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Paper 1
An Optimized Nearest Neighbor Compliant Quantum Circuit for 5-qubit Code
Arijit Mondal, Keshab K. Parhi
- Year
- 2024
- Journal
- arXiv preprint
- DOI
- arXiv:2410.06375
- arXiv
- 2410.06375
The five-qubit quantum error correcting code encodes one logical qubit to five physical qubits, and protects the code from a single error. It was one of the first quantum codes to be invented, and various encoding circuits have been proposed for it. In this paper, we propose a systematic procedure for optimization of encoder circuits for stabilizer codes. We start with the systematic construction of an encoder for a five-qubit code, and optimize the circuit in terms of the number of quantum gates. Our method is also applicable to larger stabilizer codes. We further propose nearest neighbor compliant (NNC) circuits for the proposed encoder using a single swap gate, as compared to three swap gates in a prior design.
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Entanglement-assisted Quantum Error Correcting Code Saturating The Classical Singleton Bound
Soham Ghosh, Evagoras Stylianou, Holger Boche
- Year
- 2024
- Journal
- arXiv preprint
- DOI
- arXiv:2410.04130
- arXiv
- 2410.04130
We introduce a construction for entanglement-assisted quantum error-correcting codes (EAQECCs) that saturates the classical Singleton bound with less shared entanglement than any known method for code rates below $ \frac{k}{n} = \frac{1}{3} $. For higher rates, our EAQECC also meets the Singleton bound, although with increased entanglement requirements. Additionally, we demonstrate that any classical $[n,k,d]_q$ code can be transformed into an EAQECC with parameters $[[n,k,d;2k]]_q$ using $2k$ pre-shared maximally entangled pairs. The complexity of our encoding protocol for $k$-qudits with $q$ levels is $\mathcal{O}(k \log_{\frac{q}{q-1}}(k))$, excluding the complexity of encoding and decoding the classical MDS code. While this complexity remains linear in $k$ for systems of reasonable size, it increases significantly for larger-levelled systems, highlighting the need for further research into complexity reduction.
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