Quantum Simulations Based on Parameterized Circuit of an Antisymmetric Matrix

• URL: http://arxiv.org/abs/2505.01023v1
• Date: Fri, 02 May 2025 05:40:34 GMT
• Title: Quantum Simulations Based on Parameterized Circuit of an Antisymmetric Matrix
• Authors: Ammar Daskin,
• Abstract summary: We show that a circuit framework can be used to approximate a quantum circuit for $eA$.<n>The circuit is based on $O(n2)$ quantum gates, which form the eigendecomposition of $eA$ with separate building blocks.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $\{\pm 1\}$ 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 $A$.

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