Quantum circuit synthesis for fermionic excitations in coupled cluster theory using the Jordan-Wigner mapping

TL;DR

This paper derives the Unitary Coupled Cluster ansatz from fermionic algebra, clarifying its structure and implementation in quantum computing through the Jordan-Wigner mapping.

Contribution

It provides a quantum-first derivation of the Unitary Coupled Cluster ansatz, linking fermionic algebra with circuit synthesis and addressing implementation challenges.

Findings

Derived the Unitary Coupled Cluster ansatz from fermionic algebra.

Connected second quantization, Jordan-Wigner mapping, and circuit synthesis.

Clarified operator locality and commutation for hardware realization.

Abstract

This work provides a quantum-computing-first derivation of the Unitary Coupled Cluster ansatz, showing that its structure emerges naturally from fermionic algebra under unitary constraints. By explicitly connecting second quantization, Jordan-Wigner mapping, and circuit synthesis, we clarify conceptual gaps between quantum chemistry and quantum computing implementations, particularly regarding operator locality, commutation structure, and hardware realization.