Homological product codes


Bravyi, S. (2014). Homological product codes. Perimeter Institute. https://pirsa.org/14070013


Bravyi, Sergey. Homological product codes. Perimeter Institute, Jul. 16, 2014, https://pirsa.org/14070013


          @misc{ pirsa_PIRSA:14070013,
            doi = {10.48660/14070013},
            url = {https://pirsa.org/14070013},
            author = {Bravyi, Sergey},
            keywords = {},
            language = {en},
            title = {Homological product codes},
            publisher = {Perimeter Institute},
            year = {2014},
            month = {jul},
            note = {PIRSA:14070013 see, \url{https://pirsa.org}}

Sergey Bravyi IBM (United States)


All examples of quantum LDPC codes known to this date suffer from a poor distance scaling limited by the square-root of the code length. This is in a sharp contrast with the classical case where good LDPC codes are known that combine constant encoding rate and linear distance. In this talk I will describe the first family of good quantum "almost LDPC" codes. The new codes have a constant encoding rate, linear distance, and stabilizers acting on at most square root of n qubits, where n is the code length. For comparison, all previously known families of good quantum codes have stabilizers of linear weight. The proof combines two techniques: randomized constructions of good quantum codes and the homological product operation from algebraic topology. We conjecture that similar methods can produce good quantum codes with stabilizer weight n^a for any a>0. Finally, we apply the homological product to construct new small codes with low-weight stabilizers.

This is a joint work with Matthew Hastings
Preprint: arXiv:1311.0885