![[Pasted image 20241227100940.png]] This explains the basics of **Quantum Error Correction (QEC)** using an analogy from classical computing to handle errors in quantum computers. 1. **The Problem:** - In quantum computing, we can't directly copy or look at data to find errors because measuring the data can destroy it. 2. **The Solution: Parity Checks:** - A **parity check** is a method to detect errors. It works by counting the number of `1`s in a set of bits to see if it is an **even** or **odd** number: - **Even parity:** Even number of `1`s. - **Odd parity:** Odd number of `1`s. 3. **How Parity Helps Detect Errors:** - Parity checks are added to the data without revealing what the original data is. - For example: - If two bits stored together are both `0` or both `1`, the parity is **even**. - If one bit flips (error occurs, like `1` turns into `0`), the parity becomes **odd**. - By detecting parity changes, we can find out that an error occurred. 4. **Applying This to Quantum Computers:** - This concept is extended to quantum bits (qubits), where we use **Quantum Error Correction (QEC) codes** to detect errors without looking at the quantum state directly. - In the example: - Parity checks are shown with the semi-circles. If one bit has an error, the parity of some groups changes to odd. - This allows errors to be detected and corrected. 5. **Surface Code:** - The **surface code** is a widely used QEC code today, helping quantum computers handle errors effectively. It uses parity checks to protect quantum information. In summary, parity checks help detect and correct errors in both classical and quantum systems by monitoring patterns (even or odd parity) without revealing the actual data.