Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.01023 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913816210571264 |
|---|---|
| author | Daskin, Ammar |
| author_facet | Daskin, Ammar |
| contents | Given an antisymmetric matrix $A$ or the unitary matrix $U_A = e^A$-or an oracle whose answers can be used to infer information about $A$-in this paper we present a parameterized circuit framework that can be used to approximate a quantum circuit for $e^A$. We design the circuit based on a uniform antisymmetric matrix with $\{\pm 1\}$ elements, which has an eigenbasis that is a phase-shifted version of the quantum Fourier transform, and its eigenspectrum can be constructed by using rotation $Z$ gates. Therefore, we show that it can be used to directly estimate $e^A$ and its quantum circuit representation. Since the circuit is based on $O(n^2)$ quantum gates, which form the eigendecomposition of $e^A$ with separate building blocks, it can also be used to approximate the eigenvalues of $A$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01023 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Simulations Based on Parameterized Circuit of an Antisymmetric Matrix Daskin, Ammar Quantum Physics Given an antisymmetric matrix $A$ or the unitary matrix $U_A = e^A$-or an oracle whose answers can be used to infer information about $A$-in this paper we present a parameterized circuit framework that can be used to approximate a quantum circuit for $e^A$. We design the circuit based on a uniform antisymmetric matrix with $\{\pm 1\}$ elements, which has an eigenbasis that is a phase-shifted version of the quantum Fourier transform, and its eigenspectrum can be constructed by using rotation $Z$ gates. Therefore, we show that it can be used to directly estimate $e^A$ and its quantum circuit representation. Since the circuit is based on $O(n^2)$ quantum gates, which form the eigendecomposition of $e^A$ with separate building blocks, it can also be used to approximate the eigenvalues of $A$. |
| title | Quantum Simulations Based on Parameterized Circuit of an Antisymmetric Matrix |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2505.01023 |