Selected Publications

• Beyond-mean-field fluctuations for the solution of constraint satisfaction problems
  arXiv:2507.10360 (2025).
  doi:10.48550/arXiv.2507.10360
• Quantum combinatorial optimization beyond the variational paradigm: simple schedules for hard problems
  Phys. Rev. A, 111, 032411 (2025).
  doi:10.1103/PhysRevA.111.032411
• Mean-Field Approximate Optimization Algorithm
  PRX Quantum, 4, 030335 (2023).
  doi:10.1103/PRXQuantum.4.030335

Projects

Quicopt - Helmholtz Enterprise Spin-Off

We are part of the 2024 Batch of the Helmholtz Enterprise program. Quicopt is developing optimization software inspired by quantum physics to efficiently solve optimization problems. Our technology is going to help companies in various industries to improve business decisions and reduce costs.

Master's Thesis in Quantum Optimization

We are looking for a motivated student to work on one of a variety of research ideas revolving around the general topic of quantum optimization. The direct day-to-day supervision will be provided by me. Recent papers that have come forth out of Master's projects in our group are

• Phys. Rev. Res. 7, 023165 (2025),
• Phys. Rev. A 111, 032411 (2025),
• arxiv:2507.10360.

PGI-12 is a lively and supportive institute with access to great infrastructure.

Possible research directions:

• Algorithm development for quantum optimization.
• Algorithm development for low-autocorrelation binary sequences.
• Algorithmic benchmarking: the QAOA, parallel tempering, simulated-bifurcation method, genetic algorithms, semi-definite programming etc. against our methods.
• High-performance computing: accelerate our methods via special-purpose hardware (e.g. GPUs).

Candidate requirements:

• Good grades in theoretical physics, preferably quantum mechanics.
• Programming experience in Python or similar.
• Motivation to push a research topic independently.
• The official first supervisor needs to come from the student's home university.

Applications should include a motivation letter, CV and transcripts. Contact details below.

Bachelor's Thesis Projects

We are also looking for motivated students to pursue Bachelor's projects in our group. If you are interested in learning a handy mixture of analytical and numerical techniques, have a look at the revolving list of topics below. PGI-12 is a lively and supportive institute with access to great infrastructure.

Possible research directions:

• Mathematical optimization: simplex algorithm, branch-and-bound, hybrid genetic search.
• GPU programming in Julia: acceleration of simulated quantum circuits.
• Analytical and numerical methods for dynamical systems.

Candidate requirements:

• Good grades in maths and/or theoretical physics, preferably quantum mechanics.
• Interest in programming in Julia/Python/C.
• Motivation to work somewhat independently.
• The official first supervisor needs to come from the student's home university.

Applications should include a short motivation letter and transcripts. Contact details below.

List of Publications

• Niklas Foos, Bastian Epping, Jannik Grundler, Alexandru Ciobanu, Ajainderpal Singh, Tim Bode, Moritz Helias, and David Dahmen. Beyond-mean-field fluctuations for the solution of constraint satisfaction problems. 2025. doi:10.48550/arXiv.2507.10360.
• Thorge Müller, Ajainderpal Singh, Frank K. Wilhelm, and Tim Bode. Limitations of quantum approximate optimization in solving generic higher-order constraint-satisfaction problems. Phys. Rev. Res., 7:023165, May 2025. doi:10.1103/PhysRevResearch.7.023165.
• Tim Bode, Krish Ramesh, and Tobias Stollenwerk. Quantum combinatorial optimization beyond the variational paradigm: simple schedules for hard problems. Phys. Rev. A, 111:032411, Mar 2025. doi:10.1103/PhysRevA.111.032411.
• Dmitriy S. Shapiro, Yannik Weber, Tim Bode, Frank K. Wilhelm, and Dmitry Bagrets. Quantum Simulation of the Dicke-Ising Model via Digital-Analog Algorithms. 2024. arXiv:2412.14285.
• Tim Bode and Frank K. Wilhelm. Adiabatic bottlenecks in quantum annealing and nonequilibrium dynamics of paramagnons. Phys. Rev. A, 110:012611, 2024. doi:10.1103/PhysRevA.110.012611.
• Tim Bode, Michael Kajan, Francisco Meirinhos, and Johann Kroha. Non-markovian dynamics of open quantum systems via auxiliary particles with exact operator constraint. Phys. Rev. Res., 6:013220, 2024. doi:10.1103/PhysRevResearch.6.013220.
• Kevin Lively, Tim Bode, Jochen Szangolies, Jian-Xin Zhu, and Benedikt Fauseweh. Noise robust detection of quantum phase transitions. Phys. Rev. Res., 6:043254, 2024. doi:10.1103/PhysRevResearch.6.043254.
• Aditi Misra-Spieldenner, Tim Bode, Peter K. Schuhmacher, Tobias Stollenwerk, Dmitry Bagrets, and Frank K. Wilhelm. Mean-Field Approximate Optimization Algorithm. PRX Quantum, 4:030335, 2023. doi:10.1103/PRXQuantum.4.030335.
• Tim Bode, Dmitry Bagrets, Aditi Misra-Spieldenner, Tobias Stollenwerk, and Frank K. Wilhelm. QAOA.jl: Toolkit for the Quantum and Mean-Field Approximate Optimization Algorithms. Journal of Open Source Software, 8(86):5364, 2023. doi:10.21105/joss.05364.
• Francisco Meirinhos, Michael Kajan, Johann Kroha, and Tim Bode. Adaptive numerical solution of Kadanoff-Baym equations. SciPost Phys. Core, 5:030, 2022. doi:10.21468/SciPostPhysCore.5.2.030.
• Tim Bode. The two-particle irreducible effective action for classical stochastic processes. Journal of Physics A: Mathematical and Theoretical, 55(26):265401, 2022. doi:10.1088/1751-8121/ac73c6.
• Fahri Emre Öztürk, Tim Lappe, Göran Hellmann, Julian Schmitt, Jan Klaers, Frank Vewinger, Johann Kroha, and Martin Weitz. Observation of a non-Hermitian phase transition in an optical quantum gas. Science, 372(6537):88–91, 2021. doi:10.1126/science.abe9869.
• Tim Lappe. Non-Markovian Dynamics of Open Bose-Einstein Condensates. PhD thesis, Rheinische Friedrich-Wilhelms-Universität Bonn, 2021. URL: https://hdl.handle.net/20.500.11811/8961.
• Fahri Emre Öztürk, Tim Lappe, Göran Hellmann, Julian Schmitt, Jan Klaers, Frank Vewinger, Johann Kroha, and Martin Weitz. Fluctuation dynamics of an open photon Bose-Einstein condensate. Phys. Rev. A, 100:043803, 2019. doi:10.1103/PhysRevA.100.043803.
• Tim Lappe, Anna Posazhennikova, and Johann Kroha. Fluctuation damping of isolated, oscillating Bose-Einstein condensates. Phys. Rev. A, 98:023626, 2018. doi:10.1103/PhysRevA.98.023626.

Grants & Awards

• December 2025 - Start-up Transfer.NRW.
• November 2025 - Helmholtz Enterprise Spin-Off.
• November 2024 - Helmholtz Enterprise Field Study Fellowship.
• February 2021 - Graduated with distinction (summa cum laude), University of Bonn.
• September 2016 - Honors-branch Scholarship, Bonn-Cologne Graduate School of Physics.

Talks

• December 2025 - ZEBRA Accelerator, Start-up Village Jülich, Demo-Day Pitch.
• November 2025 - Helmholtz-Gemeinschaft, Berlin, 41. Intake Pitch Helmholtz Enterprise Program.
• November 2025 - ASML, Veldhoven, Masterclass #81: Quantum Computing.
• November 2025 - Innovationsförderagentur NRW, Düsseldorf, Pitch Start-up Transfer.NRW.
• May 2025 - Deutsches Forschungszentrum für Künstliche Intelligenz (DFKI), Kaiserslautern, Quantum (-Inspired) Optimization.
• April 2025 - German Aerospace Center (DLR), Journal Club.
• April 2025 - William I. Fine Theoretical Physics Institute, University of Minnesota, Quantum-Inspired Optimization: Lessons and Perspectives.
• March 2025 - NASA Ames, Mountain View, Quantum Optimization and Simulation.
• March 2025 - DPG March Meeting, University of Bonn, Quantum optimization beyond the variational paradigm.
• February 2025 - QOQMS Seminar, University of Strathclyde, Quantum optimization beyond the variational paradigm.
• January 2025 - FZJ Workshop on Bridging Neuromorphic and Quantum Computing, Jülich, Quantum-Inspired Optimization Algorithms.
• November 2024 - HQS Workshop on QC Applications Beyond the Variational Paradigm, Karlsruhe, Quantum Simulation of Electron-Phonin Interactions in Circuit QED.
• August 2024 - FZJ Workshop on the QAOA, Jülich, Mean-Field Approximate Optimization.
• April 2024 - International Network on Quantum Annealing (INQA), Adiabatic Bottlenecks in Quantum Annealing and Nonequilibrium Dynamics of Paramagnons | YouTube.
• Feb 2024 - Institute for Advanced Simulation (IAS-6), Jülich, Mean-Field Combinatorial Optimization Algorithms.
• March 2022 - APS March Meeting, Chicago, Adaptive Numerical Solution of Kadanoff-Baym Equations.
• June 2020 - Closing Workshop SFB/TR 185, Bonn, Non-Markovian Dynamics of a Driven-Dissipative Photon Condensate.
• September 2018 - Intensive Week SFB/TR 185, Bonn, Introduction to Quantum Field Theory.
• March 2018 - Technische Universität Kaiserslautern, Kaiserslautern, Collapse and revival of photon oscillations.

Contact

Tim Bode @ PGI-12