We are proud to announce a new milestone in quantum simulation - a high-accuracy quantum algorithm for modeling rotational-vibrational (rovibrational) Hamiltonians, a key step toward understanding molecular behavior at unprecedented precision.

This work, led by Michał Szczepanik, Ákos Nagy, and Emil Żak, demonstrates how combining carefully designed mathematical frameworks with fault-tolerant quantum architectures can push the limits of what is computationally possible in molecular science.

Why Rovibrational Simulation Matters

Understanding how molecules move - how their atoms vibrate, rotate, and interact - lies at the heart of chemistry, materials science, and pharmaceuticals. These rovibrational dynamics determine reaction rates, molecular stability, and how drugs bind to their targets.

However, accurately simulating these motions on classical computers has always been extremely difficult. The challenge stems from the “curse of dimensionality”: as the number of atoms grows, the computational cost of solving the nuclear motion equations rises exponentially. Even the world’s most powerful supercomputers cannot calculate high-accuracy energy spectra for molecules beyond a few atoms without resorting to approximations.

A New Quantum Approach

Our new algorithm introduces a novel framework that integrates:

• Discrete Variable Representations (DVRs) - a compact and mathematically rigorous way to describe the molecule’s quantum states.
  
  

• An exact curvilinear kinetic-energy operator and an efficient block-encoding of the Hamiltonian - enabling the system’s full motion to be represented accurately on a quantum computer.
  
  

• A Walsh-Hadamard Quantum Read-Only Memory (WH-QROM) - a new technique that dramatically compresses how potential-energy data is loaded into quantum circuits.

This WH-QROM innovation addresses one of the biggest bottlenecks in quantum chemistry: the efficient loading of complex molecular potential energy surfaces. By combining WH-QROM with block-encoded Hamiltonians, the algorithm achieves exponential reductions in both quantum volume and memory cost compared to previous methods.

Orders-of-Magnitude Improvements

The results are striking.
For a water molecule (H₂O), the quantum volume required to simulate its rovibrational energy levels drops by up to 100,000× compared with earlier quantum approaches.

For a 12-atom molecule (around 30 vibrational degrees of freedom), a fault-tolerant quantum computer with roughly 300 logical qubits running at a 1 MHz error-correction cycle could perform the simulation with spectroscopic accuracy within months.

In contrast, even the most advanced classical supercomputer - El Capitan, rated at 1.7 exaFLOPS - would require over 30,000 years and exabytes of memory to reach comparable accuracy.

For larger systems, the quantum advantage only grows. For a 50-dimensional molecule, classical computation would take much longer than the age of the universe, whereas our algorithm provides hope for completing simulation in under a year.

These estimates, though based on future quantum hardware assumptions, clearly illustrate the emerging quantum advantage for complex molecular systems.

Implications for the Pharmaceutical Industry

Accurate modeling of molecular motion is foundational in drug discovery. Quantum algorithms that capture anharmonicity, proton tunneling, and strong coupling effects could revolutionize how we understand binding, and reaction mechanisms - processes central to drug design and optimization.

This algorithm enables a level of detail and accuracy that has simply not been achievable with classical computation. In practical terms, it could help:

• Predict and optimize dynamical drug-protein interactions with higher reliability.
  
  

• Model reaction pathways and metabolic breakdown mechanisms at a quantum-mechanical level.
  
  

• Support thermodynamic and spectroscopic studies critical for material and biochemical innovation.

Beyond pharma, the same techniques apply to astrophysics, condensed matter physics, and fundamental chemical dynamics.

The Road Ahead

While our algorithm shows favorable asymptotic scaling, it still involves large constant prefactors - mainly due to the encoding of potential-energy surfaces and quantum error-correction overhead. Our ongoing work aims to reduce these constants and collaborate across industry and academia to translate these theoretical advances into real quantum workflows.

This research marks another step toward practical quantum advantage in molecular simulation - one of the most promising frontiers for meaningful impact across science and industry.

About the Authors

This work was developed by Michał Szczepanik, Ákos Nagy, and Emil Żak at BEIT Canada Inc. and BEIT sp. z o.o., with support from the BEIT Quantum team.

We invite you to read the full preprint here.