FET: CIF: Small: Graph-Based Quantum Error Correcting Codes

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Quantum computing is inherently noisy, and errors in the processed qubits are always present. In order to correct the errors, it is therefore necessary to apply quantum error-correcting codes, which will be a key component of future practical fault-tolerant quantum computation systems. Although existing practical quantum codes use very short block lengths, future practical systems will deal with many qubits and will need to apply powerful codes with long block lengths. This project investigates the construction of novel families of quantum codes that for long block lengths are expected to achieve excellent performance in practical scenarios. Two graduate students and two undergraduate students will directly participate in this research, and state of the art results from the project will be disseminated in a new graduate course developed by the PI.Specifically, this project investigates the application of turbo-like/graph-based coding structures in quantum error correction. The introduction of graph-based codes, which are iteratively decoded using message passing, has been one of the most important developments in classical communications during the last two decades, leading to excellent performance in many different environments when the block length increases. Interestingly, the quantum codes in the important family of stabilizer codes can be designed taking as a starting point classical graph-based codes that satisfy the symplectic property, which can be seen as a constraint in the graph structure. Following this approach, excellent results can be obtained for the subset of Calderbank-Short-Steane (CSS) quantum codes. By properly modifying the graph structure, this project will explore the great potential for the development of even better non-CSS stabilizer codes that can be applied in realistic quantum channels, such as asymmetric channels and channels with memory. The objective is to achieve improved performance even when the channel parameters are not known at the decoder site, by estimating them jointly with the decoding process, leading to more robust designs.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.