Asymmetric Quantum Codes on Toric Surfaces
Johan P. Hansen
TL;DR
This paper introduces families of asymmetric quantum error-correcting codes derived from toric surfaces, addressing biased quantum channels with different error probabilities for qubit-flip and phase-shift errors.
Contribution
It presents a novel construction of asymmetric quantum codes using toric surface codes, expanding the toolkit for quantum error correction in biased channels.
Findings
Constructed new families of asymmetric quantum codes from toric surfaces
Demonstrated the applicability of toric codes to quantum error correction
Provided theoretical foundations for codes tailored to biased quantum channels
Abstract
Asymmetric quantum error-correcting codes are quantum codes defined over biased quantum channels: qubit-flip and phase-shift errors may have equal or different probabilities. The code construction is the Calderbank-Shor-Steane construction based on two linear codes. We present families of toric surfaces, toric codes and associated asymmetric quantum error-correcting codes.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum-Dot Cellular Automata · Quantum Information and Cryptography