I work on quantum algorithms: finding problems where quantum computers offer significant advantages over all classical approaches, and understanding where they don't. While quantum hardware has advanced rapidly, quantum speedups with genuine practical relevance remain rare. My goal is to help close this gap.

Selected Publications (see here for a complete list)

  1. A Spectral Proof of the Hypergraph Moore Bound
    Alexander Schmidhuber, Matthew B. Hastings
    arXiv:2607.26028

  2. The Kikuchi Hierarchy is Sharp for kXOR
    Alexander Schmidhuber, Matthew B. Hastings
    arXiv:2607.29672

  3. Adiabatic Quantum Phase Estimation
    Alexander Schmidhuber, Seth Lloyd
    arXiv:2605.22770

  4. Quartic quantum speedups for community detection
    Alexander Schmidhuber, Alexander Zlokapa
    arXiv:2510.08494, QIP '26 and XPRIZE Quantum Applications Finalist

  5. Hamiltonian Decoded Quantum Interferometry
    arXiv:2510.07913, QIP '26

  6. A quantum algorithm for Khovanov homology
    arXiv:2501.12378, TQC '25

  7. Quartic quantum speedups for planted inference
    Alexander Schmidhuber, Ryan O'Donnell, Robin Kothari, Ryan Babbush
    Phys. Rev. X 15, 021077 (2025), QIP '25 and SODA '25

  8. Optimization by decoded quantum interferometry
    Nature 646 (831–836), Invited Plenary Talk at QIP '25

  9. Classically estimating observables of noiseless quantum circuits
    Phys. Rev. Lett. 135, 170602, TQC '25

  10. Quantum computing and persistence in topological data analysis
    PRX Quantum:2410.21258, QTML '25 (Highlighted Talk)

  11. Complexity-theoretic limitations on quantum algorithms for topological data analysis
    Alexander Schmidhuber, Seth Lloyd
    PRX Quantum 4, 040349 (2023)