Almost Optimal Synthesis of Reversible Function in Qudit Model
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912738565947392 |
|---|---|
| author | Xu, Buji Nie, Junhong Sun, Xiaoming |
| author_facet | Xu, Buji Nie, Junhong Sun, Xiaoming |
| contents | Quantum oracles are widely adopted in problems, like query oracle in Grover's algorithm, cipher in quantum cryptanalytic and data encoder in quantum machine learning. Notably, the bit-flip oracle, capable of flipping the state based on a given classical function, emerges as a fundamental component in the design and construction of quantum algorithms. Devising methods to optimally implement the bit-flip oracle essentially translates to the efficient synthesis of reversible functions. Prior research has primarily focused on the qubit model, leaving the higher dimensional systems, i.e. qudit model, largely unexplored. By allowing more than two computational bases, qudit model can fully utilize the multi-level nature of the underlying physical mechanism. We propose a method to synthesize even permutations in $A_{d^{n}}$ using $Θ(d)$ $(n - 1)$-qudit sub-circuits, which achieve asymptotic optimality in the count of sub-circuits. Moreover, we introduce a technique for synthesizing reversible functions employing $O\left( n d^{n} \right)$ gates and only a single ancilla. This is asymptotically tight in terms of $d$ and asymptotically almost tight in terms of $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05237 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Almost Optimal Synthesis of Reversible Function in Qudit Model Xu, Buji Nie, Junhong Sun, Xiaoming Quantum Physics Quantum oracles are widely adopted in problems, like query oracle in Grover's algorithm, cipher in quantum cryptanalytic and data encoder in quantum machine learning. Notably, the bit-flip oracle, capable of flipping the state based on a given classical function, emerges as a fundamental component in the design and construction of quantum algorithms. Devising methods to optimally implement the bit-flip oracle essentially translates to the efficient synthesis of reversible functions. Prior research has primarily focused on the qubit model, leaving the higher dimensional systems, i.e. qudit model, largely unexplored. By allowing more than two computational bases, qudit model can fully utilize the multi-level nature of the underlying physical mechanism. We propose a method to synthesize even permutations in $A_{d^{n}}$ using $Θ(d)$ $(n - 1)$-qudit sub-circuits, which achieve asymptotic optimality in the count of sub-circuits. Moreover, we introduce a technique for synthesizing reversible functions employing $O\left( n d^{n} \right)$ gates and only a single ancilla. This is asymptotically tight in terms of $d$ and asymptotically almost tight in terms of $n$. |
| title | Almost Optimal Synthesis of Reversible Function in Qudit Model |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2501.05237 |