NAT7038: High-rate codes (Construction and Logical Operations)

Course Description: 

Conventional error-correcting codes store a very small number qubits at the expense of much larger number of physical qubits. Given the stringent limitation on the number of physical qubits available in experimental platforms, recent years have seen the development of different families of high-rate codes including hypergraph product codes, lifted product codes, bicycle codes, as well as good qLDPC codes. This module will provide an introduction to the key mathematical and physical ideas behind the construction of these codes and an analysis of their error-correction abilities. Furthermore, we will go beyond simple code construction, and also provide algorithms for error decoding, and protocols for encoded operations and lattice surgery.

References and reading

The course will be based on several research papers.

• Bravyi, Hastings "Homological product codes" (2013), link

• Tillich, Zemor "Quantum LDPC codes with positive rate and minimum distance proportional to n1/2" (2013), link

• Kovalev, Pryadko "Quantum Kronecker sum-product low-density parity-check codes with finite rate" (2013), link

• Hastings, Haah, Donnell "Fiber bundle codes: Breaking the N1/2 polylog(N) barrier for Quantum LDPC codes" (2020), link

• Panteleev, Kalachev "Quantum LDPC codes with almost linear minimum distance" (2020), link

• Dinur, Evra, Livne, Lubotzky, Mozes "Locally Testable Codes with constant rate, distance, and locality" (2021), link

• Leverrier, Zemor "Quantum Tanner codes" (2022), link

• Roffe, White, Burton, Campbell "Decoding across the quantum low-density parity-check code landscape". (2020).

• Panteleev, Kalachev "Degenerate quantum LDPC codes with good finite length performance". (2019).

• Cohen, Kim, Bartlett, Brown "Low-overhead fault-tolerant quantum computing using long-range connectivity" (2022), link

Prerequisites
Basics of quantum error correction at the level of NAT3045: Quantum Error Correction.

When and where
Lectures: Mondays, 14:00 - 16:00 @ MPQ, Herbert Walther Lecture Hall.
Zoom for Lectures (only with previous permission): https://eu02web.zoom-x.de/j/3598685293

Course evaluation
Grades are awarded based on a final presentation on one of the topics covered in the course, no written examination. For Doctoral students enrolling in the course for fulfilling IMPRS requirements, an attendance of approximately 70% is required.

Lecture Slides

Tutorials