Fri, May 2, 1:30 in 6C-442
Sergei Bravyi (IBM)
Good Quantum Codes with Low-Weight Stabilizers
Quantum codes with low-weight stabilizers known as LDPC codes have
been actively studied recently due to their potential applications in
fault-tolerant quantum computing. However, all families 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 families of LDPC codes are
known that combine constant encoding rate and linear distance. In this
talk I will describe the first family of good quantum codes with
low-weight stabilizers. 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 stabilizer 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
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