what is Quantum State in quantum computing explain with examples

 In quantum computing, a Quantum State is the mathematical description of a quantum system (like a qubit) at any specific moment.¹ It acts as a "container" for all the information we can possibly know about that system, specifically the probabilities of what we will find when we measure it.²

While a classical state is a definite reality (e.g., "the light is ON"), a quantum state is often a potentiality (e.g., "there is a 50% chance it is ON and a 50% chance it is OFF").³

Here is a simple breakdown with examples.

1. The Core Concept: The "Recipe" of Reality

Think of a quantum state not as the outcome of a coin toss, but as the motion of the coin while it is in the air.⁴

• Classical State: Describes the coin after it lands (Heads OR Tails).⁵

• Quantum State: Describes the coin while it is spinning.⁶ It captures the speed, angle, and probability of landing on either side. It is a precise mathematical "recipe" of the spin.

2. Physical Examples of Quantum States

To build a quantum computer, scientists use tiny particles that can hold these "spinning" states.⁷

• Electron Spin (The Magnetic Example):

  Imagine an electron as a tiny magnet.

  • State |0⟩ (Spin Up): The north pole points up.⁸

  • State |1⟩ (Spin Down): The north pole points down.

  • Superposition State: The electron is in a state where the magnetic pole is pointing sideways (like the equator). In this state, it is neither purely Up nor Down but a specific combination of both.⁹

• Photon Polarization (The Light Example):

  Light particles (photons) vibrate as they travel.

  • State |0⟩ (Horizontal): The photon vibrates side-to-side (like a snake).

  • State |1⟩ (Vertical): The photon vibrates up-and-down (like a wave).

  • Superposition State: The photon vibrates diagonally. This diagonal state is a quantum state that combines horizontal and vertical movements.

3. Visual Example: The Bloch Sphere¹⁰

In quantum computing, we often visualize a quantum state using a geometric tool called the Bloch Sphere.¹¹

• Imagine a sphere (like a globe).

• The North Pole represents the state |0⟩.

• The South Pole represents the state |1⟩.

• The Quantum State is an arrow pointing from the center to the surface.

  • If the arrow points to the Equator, the qubit is in a "50/50" Superposition state.

  • The "State" is essentially the coordinates (latitude and longitude) of where that arrow points.

4. Mathematical Representation (The "Ket")¹²

In formal terms, a quantum state is usually written as a vector using Dirac notation (bra-ket notation).¹³

• A classical bit is just $0$ or $1$.

• A quantum state vector, denoted as $|\psi\rangle$, describes the superposition:

  $$|\psi\rangle = \alpha|0\rangle + \beta|1\rangle$$

  Here, $\alpha$ and $\beta$ are numbers that tell us the probability of the qubit collapsing to 0 or 1 when measured.

Summary Table

Feature	Classical State	Quantum State
Analogy	A coin flat on the table	A coin spinning in mid-air
Value	Definite (0 or 1)	Probabilistic (Combination of 0 and 1)
Information	Contains 1 piece of data	Contains complex probability amplitudes
Measurement14	Reveals what is15	Forces the state to choose (collapse)16

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Next Step

Would you like to know how Quantum Gates are used to change these states (like swatting the spinning coin) to perform calculations?

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... Classical vs Quantum States Explanation ...

This video is relevant because it clearly visualizes why classical logic fails to describe quantum states and explains how measuring a quantum state fundamentally changes it.