Pushing Quantum Simulation to 3D

The quantum lattice Boltzmann method models how particles move and interact on a lattice over time. Unlike classical simulations, QLBM uses quantum superposition to encode multiple flow directions in parallel, enabling a more efficient way to represent complex physical processes.

In this collaboration, Quanscient used the IQM 54-qubit QPU (Emerald) to simulate a 3D advection-diffusion process, such as when a dye droplet disperses through a liquid. For the first time, Quanscient simulated a lattice in 3 dimensions and encoded the 27 flow directions that they evolved in a real quantum circuit.

“We are really excited to be able to show our method for a 3D problem for the first time,” said Dr. Valtteri Lahtinen, Chief Scientist and co-founder at Quanscient. “IQM’s Crystal 54 Emerald QPU is of a size and quality where we can test scenarios that get step by step closer to industry applications. We are excited to work with IQM and push our development with their state-of-the-art hardware.”

 

How Emerald Enabled the Breakthrough

Simulating the lattice in 3D significantly increases circuit complexity. In 2D, one only needs to compute the flows for 9 adjacent lattice sites, so going from 2D to 3D required more qubits, deeper circuits, and higher connectivity between them.

The 54-qubit Emerald QPU was key to overcoming these challenges. With improved gate fidelity, faster gate speeds, and an architecture optimised for gate connectivity, the team was able to:

• Reduce the circuit depth by 71% compared to other superconducting quantum devices and
• Shorten the circuit duration of each shot by 62%
• Reduce the number of entangling gates by 23%
• Use dynamical decoupling – enabled via IQM’s API – to extend the coherence time of the qubits encoding the flows by 48%

These improvements made it possible to run a deeper and more complex circuit while preserving the quantum state long enough to get meaningful results.

 

The Simulation

To run the 3D simulation, 15 qubits on Emerald were used to encode both the 27 discrete flow directions and an 8×8×8 lattice. The process involved:

• Encoding the initial concentration of particles and directional weights into the quantum state
• Evolving the state over each step using a quantum circuit of ~100 gates
• Using quantum measurements to combine flows for the updated concentrations

The figure on above shows how the qubit layout was used, and the video below captures the simulation in action – visualizing the diffusion of a droplet over time. The two pictures below compare the computed and the theoretical concentrations for the last timestep.

Running the simulation required a high degree of connectivity between the qubits to avoid costly SWAP operations. This was made possible by the physical layout of the IQM Emerald chip. Still, due to the inherent noise in superconducting qubits – each with unique noise characteristics – the raw data required error mitigation techniques to bring results closer to theoretical predictions.

 

Above: Video of the simulation over multiple time steps. Right Top: The theoretical concentrations for the final timestep compared to Right Bottom, showing the calculated results for the final timestep.

 

What This Means

This 3D simulation demonstrates how quantum processors can now handle simulations of increasing practical complexity. As quantum hardware improves, techniques like QLBM could offer a path towards quantum advantage in applications like engineering, energy systems, or climate modeling.

This work highlights how advances in both quantum algorithm design and hardware capability are coming together to make quantum simulation a powerful tool for the future.

 

Find out more about Quanscient and contact  to pilot their quantum algorithms

Find out more about the 54 square lattice chip Emerald on IQM Resonance