Quantum computing under physical limitations

• Applicant: Dr. Dominik Hangleiter
• Subject Area: Theoretical Computer Science ; Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
• Term: since 2026
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 563402105

Using operations allowed by quantum theory, it is in principle possible to build computers that can solve tasks which are intractable for standard, classical computers. However, physical limitations on computational resources---for example, an absence of interference---can restrict which computations are physically possible. For quantum computers, the impact of such limitations on computational power are not fully explored yet. At the same time, we do not yet well understand which properties of quantum computations allow them to outperform classical ones. I will simultaneously address those important challenges by studying quantum computations under physical restrictions. I will do so by using and developing new concepts for the study of physical limitations on computers synethizing perspectives of theoretical computer science and physics. First, motivated by early fault-tolerant computers based on atomic qubits, I will study how (noisy) computations can be performed in codes beyond the surface code, whether there are natural implementations of algorithmic primitives in bespoke codes, and develop new ways to quantify and measure noise in encoded computations. Second, motivated by quantum annealing devices, I will study quantum computations without interference or a sign problem, which is not only relevant to annealing devices but also important to understanding whether interference is necessary for quantum advantage. I will develop a bottom-up understanding of the computations that can be performed using sign-problem-free Hamiltonians, a theory of how the sign problem relates to other physical resources and determine to what extent the power of quantum algorithms can be reduced to a sign problem. My research will thus not only develop a new, integrated understanding of quantum speedups, but also has the potential to reveal ground-breaking new algorithmic primitives which may yield new applications of quantum computing.

• DFG Programme: Emmy Noether Independent Research Groups