fourier-lcu-quantum-optimization

name	fourier-lcu-quantum-optimization
description	Fourier-based Linear Combination of Unitaries (LCU) methodology for efficient quantum circuit decomposition in optimization algorithms. Covers ancilla-free LCU constructions, Fourier decomposition of diagonal/non-diagonal unitaries, formal connection to Lagrangian relaxation, and hardware-friendly gate layer simplification. Activation: LCU, linear combination of unitaries, Fourier quantum, quantum optimization decomposition, constraint penalty, XY-mixer, cardinality constraint, ancilla-free quantum, sampling overhead, circuit complexity tradeoff
license	Complete terms in LICENSE.txt
metadata	{"arxiv_id":"2605.18985","published":"2026-05-18","authors":"Almudena Carrera Vazquez, Daniel J. Egger, Stefan Woerner","tags":["LCU","Fourier","quantum-optimization","QAOA","constraint-handling","ancilla-free","Lagrangian-relaxation"]}

Fourier-Based LCU for Quantum Optimization

Efficient circuit decomposition via Fourier-based Linear Combination of Unitaries (LCU) for quantum optimization algorithms.

Context

Quantum optimization algorithms (QAOA, VQE) require complex multi-qubit interactions that are expensive to implement. LCU provides a framework for approximating these circuits by decomposing unitaries into simpler components with polynomial sampling overhead.

Core Methodology

1. Fourier-Based LCU Decomposition

Decompose complex unitaries U = exp(-iH) via Fourier series:

U ≈ Σ_k c_k · V_k

where V_k are simple single-qubit or low-connectivity gate layers, and c_k are Fourier coefficients.