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Paper 1
Clifford synthesis via generalized S and CZ gates
Vadym Kliuchnikov, Marcus P. da Silva
- Year
- 2026
- Journal
- arXiv preprint
- DOI
- arXiv:2603.24731
- arXiv
- 2603.24731
We show that any $n$-qubit Clifford unitary can be implemented using at most $2n$ multi-qubit joint measurements. All the multi-qubit joint measurements used for implementing the Clifford unitary can be chosen to form at most two sets of independent mutually-commuting measurements. Each of these sets is of size at most $n$. This enables very flexible space-time trade-offs when implementing Clifford unitaries. We also discuss a version of the result that relies on multi-target CNOTs and is more relevant for targeting fault-tolerant hardware based on Quantum LDPC codes.
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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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