[Tensor Learning Team Seminar] Talk by Dr. Patrick Gelß (ZIB, Germany) on Optimization-Driven Quantum Circuit Decomposition

This talk will be held in a hybrid format, both in person at Open Space of RIKEN AIP (Nihonbashi office) and online by Zoom. AIP Open Space: *only available to AIP researchers.

Date & Time: May 23, 2025: 14:00 - 15:00 (JST)

Speaker: Patrick Gelß, Zuse Institute Berlin (ZIB), Germany

Title: Optimization-Driven Quantum Circuit Decomposition

Abstract: In this work, we investigate an optimization-based approach to quantum circuit decomposition. Starting with a fixed layout of one- and two qubit gates to be used, we aim to find suitable unitary gates to minimize the error between the operator resulting from the circuit and a given target gate. This results in a nonlinear, nonconvex optimization problem over complex, matrix-valued arguments with equality constraints.

To solve this problem, we use a penalty approach in which the unitarity constraints are relaxed. This introduces a sequence of surrogate problems. Analyzing the problem, we show that the penalty functional can be rewritten as the difference of two convex functionals. Together with results from Toland duality, this allows the derivation of a multiconvex reformulation of the penalized problem. Using this, we propose a descent-based optimization algorithm to solve the problem.

Bio:
Since July 2022, Patrick Gelß has been leading the research group Quantum Computation & Optimization at the Zuse Institute Berlin (ZIB), within the department AI in Society, Science, and Technology, jointly with Sebastian Pokutta. Prior to this, he was a postdoctoral researcher in the Collaborative Research Center (CRC) 1114, funded by the German Research Foundation (DFG), from 2017 to 2022, contributing to several projects on data-driven and tensor-based analysis of multiscale systems in collaboration with Jens Eisert, Stefan Klus, and Christof Schütte.

Patrick Gelß received his PhD in 2017 with a thesis entitled "The Tensor-Train Format and Its Applications – Modeling and Analysis of Chemical Reaction Networks, Catalytic Processes, Fluid Flows, and Brownian Dynamics". He previously studied mathematics and physics at Freie Universität Berlin, earning a diploma in 2013 with a thesis on "Transition Path Theory for Markov Jump Processes".