Quantum circuit synthesis for fermionic excitations in coupled cluster theory

Abstract

This work provides a step-by-step quantum computing derivation of the unitary coupled cluster singles and doubles ansatz. We show how the structure of the ansatz emerges from fermionic algebra under unitary constraints. By explicitly connecting second quantization, Jordan-Wigner mapping, and quantum circuit synthesis, we clarify conceptual gaps between quantum physics and quantum computing implementations, particularly regarding operator locality, commutation structure, and hardware realization. We exemplify the procedure on the singles and doubles coupled cluster ansatz for the hydrogen molecule.

arXiv comment14 pages. 2 figures