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Quantum Simulations Based on Parameterized Circuit of an Antisymmetric Matrix
Ammar Daskin
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Given an antisymmetric matrix A or the unitary matrix U_A = eᴬ-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 eᴬ. 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 eᴬ and its quantum circuit representation. Since the circuit is based on O(n²) quantum gates, which form the eigendecomposition of eᴬ with separate building blocks, it can also be used to approximate the eigenvalues of A.
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