what is Physical vs. Logical Qubit in quantum computing. explain with examples

 The distinction between a Physical Qubit and a Logical Qubit is the single most important concept for understanding why we don't have powerful quantum computers on our desks yet.

In short: A physical qubit is the unstable hardware; a logical qubit is the stable, reliable software unit built from many physical ones.¹

Here is the detailed breakdown with examples.

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1. Physical Qubit (The "Hardware")

A physical qubit is the actual physical device used to encode quantum information.² It is a tangible, microscopic object or circuit.

• What it is: It could be a single electron spinning in a magnetic field, a photon of light, or a superconducting electrical circuit (like those used by Google and IBM).³

• The Problem: They are incredibly fragile.⁴ "Noise" from the environment—like a tiny temperature fluctuation or a stray electromagnetic wave—can flip their state, causing calculation errors in a fraction of a second.⁵

• Analogy: Imagine trying to balance a sharp pencil on its tip. It works for a split second, but the slightest vibration makes it fall.⁶ That falling pencil is a physical qubit losing its data (decoherence).

2. Logical Qubit (The "Stable Unit")⁷

A logical qubit is not a single physical object.⁸ It is a group of many physical qubits working together to act as one robust unit of information.⁹

• What it is: A software abstraction.¹⁰ You take, say, 1,000 physical qubits and entangle them.¹¹ You store your single bit of data ($0$ or $1$) across this entire group.

• The Solution: If one physical qubit in the group errors out (the pencil falls), the other 999 hold the pattern long enough for the system to detect the error and fix it without losing the data.¹² This process is called Quantum Error Correction (QEC).¹³

• Analogy: Imagine a choir of 100 people singing the same note. If one person goes off-key or sneezes, the "note" (the information) remains clear and steady because the group corrects for the individual's error.¹⁴

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Comparison Table

Feature	Physical Qubit	Logical Qubit
Nature	Hardware (atom, circuit, photon).	Software/Abstract (a cluster of hardware).
Reliability	Very Low. Error-prone.	High. Fault-tolerant.
Quantity needed	We have machines with ~100-1,000 today.	We need millions of physical qubits to create enough logical ones.
Role	The raw material.	The actual processing unit for algorithms.

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Concrete Examples

Example 1: The "Repetition Code" (Simplest Logical Qubit)

Imagine you want to store a "Logical 0".

• Physical way: You store it on one physical qubit. If that qubit accidentally flips due to heat, your "0" becomes a "1". Your calculation is ruined.

• Logical way: You use 3 physical qubits to represent one logical qubit. You set all three to 0.

  • State: 0 0 0

  • If one qubit errors: 0 1 0

  • Correction: The computer looks at the group, sees that two are 0 and one is 1. It assumes "majority rules," concludes the 1 is an error, and flips it back to 0. The information survived the error.

Example 2: The Surface Code (Real-world standard)

In modern research (like Google's Sycamore processor), they use a method called the Surface Code.¹⁵

• They arrange physical qubits in a checkerboard pattern.

• Half the qubits hold data, and the other half are "measurement" qubits that constantly check their neighbors for errors.

• The Ratio: It is currently estimated that we need roughly 1,000 physical qubits to build 1 perfect logical qubit.¹⁶

  • To run a useful algorithm requiring 100 logical qubits, you might need a machine with 100,000+ physical qubits.

Summary

If you read a headline saying "Company X creates 50-qubit chip," they are talking about physical qubits (noisy, hard to use).

If you read "Company Y demonstrates 1 error-corrected qubit," they have successfully tied many physical qubits together to create one logical qubit (stable, useful).¹⁷ This is the "Holy Grail" milestone the industry is currently chasing.

Would you like me to explain what "Quantum Error Correction" actually does mathematically, or how companies like Google and IBM are trying to lower that 1000:1 ratio?