Quantum Simulations Based on Parameterized Circuit of an Antisymmetric Matrix

2025/05/02 by Ammar Daskin, Daskin, Ammar · 1 citation
Computer Science · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum-Dot Cellular Automata

paper · pdf · doi:10.48550/arxiv.2505.01023

openalex publication_date 2025/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 \± 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(n²) quantum gates, which form the eigendecomposition of e^A with separate building blocks, it can also be used to approximate the eigenvalues of A.

Citations

• Quantum theory does not need complex numbers
• Skew-Symmetric Adjacency Matrices for Clustering Directed Graphs
• A Survey of Complex-Valued Neural Networks
• Time integration of symmetric and anti-symmetric low-rank matrices and\n Tucker tensors
• Deep Complex Networks
• A survey on the skew energy of oriented graphs
• Synthesis of Quantum Logic Circuits
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems

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