Research

Quantum Simulation and Algorithms for fundamental physics problems

Exciting advances in Quantum Technologies are expected to generate significant economic growth and allow us to address previously unsurmountable fundamental questions in science with wide societal impact. However, because the technology is comparatively young and not yet reliable, their role in enabling progress in fundamental physics problems is not yet clearly understood.

Grand-challenge problems in nuclear and high energy particle physics are key near-term applications, benchmarking opportunities, and important drivers for progress in Quantum Information Science and Technology (QIST). Currently, I am most interested in the following aspects:

• Algorithms and simulation protocols for Abelian and non-Abelian Lattice Gauge theories on digital quantum computers and analog quantum simulation with atomic, molecular, and optical systems. 

• Quantum computing non-equilibrium topological phenomena and thermalization / quantum chaos in lattice gauge theories; dynamical quantum phase transitions and topological phenomena. 

• Quantum algorithms and analog simulation for scattering problems in  particle and nuclear physics.

• Thermal state preparation algorithms.  
  

Entanglement Structure and Tomography

In nature, many of the intricacies of quantum system, when contrasted with our classical intuition, come from features such as quantum mechanical superposition and entanglement. While quantum mechanics has long been "proven" in Bell experiments, entanglement has long bewildered scientist. Many have even considered it an exotic curiosity without practical implications.  In recent years, it has become obvious that entanglement is a valuable resource in quantum information science, and entanglement structure a powerful tool to understand e.g. novel phases in condensed matter systems and beyond. Best of all, those latter two features are intimately related! I am currently focused on the following aspects:

• Entanglement Structure of Lattice Gauge Theories, and fermionic and bosonic quantum many-body systems.

• Tomography protocols using random measurements, classical shadow and entanglement Hamiltonian tomography.

• Symmetry conscious random measurement schemes.  
  

Thermalization and Non-equilibrium phenomena

With the advent of increasingly reliable quantum computers and simulators, based on atomic, molecular, optical and superconducting technology, comes the possibility to study quantum many body systems far from equilibrium and in thermal situations where classical Monte-Carlo importance sampling techniques break. What I find exciting is not so much the computational advance brought by QIST, but rather the opportunity to think differently about old problems, establish new paradigms and concepts, and discover novel phenomena:

• Dynamical Quantum Phase Transitions

• Thermalization, Many-Body Localization and Scars

• Role of entanglement structure and resource theory for non-equilibrium phenomena.

• Quantum Thermodynamics
  

Topological Phases

Quantum many body systems are sometimes weird, often defying everything we once learned about how phases of matter should behave. Such phases have important applications in QIST as a pathway to fault-tolerant computation, but also have implications for finding and designing new materials. Potentially, QIST implications will even help understanding extreme matter created in the early universe or in ultra-relativistic relativistic heavy ion collisions.

• Topologically ordered and SPT phases in high energy, nuclear, and condensed matter physics, Abelian and non-Abelian LGTs

• Topological quantum computation and error correction.

Publications

Recent Publications

• "High-Energy Collisions of Quarks and Hadrons in the Schwinger Model: From Tensor Networks to Circuit QED", Ron Belyanski, Seth Whitsitt, Niklas Mueller, Ali Fahimniya, Elizabeth R. Bennewitz, Zohreh Davoudi, Alexey Gorshkov, arXiv:2307.02522 (2023)

• "Randomized measurement protocols for lattice gauge theories", Jacob Bringewatt, Jonathan Kunjummen, Niklas Mueller, arXiv:2303.15519 (2023)

• "Quantum Information Science and Technology for Nuclear Physics. INput into U.S. Long-Range Planning, 2023" Beck et al. arXiv:2303.00113 (2023)

• “Quantum computation of dynamical quantum phase transitions and entanglement tomography in a lattice gauge theory”, Niklas Mueller, Joseph A. Carolan, Andrew Connelly, Zohreh Davoudi, Eugene F. Dumitrescu, Kübra Yeter-Aydeniz, PRX Quantum 4, 030323 (2023)

• Toward Quantum Computing Phase Diagrams of Gauge Theories with Thermal Pure Quantum States”, Z. Davoudi, Niklas Mueller, C. Powers, Phys. Rev. Lett. 131, 081901 (2023)

• “Thermalization of gauge theories from their Entanglement Spectrum”,  Niklas Mueller, Torsten Zache, Robert Ott, Phys. Rev. Lett. 129 (2022), 13112

Education / CV