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Paper 1

The PPKN Gate: An Optimal 1-Toffoli Input-Preserving Full Adder for Quantum Arithmetic

G. Papakonstantinou

Year

2025

Journal

arXiv preprint

DOI

arXiv:2512.12073

arXiv

2512.12073

Efficient arithmetic operations are a prerequisite for practical quantum computing. Optimization efforts focus on two primary metrics: Quantum Cost (QC), determined by the number of non-linear gates, and Logical Depth, which defines the execution speed. Existing literature identifies the HNG gate as the standard for Input-Preserving Reversible Full Adders. HNG gate typically requires a QC of 12 and a logical depth of 5, in the area of classical reversible circuits. This paper proposes the PPKN Gate, a novel design that achieves the same inputpreserving functionality using only one Toffoli gate and five CNOT gates. With a Quantum Cost of 10 and a reduced logical depth of 4, the PPKN gate outperforms the standard HNG gate in both complexity and speed. Furthermore, we present a modular architecture for constructing an n-bit Ripple Carry Adder by cascading PPKN modules.

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Paper 2

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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