root) ko unki jagah wapas rakhte hain: Normalized State |ψ> = [ 3/6, -4i/6, √11/6 ] Jo simplify hokar banta hai: [ 1/2, -2i/3, √11/6 ]

In sawalat ki paper par practice karein: https://gemini.google.com/share/481ed6ba02bc

#QiskitAdvocate #QuantumMechanics #LinearAlgebra #Qiskit #STEMEducation #RAQT #QuantumForAll

IonQ QuLearnLabs Miguel Alfonso Martinez Nathaniel Walker Lee Chang Xin

Credit: Content phrasing improved by Google DeepMind.

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