Efficient Fourier-Based Linear Combination of Unitaries and Applications in Quantum Optimization by Dr. Stefan Woerner

Abstract

We investigate ancilla-free linear combination of unitaries (LCU) as a framework for approximating complex quantum circuits. This is particularly effective for quantum optimization algorithms, where candidate solutions can be evaluated classically and the task is to sample high-quality bitstrings rather than reproduce the full output distribution. We show that Fourier-based LCU constructions efficiently decompose broad classes of diagonal and non-diagonal unitaries, replacing highly connected qubit interactions with single-qubit gate layers or significantly simpler structures at the cost of a polynomial sampling overhead. Applied to algorithms such as QAOA, this yields efficient, hardware-friendly decompositions of, for instance, cardinality-constraint penalties and the fully connected XY-mixer, while maintaining rigorous performance guarantees compared to fully coherent implementations. Furthermore, we establish a formal connection between Fourier-based quantum penalties and Lagrangian relaxation, offering a unified perspective on constraint handling. We validate our approach using exact statevector simulations of 12-qubit circuits and large-scale experiments on 106 superconducting qubits. Our results illustrate how approximate sampling via an LCU systematically trades circuit complexity for sampling overhead, extending the practical reach of near-term quantum optimization.

About the Speaker

Dr. Stefan Woerner is a Principal Research Scientist and Senior Manager of Applied Quantum Optimization Research at IBM Research, based in Zurich, Switzerland. He leads a global team advancing quantum optimization algorithms and their applications to deliver practical quantum advantage for real-world challenges in industry and science. Stefan received his PhD from ETH Zurich and is internationally recognized for his contributions to quantum optimization, quantum finance, and quantum machine learning. He has authored influential scientific publications and collaborates extensively with leading partners in academia and industry.