what is Quantum State in quantum computing explain with example

 In simple terms, a Quantum State is a mathematical description of a quantum system (like a qubit) at a specific point in time.¹ It contains all the information we can possibly know about that system, such as its energy, position, or spin.²

In classical computing, the "state" of a bit is easy to define: it is either 0 (off) or 1 (on).³ In quantum computing, the state is more complex because of a property called superposition.⁴

Here is an explanation using a simple analogy.

The Coin Analogy

To understand a quantum state, imagine a simple coin.

1. The Classical State (Traditional Computer)

Imagine you place a coin on a table. It will sit there showing either Heads or Tails.5

• State: It is definitely Heads OR definitely Tails.⁶

• Computer Equivalent: A classical bit is definitely a 0 or a 1.⁷

2. The Quantum State (Quantum Computer)

Now, imagine you spin that coin on the table. While it is spinning, what is its state? You cannot say it is just Heads, and you cannot say it is just Tails.8 It is in a dynamic mix of both.

• State: It is in a superposition of both Heads and Tails simultaneously.⁹ This "spinning" motion represents the Quantum State.¹⁰

• Computer Equivalent: A qubit (quantum bit) can represent 0 and 1 at the same time.¹¹ The "Quantum State" describes exactly how it is spinning (e.g., is it leaning more toward Heads or more toward Tails?).

Key Characteristics

• It is Probabilistic: The quantum state does not tell you exactly what you will get. It tells you the probability of getting a specific result.¹² For example, a quantum state might tell you: "If you measure this qubit, there is a 70% chance it will be a 0 and a 30% chance it will be a 1."¹³

• Collapse: Just like stopping the spinning coin with your hand forces it to land on either Heads or Tails, measuring a quantum state forces it to "collapse" into a single, definite value (0 or 1).¹⁴ The complex quantum state disappears, and you are left with a classical result.¹⁵

Visual Representation (The Bloch Sphere)

Scientists often visualize a quantum state using a sphere called the Bloch Sphere.¹⁶

• The North Pole represents the state 0.¹⁷

• The South Pole represents the state 1.¹⁸

• The Quantum State is a point anywhere on the surface of this sphere.¹⁹ It could be at the equator (perfectly between 0 and 1), or closer to the North Pole (mostly 0, but a little bit 1). This arrow pointing to a specific spot on the sphere is the vector representing the quantum state.

Summary Table

Feature	Classical State	Quantum State
Basic Unit	Bit	Qubit
Values	0 OR 1	0 AND 1 (Superposition)
Certainty	100% Deterministic	Probabilistic
Analogy	Coin resting on a table	Coin spinning on a table