Quantum Simulations Based on Parameterized Circuit of an Antisymmetric Matrix

2025/05/02 by Daskin, Ammar · 1 citation
#FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2505.01023

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.

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