Warsaw Quantum Computing Group

We invite you to attend (online) Episode LXXIV
of Warsaw Quantum Computing Group meetups!

"Simulating high-accuracy nuclear motion Hamiltonians in discrete variable representation using Walsh-Hadamard QROM with fault-tolerant quantum computers "

Dr Emil Żak

19.02.2026, 18:00 UTC+1

Registration (was open until 18.02.2026, EOD)

Abstract:

We introduce a quantum algorithm for the simulation of rovibrational Hamiltonians on fault-tolerant quantum computers. The method included exact curvilinear kinetic energy operators together with general, non-separable many-body potential energy surfaces represented in a hybrid finite-basis and discrete-variable representation. The resulting Hamiltonian is encoded as a unitary quantum circuit using a quantum read-only memory construction based on the Walsh-Hadamard transform, enabling high-precision quantum phase estimation of rovibrational spectra and the simulation of nuclear dynamics.

Relative to existing block-encoding strategies based on linear combinations of unitaries and variational basis representations, the method achieves asymptotic reductions in both logical qubit requirements and T-gate complexity that scale exponentially with the number of atoms and at least polynomially with the total Hilbert-space dimension. When compared with classical variational approaches, the algorithm offers exponential savings in memory usage together with polynomial reductions in computational time.

Resource estimates indicate that the quantum volume required to compute the rovibrational spectrum of water can be reduced by up to a factor of 100 000 relative to other quantum methods, increasing to at least 1 000 000 for a classically intractable 30-dimensional molecular system. For such a system with a six-body coupled potential, achieving spectroscopic accuracy would require approximately three months of runtime on a 1 MHz fault-tolerant quantum processor using fewer than 300 logical qubits, compared with more than 30 000 years on the fastest currently available classical supercomputers. These estimates are approximate and subject to technological uncertainties, and the realization of the full asymptotic advantage will depend on continued progress in both quantum hardware and algorithmic design.

BIO:

Emil Żak is a physicist and currently serves as Head of Quantum Algorithms at BEIT, a quantum-classical computing software R&D company based in Kraków, Poland. He leads a research team funded by the European Innovation Council (EIC) focused on the development of fault-tolerant quantum computing algorithms for physics and chemistry simulations.
Emil received his PhD in Theoretical Physics from University College London (UCL), UK, in 2017. During his doctoral studies, he was a member of the ExoMol group, where he specialized in simulations of rotational, vibrational, and electronic spectra of small molecules using high-performance computing.
In 2018, Emil joined Queen’s University in Kingston, Ontario, Canada, as a postdoctoral fellow, where he focused on method development for high-dimensional quantum dynamics calculations. He later became a research associate at the Center for Free-Electron Laser Science (CFEL) at the Deutsches Elektronen-Synchrotron (DESY) in Hamburg, Germany. As part of the theory team in the Controlled Molecule Imaging group, his research addressed ultrafast molecular dynamics in tailored laser fields, dynamical chirality, molecular super-rotors, high-accuracy hyperfine spectroscopy, and photoelectron circular dichroism.

In 2022, Emil joined BEIT as a staff physicist. His current work focuses on the development of quantum and classical algorithms for simulating complex molecular systems, including molecular dynamics, molecular docking for drug discovery, and hybrid quantum-classical approaches for chemistry simulations.

The meeting is organized by the Fundacja Quantum AI and QPoland.