Problems, Progress, and Prospects of Quantum Algorithms for Quantum Chemistry : Karl Michael Ziems

Karl Michael Ziems A Journey Through Quantum Chemistry Algorithms on Quantum Computers: Problems, Progress, and Prospects 11th June 2026 https://talks.cam.ac.uk/talk/index/24... Quantum Computing for Quantum Chemistry Seminar Series https://thom.group.ch.cam.ac.uk/quant... Yusuf Hamied Department of Chemistry, University of Cambridge ------------------------------------------------------- Molecular simulation has been discussed as one of the first practical applications where quantum computers could demonstrate utility, prompting extensive research into quantum algorithms for chemistry. In this talk, we will discuss various quantum algorithms for quantum chemistry and highlight some of the challenges and potential solutions. We begin with quantum selected configuration interaction (QSCI / SQD), an algorithm designed for current quantum devices, and discuss its limitations arising from exponential scaling, redundant sampling, and limited wavefunction compactness, which hinders its competitiveness with classical counterparts in chemistry.[1] The variational quantum eigensolver (VQE) is a prominent near-term algorithm that trades circuit depth for measurement overhead. Reducing this overhead is therefore an active area of research. We present our recent work on resource-efficient, energy-based operator selection in fermionic ADAPT-VQE using exact Hamiltonian transformations.[2] Applying VQE to current hardware also requires effective quantum error mitigation. We introduce tiled M0[3] an extension to readout error mitigation tailored to tiled Ansätze. By incorporating the quantum chemical Ansatz into the construction of assignment matrices[4], tiled M0 enables additional gate-level noise characterization, while a locality approximation exploiting the tiled structure renders the noise characterization cost constant. This approach has enabled applications beyond ground-state energy estimation, including simulations of ground- and excited-state properties. Examples include spectroscopic simulations using our quantum linear-response theory,[4-6] spin-adapted orbital-optimized state-averaged VQE, and the calculation of hyperfine coupling constants.[7] Finally, looking towards an early fault-tolerant era with a limited number of fault-tolerant operations, algorithms based on quantum time evolution become particularly attractive. We discuss quantum Krylov subspace (QKS) methods and examine their principal challenges, including numerical instabilities and sensitivity to the chosen time step.[8] [1] Reinholdt, Ziems, Kjellgren, Coriani, Sauer, Kongsted, J. Chem. Theory Comput. 2025, 21, 6811 [2] Rossi, Kjellgren, Izmaylov, Sauer, Ziems, Coriani, arXiv:2606.04786 [3] Rasmussen, Kjellgren, Reinholdt, Sauer, Coriani, Ziems, Kongsted, arXiv:2511.21236 [4] Ziems, Kjellgren, Sauer, Kongsted, Coriani, Chem. Sci., 2025, 16, 4456 [5] Ziems, Kjellgren, Reinholdt, Jensen, Sauer, Kongsted, Coriani, J. Chem. Theory Comput. 2024, 20, 3551 [6] Buchwald, Ziems, Kjellgren, Sauer, Kongsted, Coriani, J. Chem. Theory Comput. 2024, 20, 7093 [7] Jensen, Hedemark, Ziems, Kjellgren, Reinholdt, Knecht, Coriani, Kongsted, Sauer, J. Chem. Theory Comput. 2025, 21, 16, 7878 [8] Oliveira, Ziems, Glaser, arXiv:2604.11532 -------------------------------------------------------