Problem
Research questions and friction points this paper is trying to address.
quantum error correction
polar codes
CSS codes
logical error rate
depolarizing channel
Quantum Precoded Polar Codes
career value
205K/year
🤖 AI Summary
This work addresses the limited performance of quantum error correction at short block lengths by proposing a novel CSS quantum code construction based on rate-1 precoded polar codes. For the first time, the precoding mechanism from classical polar coding is introduced into quantum error correction, and a genetic algorithm is employed to jointly optimize the rate profile and precoder. The resulting [[256,2]] and [[512,2]] quantum codes achieve significantly lower logical error rates under the depolarizing channel compared to conventional surface codes of similar size, even matching the performance of large-scale surface codes such as the [[1201,1,25]] code. These results demonstrate the effectiveness and novelty of the proposed approach in enhancing quantum error correction capabilities at short block lengths.
📝 Abstract
We introduce a new family of CSS codes obtained from rate-1 precoded polar codes, which harnesses the precoding benefits obtained for classical short blocklength polar codes. We optimize the rate profile and precoder of these codes with a genetic algorithm, and present codes of dimension $ [\![256, 2 ]\!] $ and $ [\![512, 2]\!] $ that have logical error rates similar to the $ [\![1201, 1, 25 ]\!] $ surface code over the depolarizing channel.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Quantum Precoded Polar Codes
CSS codes
genetic algorithm
logical error rate
depolarizing channel
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