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Paper 1
Towards low overhead magic state distillation
Anirudh Krishna, Jean-Pierre Tillich
- Year
- 2018
- Journal
- arXiv preprint
- DOI
- arXiv:1811.08461
- arXiv
- 1811.08461
Magic state distillation is a resource intensive sub-routine for quantum computation. The ratio of noisy input states to output states with error rate at most $ε$ scales as $O(\log^γ(1/ε))$ (Bravyi and Haah, PRA 2012). In a breakthrough paper, Hastings and Haah (PRL 2018) showed that it is possible to construct distillation routines with sub-logarithmic overhead, achieving $γ\approx 0.6779$ and falsifying a conjecture that $γ$ is lower bounded by $1$. They then ask whether $γ$ can be made arbitrarily close to $0$. We answer this question in the affirmative for magic state distillation routines using qudits ($d$ dimensional quantum systems).
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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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