Introduction to Quantum Computing: Quantum Error Correction

Flashcards covering classical and quantum error correction techniques, including parity, Hamming, Reed-Solomon, and Shor codes, and Shannon's information theory.

Parity Error Detection

A method that uses a parity bit to identify errors in data transmission or storage.

Parity Bit

An extra bit added to a binary code to make the total number of ones either even or odd.

Barker Code

A finite sequence of digital values with the ideal autocorrelation property used as a synchronizing pattern between the sender and receiver of a stream of bits.

Hamming Code

An error correction system that can detect and correct errors when data is stored or transmitted by adding additional parity bits with the data.

Reed-Solomon Code

A type of error correction code that operates on blocks of data and can detect and correct multiple symbol errors within that block.

No-Cloning Principle

Forbids the copying of quantum states, complicating quantum error correction.

Quantum Error Correction Complications

Classical error correction techniques cannot be directly transferred to quantum error correction because the no-cloning principle forbids copying, measurement destroys quantum information, and quantum states are continuous.

3-bit Repetition Code

Corrects for bit flip errors.

Phase Flip Error

Corrected by a three-qubit phase-flip code.

9-Qubit Shor Code

Constructed by concatenating the three-qubit bit-flip and three-qubit phase-flip codes; can detect and correct a bit-flip or phase-flip on any single qubit.

Shannon's Information Theory

A quantitative theory that measures the amount of information that can be transmitted through a communication channel, defining information as a measurable quantity.

What is Entropy?

Entropy quantifies the amount of uncertainty involved in the value of a random variable or the outcome of a random process