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1
Intro
2
What is a communication channel?
3
What is a coding scheme for classical communication T
4
Examples of coding schemes
5
Qualitative plot of rate-error pairs
6
Shannon's capacity theorem
7
The capacity theorem
8
Types of noise
9
Compound channel capacity
10
Quantum arbitrarily varying channel
11
Arbitrarily varying perturbation (AVP)
12
AVP coding scheme
13
What rates are possible in the AVP setting?
14
Challenges of implementing coding schemes
15
Coding schemes on quantum computers
16
Applying the threshold theorem to coding scheme
17
Separating data from noise in 7-qubit Steane code
18
Finding the effective channel
19
The threshold theorem for capacity
Description:
Learn about fault-tolerant quantum communication in this technical lecture that explores the challenges and solutions for reliable message transmission over noisy quantum channels. Delve into the intersection of fault-tolerant quantum computation and quantum communication, examining how to design encoding and decoding circuits that can withstand gate errors. Explore threshold theorems for classical and quantum capacity, understanding how to achieve optimal transmission rates with minimal error even when dealing with imperfect quantum gates. Follow along as fundamental concepts like communication channels, coding schemes, Shannon's capacity theorem, and various types of noise are explained. Discover practical applications through examples including the 7-qubit Steane code and effective channel analysis. Gain insights from Alexander Müller-Hermes, an associate professor at the University of Oslo, whose expertise spans quantum information theory, quantum Shannon theory, and entanglement theory. Read more

Fault-Tolerant Coding for Quantum Communication - Threshold Theorems and Error Rates

Illinois Quantum
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