Fault-tolerant quantum computing (FTQC) offers a pathway beyond the limits of current noisy processors and classical supercomputers. Many chemically relevant systems remain intractable because achieving chemical accuracy scales beyond even the largest HPC facilities. FTQC could reduce this scaling, enabling predictive simulations for energy, catalysis and pharmaceutical discovery.
The project aims to develop quantum algorithms and software that make such simulations feasible on future FT hardware. The focus lies on reducing qubit counts, logical gate depth and runtime, since resource efficiency will determine whether simulations become practical on first-generation error-corrected devices. Methods are designed to be hardware-agnostic and compatible with photonic, superconducting and trapped-ion platforms.
Main objectives were:
• Develop quantum algorithms for electronic and nuclear dynamics using fewer qubits and gates while retaining accuracy.
• Create resource-estimation methodology for FTQC
• Optimise implementations for multiple architectures and validate through simulation and early hardware trials.
During the reporting period, multiple new algorithms and representations were developed with substantial reductions in gate complexity. Highlights include algorithms for strongly coupled Hamiltonians, relativistic electronic structure, symmetry-driven tensor factorisation, Walsh–Hadamard QROM for molecular dynamics, quantum generalised eigenvalue solving, and compact UVCC circuits for vibrational structure. We also produced the first quantum discrete-variable-representation (DVR) oracle and a dedicated quantum resource estimator.
Impact is illustrated with FeMoCo simulation. Ammonia production consumes ~4% of global energy; improved catalytic design has large economic relevance. Classical high-accuracy FeMoCo calculations remain out of reach. Our algorithms reduce quantum resources for electronic structure by ~40% and for vibrational simulation by several orders of magnitude (up to 100 000x), suggesting that FTQC could ultimately enable direct computational catalyst screening.
This progress forms a foundation for future FTQC molecular simulation, accelerating discovery of catalysts, batteries and pharmaceuticals and supporting energy-efficient industrial technologies.
