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L5-10 · Noise, encoding, and error correction

Distinguish a noise channel from an error-correction procedure.

Level 5 icon Level 5 · Advanced undergraduate
Objective. Distinguish a noise channel from an error-correction procedure.
Before this lesson. L5-06, L5-09
Hands-on lab. Noise and quantum channels

Learn

Noise changes a quantum state through unwanted coupling or control error. Depolarization moves a state toward the maximally mixed state. Dephasing reduces coherence in a selected basis. These channels have different effects even when a single chosen measurement produces similar counts.

Quantum error correction stores logical information across several physical systems. Syndrome measurements reveal selected error properties without directly reading the logical state. A recovery operation then corrects an allowed error set. This procedure does not copy an unknown state into independent identical copies.

An encoding is useful only under its stated noise and control assumptions. A repetition code can correct certain bit flips but not arbitrary single-qubit errors. Fault tolerance also addresses faults during the correction process. Report logical error rates with the complete experimental procedure.

Practice

Solution

The output diagonal is (0.2,0.8). Its purity is 0.2 squared plus 0.8 squared, which is 0.68. Increasing depolarization reduces this initially pure state purity.

Check your understanding

What does a syndrome measurement seek to reveal?

Show the answer

B. Information about an error without directly reading logical data

A syndrome is designed to diagnose a correctable error class while preserving logical information. Reading the logical state itself would defeat that goal.

Sources

This lesson draws on Wang et al., 2021Preskill, n.d..

Next: L6-01 · Quantum common causes

References
  1. Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., & Coles, P. J. (2021). Noise-Induced Barren Plateaus in Variational Quantum Algorithms. Nature Communications, 12(1). 10.1038/s41467-021-27045-6
  2. Preskill, J. (n.d.). Course Information for Physics 219/Computer Science 219 Quantum Computation (Formerly Physics 229). California Institute of Technology course page with lecture notes. https://www.preskill.caltech.edu/ph219/